HYDRAULICS

Hydraulics: The subject of hydraulics may be defined as that branch of

engineering science, which deals with water (at rest or at motion). The subject

of fluid mechanics may be defined as the mechanics of fluids (including water).

Properties of liquids: Ordinarily, there is no difficulty in distinguishing a liquid

from a solid or a gas. A solid has a definite shape, which it retains, until some

external force is applied to alter it. On the contrary, a liquid takes the shape of a

vessel, into which it is poured. On the other hand, a gas completely fills up the

vessel which contains it.

1. Density: The density of a liquid may be defined as the mass per unit

volume at a standard temperature and pressure. The variation in the density

of water, with the variation of pressure and temperature, is so small, that

for all practical proposes it is generally neglected. It is known as mass

density or specific mass of the liquid. Mass density is usually denoted by

rho (p).

2. Specific weight of water: The specific weight (briefly written as sp. wt.)

of a liquid may be defined as the weight per unit volume, at the standard

temperature and pressure. The variation in the specific weight of water,

with the variation of pressure and temperature, is also so small, that for all

practical purposes, it is generally neglected. It is also known as weight

density and is usually denoted by w. The specific weight of water is taken

as 1000 liters / m3or 1000 kg / m3 or 1 gm / cm3. In SI units the specific

weight of water is taken as 9.81 kN/m3.

3. Specific gravity of water: The specific gravity of a liquid may be defined

as the ratio of its specific weight to that of a standard substance at a

standard temperature. For liquids, pure water is taken as a standard

substance and at 4 C. the specific gravity of water, in the calculation of

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Hydraulics, Fluid mechanics and Hydraulic machines, is taken as unity.

As it is a ratio, hence it has no unit.

4. Compressibility of liquid: The compressibility of a liquid may be defined

as the variation in its volume, with the variation of pressure. The variation

in the volume of water, with the variation for pressure, is so small that for

all practical purposes it is neglected.

5. Surface tension of water: It is the property, which enables it to resist

tensile stress. It is due to the cohesion between the molecules at the surface

of a liquid. When a glass tube of small diameter is dipped in water, the

water rises up in the tube with an upward concave surface. But when the

same tube is dipped in mercury, the mercury depresses down in the tube

with an upward convex surface. As a result of surface tension, the liquid

surface has a tendency to reduce its surface as small as possible. That is

why the falling drops of rain water become sphere. This property of

surface tension is utilized in the manufacturing of lead shots. The molten

lead is made to pass through a sieve from a high tower, and allowed to fall

into water. The molten lead particles, while descending assume a spherical

shape and solidify in this form, before falling into the water.

6. Viscosity: Viscosity is a measure of the resistance to flow or the internal

friction of oil / fluid. Heavy oil has high viscosity, light oil has low

viscosity and medium oil has medium viscosity. The viscosity of oil is

usually specified as the time in seconds that it takes for a given amount of

the oil to flow by gravity through a standard sized orifice at a given

temperature. Viscosity is inversely proportional to temperature. It

decreases as the temperature rises, and increases as it falls. That is why the

lighter oil is recommended for automobile engines in winter than in

summer. It also explains why engines are so hard to start in very cold

weather. The viscosity of an engine lubricating oils should be just

sufficient to ensure hydrodynamic lubrication. If it is more than this value,

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it will involve higher power losses due to the increased oil resistance. The

viscosity is measured by viscometer. These are 1. Saybolt universal

viscometer 2. Redwood viscometer 3. Engler viscometer 4. Barbey

viscometer. The unit of viscosity is given as "seconds saybolt" or "seconds

redwood". Temperature is also specified with the viscosity.

7. Capillarity of water:

Fluid pressure: Whenever a liquid is contained in a vessel, it exerts force at the

points on the sides and bottom of the container. This force per unit area is called

pressure. Thus the intensity of pressure p = P/ a. the direction of this pressure is

always at right angles to the surface, with which the fluid is at rest, comes in

contact.

Pressure head: the pressure at the base of a container containing liquid is the

weight of the liquid. P = wh. This equation shows that the intensity of pressure

at any point, in a liquid, is proportional to its depth, from the surface.

Pascal's law: It states, "The intensity of pressure at any point in a fluid at rest is

the same in all directions".

1. Atmospheric pressure: It has been found that the air possesses some

weight. Subsequently, it was also thought that the air due to its weight

must exert some pressure on the surface of the earth. Since the air is

compressible, its density is different at different heights. The density for

air has also been found to vary from time to time due to the changes in its

temperature and humidity. It is thus obvious, that due to these difficulties,

the atmospheric pressure cannot be calculated, as is done in the case of

liquids. However, it is measured by the height of the column of liquid that

it can support. Atmospheric pressure at sea level is 1.03 kg/cm2. It can

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also be expressed as 10.3 m of water, in terms of equivalent water column

or 76 cm of mercury in terms of mercury column.

2. Gauge pressure: It is the pressure, measured with the help of a pressure

measuring instrument, in which the atmospheric pressure is taken as

datum. Or in other words, the atmospheric pressure on the gauge scale is

marked as zero. Generally, this pressure is above the atmospheric

pressure.

3. Absolute pressure: It is the pressure equal to the algebraic sum of

atmospheric and gauge pressures. It may be noted that if the gauge

pressure is minus (as in the case of vacuum or suctions), the absolute

pressure will be atmospheric pressure minus gauge pressure, e.g. if the

absolute pressure at any point is 1.050 kg/ cm2 and the atmospheric

pressure is 1.03 kg/ cm2. Then the gauge pressure at that point is 1.50-

1.03= 0.47 kg/ cm2.

Pressure measuring instrument:

1. Piezometer tube: It is the simplest form of manometer, used for

measuring, moderate pressures. It consists of a tube, open at one end to

the atmosphere, in which the liquid can rise freely without overflow. The

height, to which the liquid rises up in the tube, gives the pressure head

directly. If the pressure of a liquid flowing in a pipe is to be found out, the

piezometer tube is connected to the pipe. A piezometer tube is also not

suitable for measuring negative pressure; as in such a case the air will

enter in the pipe through the tube.

2. Manometer: A manometer is an improved from of a piezometer tube.

With the help of a manometer, we can measure comparatively high

pressures and negative pressures also. Following are the few types of

manometers.

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3. Simple manometer: Is used for measuring high as well as negative

pressures. The liquid used in the bent tube or simple manometer is,

generally, mercury which is 13.6 times heavier than water. Hence it is

suitable for measuring high pressure also.

4. Micromanometer: It is a modified form of manometer, in which cross

sectional area of one of the limbs (say left limb) is made much larger

(about 100 times) than that of the other limb. A micromanometer is used

for measuring low pressures; where accuracy is of much importance.

Though there are many types of micrometers, yet the following two types

are important. 1. Vertical tube micromanometer 2. Inclined tube

micromanometer.

5. Differential manometer: It is a device used for measuring the difference

of pressures, between two points in a pipe, or in two different pipes.

6. Inverted differential manometer: It is particular type of differential

manometer, in which an inverted U-tube is used. It is used for measuring

difference of low pressures, where accuracy is the prime consideration. It

consists of an inverted U-tube, containing a light liquid whose ends are

connected to the point whose difference of pressures to be found out.

7. Mechanical gauges: Whenever a very high fluid pressure is to be

measured, a mechanical gauge is best suited for the purpose. A mechanical

gauge is also used for the measurement of pressure in boilers or other

pipes, where tube gauges cannot be conveniently used. These are:

1. Bourdon's tube pressure gauge

2. diaphragm pressure gauge

3. Dead weight pressure gauge.

Centre of pressure: The intensity of pressure, on an immersed surface is not

uniform, but increases with depth. As the pressure is greater over the lower

portion of the figure, therefore the resultant pressure,

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Hydrostatics: The term hydrostatics means the study of pressure, exerted by a

liquid at rest. It has been observed that the direction of such a pressure is always

at right angles to the surface, on which it acts.

Total pressure: The total pressure, on an immersed surface may be defined as

the total pressure exerted by the liquid on it.

Centre of pressure: The point, through which the resultant pressure acts, is

known as centre of pressure and always expressed in terms of depth from the

liquid surface.

Hydrokinematics: The subject of hydrokinematics deals with the study of

velocity and acceleration of the liquid particles without taking into

consideration of any force or energy.

Rate of discharge: The quantity of a liquid, flowing per second through a

section, of a pipe or a channel, is known as the rate of discharge or simply

discharge. It is generally denoted by Q = a.v = area x velocity.

In actual practice the velocity of a liquid is maximum at the centre of a pipe and

is minimum near the walls. For al calculations in hydraulics, the average

velocity of flow at a section is taken.

Motion of fluid particles:

1. Lagrangian method: It deals with the study of flow pattern of the

individual particles. In this method, the path traced by the particle under

consideration with the passage of time is studied in detail.

2. Eulerian method: It deals with the study of flow pattern of all the

particles simultaneously at one section. In this method, the paths traced by all

the particles at one section and one time are studied in detail.

Types of flow lines: Whenever a fluid is in motion, its innumerable particles

move along certain lines depending upon the conditions of flow. Though there

are many types of flow lines, yet the following are important from the subject

point of view.

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Path lines: The path followed by a fluid particle in motion is called a path line.

Thus the path line shows the direction of a particle, for a certain period of time

or between two given sections.

Stream lines: The imaginary line drawn in the fluid, in such a way that the

tangent to which at any point gives the direction of motion at the point, is called

stream line. Thus the stream line shows the direction of motion of a number of

particles at the same time.

Stream tube: An element of fluid, bounded by a number of stream lines, which

confine the flow, is called stream tube. As there is no movement of fluid across

a stream line, therefore no fluid can enter or leave the stream tube except at the

ends. It is thus obvious that a stream tube behaves like a solid tube.

Streak lines or filament lines: The instantaneous pictures of the position of all

fluid particles, which have passed through a given point at some previous time,

is called streak lines or filament lines. For example, the line formed by smoke

particles ejected from a nozzle is a streak line.

Flow net: If we draw stream lines and potential lines for a flow, the pattern

obtained by the intersection of the two sets of lines is called flow net. It helps in

depicting and analyzing the behaviour of irrotational flow. It will be interesting

to know, that certain flow phenomenon which can not be easily analysed by

mathematical means may be analysed and studied by drawing flow nets. A flow

net may be constructed by drawing a system of stream lines between the

boundaries by judgement and then a system of equipotential lines, so as to form

a square mesh net.

Uniform flow: A flow, in which the velocities of liquid particles at all sections

of the pipe or channel are equal, is called a uniform flow. This term is generally

applied to flow channels.

Non uniform flow: A flow, in which the velocities of liquid particles at all

sections of the pipe or channel are not equal, is called a non-uniform flow.

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Streamline flow: A flow, in which the velocity of liquid particle has a definite

path and the paths of individual particles do not cross each other, is called a

streamline flow.

Turbulent flow: A flow, in which each liquid particle does not have a definite

path, and the paths of individual particles also cross each other, is called a

turbulent flow.

Steady flow: A flow, in which the quantity of liquid flowing per second is

constant, is called a steady flow. A steady flow may be uniform or non-uniform.

Unsteady flow: A flow, in which the quantity of liquid flowing per second is

not constant, is called unsteady flow.

Compressible flow: A flow, in which the volume and thus the density of the

flowing fluid changes during the flow, is called a compressible flow. All the

gases are, generally, considered to have compressible flows.

Incompressible flow: A flow, in which the volume and thus the density of the

flowing fluid do not change during the flow, is called an incompressible flow.

All the liquids are, generally, considered to have incompressible flow.

Rotational flow: A flow, in which the fluid particles also rotate about their own

axes, while flowing, is called a rotational flow.

Irrotational flow: A flow, in which the fluid particles do not rotate about their

own axes, and retain their original orientations, called an irrotational flow.

One-dimensional flow: A flow, whose streamline may be represented by a

straight line, is called one-dimensional flow. It is because of the reason that a

straight streamline, being a mathematical line, possesses one dimension only.

Two dimensional flow: A flow, whose streamlines may be represented by a

curve, is called a two dimensional flow. It is because of the reason that a sa

curved streamline will be along any two mutually perpendicular directions.

Three dimensional flow: A flow, whose streamlines may be represented in

space i.e., along three mutually perpendicular directions, is called three

dimensional flow.

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Stream function: It is a function, which describes the form of pattern of flow,

or in other words it is the discharge per unit thickness.

Energy of a liquid in motion

The energy, in general, may be defined as the capacity to do work. Though the

energy exists in many forms, yet the following are important.

Potential energy: It is the energy possessed by a liquid particle, by virtue of its

position. If a liquid particle is Z meters above the horizontal datum the potential

energy of the particle will be Z meter-kilogram per kg of the liquid. Potential

head of the liquid, at that point will be Z meters of the liquid.

Kinetic energy of a liquid particle in motion: it is the energy, possessed by a

liquid particle, by virtue of its motion or velocity. If a liquid particle is flowing

with a mean velocity of v meters per second, then the kinetic energy of the

particle will be v2/2gmkg per kg of the liquid. Velocity head of the liquid, at

that velocity, will be v2/2g meters of the liquid.

Pressure energy of a liquid particle in motion: It is the energy, possessed by a

liquid particle, by virtue of its existing pressure. If a liquid particle is under a

pressure of p kg per square meter, then the pressure energy of the particle will

be p/w mkg per kg of the liquid, where w is the sp. weight of the liquid.

Pressure head of the liquid under that pressure will be p/w meters of the liquid.

Total energy of a liquid particle in motion: The total energy of a liquid

particle, in motion, is the sum of its potential energy, kinetic energy and

pressure energy, thus total energy, E =Z +v2/2g + p/w mkg of liquid.

Total head of a liquid particle in motion: The total head of a liquid particle in

motion is the sum of its potential head, kinetic head and pressure head. thus

total head, H =Z + v2/2g + p/w m of liquid.

Bernoulli's equation: It states, "For a perfect incompressible liquid, flowing in

a continuous stream, the total energy of a particle remains the same; while the

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particle moves from on e point to another." This statement is based on the

assumption that there are no losses due to friction in the pipe.

Thus Z +v2/2g + p/w = constant

Euler's equation for motion: The Euler's equation for steady flow on an ideal

fluid along a streamline is based on the Newton's second law of motion. The

integration of the equation gives Bernoulli's equation in the form of energy per

unit weight of the flowing fluid. It is based on the following assumptions:

1. The fluid in non-viscous (i.e., the friction losses are zero)

2. The fluid is homogeneous and incompressible (i.e., mass density of the

fluid is constant.)

3. The flow is continuous, steady and along the streamline.

4. The velocity of flow is uniform over the section.

5. No energy or force, except gravity and pressure forces, is involved in the

flow.

Venturimeter: It is an apparatus, for finding out the discharge of a liquid

flowing in a pipe. A venturimeter, in its simplest form, consists of the following

three parts. Convergent cone, throat and divergent cone.

Orifice meter: It is used to measure the discharge in a pipe. And orifice meter,

in its simplest form, consists of a plate having a sharp edged circular hole

known as an orifice. This plate is fixed inside a pipe. A mercury manometer is

inserted to know the difference of pressures between the pipe and the throat.

(i.e. the orifice)

Pitot tube: A pitot tube is an instrument to determine the velocity of flow at the

required point in a pipe or a stream. In its simplest form, a pitot tube consists of

a glass tube bent through 90 degree. The lower end of the tube faces the

direction of the flow. The liquid rises up in the tube due to the pressure exerted

by the flowing liquid. By measuring the rise of liquid in the tube, we can find

out the velocity of the liquid flow.

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Orifice: An opening, in a vessel, through which the liquid flows out, is known

as an orifice. This hole or opening is called an orifice, so long as the level of the

liquid on the upstream side is above the top of the orifice. The usual purpose of

an orifice is the measurement of flow.

Vena contracta: It has been observed that the jet after leaving the orifice gets

contracted. The maximum contraction takes place at a section slightly on the

downstream side of the orifice, where the jet is more or less horizontal. Such a

section is known as vena contracta.

Hydraulic coefficients

The following four coefficients are known as hydraulic coefficients or

orifice coefficients:

1. Coefficient of contraction: The ratio of area of the jet, at vena contracta,

to the area of the orifice is known as coefficient of contraction. Thus, Cc

= area of jet at vena contracta / area of orifice. The value varies slightly

with the available head of the liquid, size and shape of the orifice.

Average value is about 0.64.

2. Coefficient of velocity: The ratio of actual velocity of the jet, at vena

contracta, to the theoretical velocity is known as coefficient of velocity.

Thus, Cv =actual velocity of vena contracta /theoretical velocity. The

difference between the velocities is due to friction of the orifice. It lies

between .959 to .994. An average value of Cv is about .97.

3. Coefficient of discharge: The ratio of a actual discharge through an

orifice to the theoretical discharge, is known as coefficient of discharge.

Thus, Cd = actual discharge/ theoretical discharge =Cv x Cc. an average

value is about .62.

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1. Coefficient of resistance: The ratio of loss of head in the orifice to the

head of water available at the exit of the orifice is known as coefficient of

resistance. Thus Cr = loss of head in the orifice/ head of water. This takes

place because the walls of the orifice offer some resistance to the liquid, as

it comes out. The coefficient of resistance is generally neglected, while

solving numerical problems.

Equivalent size of a pipe: Sometimes a compound pipe is required to be

replaced by a pipe of a uniform diameter and of the same length as that of the

compound pipe; such that the loss of head as well as the discharge is the same in

both the cases. The new pipe of uniform diameter is called equivalent pipe and

its diameter is called equivalent size of the pipe.

Nozzle: It is a tapering mouthpiece, which is fitted to the outlet end of a pipe. A

nozzle is, generally, used to have a high velocity of water, as it converts

pressure head into kinetic head at its outlet. A high velocity of water is required

in fire fighting, mining and power developments.

The power transmitted through the nozzle is maximum when the head lost

due to friction in the pipe is equal to 1/3 of the total supply head.

Assumptions for the effect of viscosity: While considering the effect of

viscosity, the following two assumptions are made.

1. When a liquid is in contact with a solid boundary, the liquid particles

(immediately adjacent to the boundary) and the solid boundary does not

exit. Or in other words, if the boundary is at rest the liquid particles are

also at rest. But if the boundary moves with some velocity, the liquid

particles also move with the same velocity.

2. The shear stress between the two adjacent liquid layers is proportional to

the rate of shear in the direction perpendicular to the motion. Or in other

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words if two adjacent layers move with a relative velocity of v, the rate of

shear is v/y. the shear stress between the two liquid layers is also

proportional to v / y. the shear stress between the two liquid layers is also

proportional to v/y where y is the distance between the two layers.

Newton's law of viscosity: It states, "The shear stress on a layer of a fluid is

directly proportional to the rate of shear strain."

Units of viscosity: in C.G.S. units, the unit of viscosity is poise; such that 1

poise =dyne-sec/ cm2

Sometimes a small unit centipoises is also used, which is 1/100th of poise.

Kinematic viscosity: It is the ratio of absolute viscosity to the density of the

liquid. In c.g.s. units, the unit of kinematic viscosity is stoke. Such that 1 stoke

= cm2/sec.

1 centistoke =1/100 th of a stoke.

Classification of fluids:

The fluids may be classified into the following four types depending upon the

presence of viscosity.

1. Ideal fluid: A fluid, having no viscosity, is known as an ideal fluid. In

actual practice, there is hardly any fluid, as every fluid has some viscosity.

2. Real fluid: A fluid, having viscosity, is known as a real fluid. In actual

practice, all the fluids met with in engineering-science, are real fluids.

3. Newtonian fluid: A fluid, which obeys the law of viscosity, is termed as

Newtonian fluid.

4. Non-Newtonian fluid: A fluid, which does not obey the Newton's law of

viscosity, is termed as non-Newtonian fluid. Or in other words, a fluid,

whose viscosity changes with the rate of deformation of shear strain is

known as a Non-Newtonian fluid.

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Classification of viscous flows:

The viscous flows may be classified into the following two types depending

upon the factor, whether the viscosity is dominating or not.

Laminar flow: It is a flow, in which the viscosity of the fluid is dominating

over the inertia forces. It is more or less a theoretical flow, which rarely comes

in contact with the engineers and is also known as a viscous flow. A laminar

flow can be best understood by the hypothesis that the liquid moves in the form

of concentric cylinders sliding one within the other. These concentric cylinders

move like laminae. Such a flow takes place at very low velocities, is known as

laminar flow.

Turbulent flow: It is a flow, in which the inertia force is dominating over the

viscosity. It is a practical flow which comes in contact with the engineers. In

this flow the concentric cylinders diffuse or mix with each other and the flow is

a disturbed one. Such a flow, which takes place at high velocities, is known as a

turbulent flow.

Critical velocity: It is a velocity at which the flow changes from the laminar

flow to the turbulent flow. The critical velocity may be further classified into

the following two types.

Lower critical velocity: It has been experimentally found that when a laminar

flow changes into a turbulent flow, it does not change abruptly. But it has got

some transition period between the two types of flows. Thus a velocity, at

which the laminar flow stops ; or in other words, a velocity at which the flow

enters from laminar to transition period is known as a lower critical velocity.

Upper critical velocity: A velocity, at which the turbulent flow starts; or in

other words, a velocity at which the flow enters from transition period to

turbulent flow is known as an upper critical velocity or higher critical velocity.

Reynolds’s number: He found that the value of critical velocity is governed by

the relationship between the inertia force and viscous forces. He derived a ratio

of these two forces and found out a dimensionless number known as Reynolds’s

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number. Thus, Re = inertia force / viscous forces = mean velocity x diameter of

pipe / kinematic viscosity of liquid. If the Reynolds number for a particular flow

is less than 2000, the flow is a laminar flow. But if the Reynolds number is

between 2000 and 2800, it is neither laminar flow nor turbulent flow. But if the

Reynolds number exceeds 2800, the flow is a turbulent flow.

Hagen-Poiseuille law for laminar flow in pipes: We have seen that some loss

of head takes place, in a laminar flow, due to viscosity of the flowing liquid.

The equation which gives us the value of loss of head due to the viscosity in a

laminar flow is known as

Hagen-Poiseuille's law.

Lubrication of bearings: The theory of viscosity has been successfully applied

to the theory of lubrication of machine parts. It has been experienced, that

highly viscous oil leads to a greater resistance, and thus causes a greater power

loss. On the other hand, light oil may not be able to maintain the required film

between the metal surfaces. As a result of this, the metal may come in contact

with the other, which leads to wear of the two surfaces. It is thus obvious, that

the oil used for lubrication should have a correct viscosity. Since the viscosity

of an oil changes with temperature, that is why motorists use oil of different

viscosities in different seasons.

Methods for determination of coefficient of viscosity: The coefficient of

viscosity of a liquid may be found out experimentally by the following four

methods:

1. By capillary tube methods.

2. By orifice type viscometer.

3. By rotating cylinder method

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4. By falling sphere method.

Compressible flow: If there is more than 5% change in density, the fluid is

treated as compressible fluid.

The physical properties of a gas are controlled by the following three variables:

1. Pressure exerted by the gas.

2. Volume occupied by the gas.

3. Temperature of the gas.

Boyle's law: It states that the absolute pressure of a given mass of a perfect gas

varies inversely as its volume, when the temperature remains constant. PV =

constant.

Charles' law: It states, "The volume of a given mass of a perfect gas varies

directly as its absolute temperature, when the pressure remains constant."

Gay-lussac law: It states, "The absolute pressure of a given mass of a perfect

gas varies directly as its absolute temperature, when the volume remains

constant."

General gas equation: In actual practice, all the three variables i. e., pressure,

volume and temperature change simultaneously. In order to deal with all

practical cases, the Boyle's law and Charles' law are combined together, which

give us the general gas equations in the following two types. PV/T =constant or

PV =m RT (the value of R is 287 J/ kg K in SI units. And 29.2 kg-m/kg K.

Specific heats of a gas: The specific heat of a substance may be broadly

defined as the amount of heat required to heat a unit mass of a substance

through 1 degree rise in temperature. All the liquids and solids have only one

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specific heat. But a gas may have any number of specific heats (say infinite.)

depending upon the conditions, under which it is heated. The two specific heats

of a gas are:

Specific heat at constant volume: The amount of heat required to raise a unit

mass of the gas through 1 degree, when its volume remains constant, is known

as specific heat at constant volume and is denoted by Cv. therefore the heat

added to the gas, H =m Cv ( T2-T1)

Specific heat at constant pressure: The amount of heat required to raise a unit

mass of the gas through 1 degree, when its pressure remains constant, is known

as specific heat constant pressure, and is denoted by Cp. Thus the heat added to

the gas, H = mCp (T2-T1).

Relation between specific heats: Cp-Cv = R/J

v = Cp /Cv. Cp = v R /J (v-1) The value of R and v depends upon the type of

gas and its temperature. The value of v for air at usual temperature is taken as

1.4.

Isothermal process: A process, in which the temperature of the working

substance, i.e., gas remains the same during its expansion or compression, is

called an isothermal process. Thus for an isothermal process,

1. there is no change in temperature, and

2. there is no change in internal energy.

An isothermal process is governed by Boyle's law, thus, the isothermal equation

of a perfect gas is given by PV = constant. The heat absorbed by the gas during

isothermal process is equal to the work done by the gas. The work done during

an isothermal expansion is given by the relation, w = 2.3 P1V1 log r

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Adiabatic process: A process in which the working substance, i.e., gas, neither

receives nor gives out any heat to its surroundings during its expansion or

compression, is called an adiabatic process. Thus an adiabatic process:

1. No heat leaves or enters the gas.

2. The temperature of the gas changes, as the work done is at the cost of

internal energy.

The change in internal energy is equal to the mechanical work done. The

adiabatic equation of a perfect gas is PV =constant. Thus P1 / P2 = (V2 / V1) v.

T1 / T2 = (V2 /V1) v-1 T2 /T1 = ( P2 / P1) v-1/v

If the adiabatic process is reversible, it is called an isentropic process. The

equation for isentropic process is the same as that of adiabatic process.

Bulk modulus of a fluid: The bulk modulus of a fluid is the ratio between the

increase of pressure, and the volumetric strain, caused by this pressure increase.

It may be noted that this ratio is applied to liquids and gases. Thus, bulk

modulus K = - dp / (dV/V).

Types of flow

Subsonic flow: When the Mach number is less than unity, the flow is called a

subsonic flow.

Sonic flow: When the Mach number is equal to unity, the flow is called a

supersonic flow.

Supersonic flow: When the Mach number is between 1 and 6, the flow is called

a supersonic flow.

Hypersonic flow: When the Mach number is more than 6, the flow is called a

hypersonic flow.

Stagnation pressure: A point in the flow, where the velocity of the fluid is

zero, is called a stagnation point; the pressure at the stagnation point is always

high.

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** The head measured by Pitot tube is only the velocity head of the flowing

stream.

Flow around immersed bodies: When a solid body is held in the path of a

moving fluid and is completely immersed in it, the body will be subjected to

some pressure or force. Conversely, if a body is moved with a uniform velocity

through a fluid at rest, it offers some resistance to the moving body, or the body

has to exert some force to maintain its steady movement. It is thus obvious, that

when a submarine moves through the water or an aeroplane flies through the

atmosphere, its engine must supply a sufficient force not only to run it, but also

to balance the resistance offered.

Newton's law of resistance: It states, "The force exerted by a moving fluid on

an immersed body is directly proportional to the rate of change of momentum

due to the presence of the body." Mathematically, P = waV2/g

The above law of resistance is based on the following assumptions:

1. The planes of the body are completely smooth.

2. The space around the body is completely filled with the fluid.

3. The fluid has a large number of fine particles having mass, but no

dimension.

4. The fluid particles do not exert any influence on one another.

5. The body experiences impacts from all the particles in its path.

Drag: Whenever a plate is held immersed at some angle with the direction of

flow of the liquid, it is subjected to some pressure. As this pressure acts at right

angles to the plate, therefore it will have some component (i) in the direction of

flow of the liquid and (ii) at right angles to the direction of flow of the liquid.

The component of this pressure, in the direction of flow of the liquid, is known

as drag.

19

Therefore, Drag = PD = waV2 sin a / 2g = KD. waV2 /2g. Its value depends

upon the type of plate and the angle of inclination of the plate which is

determined experimentally.

Lift: The component of this pressure at right angle to the direction of flow of

the liquid is known as lift.

Therefore, Lift, PL = waV2cosa /2g = KL. waV2 / 2g. Where, KL is a

coefficient, known as coefficient of lift. Its value depends upon the type of plate

and the angle of inclination of the plate, which is determined experimentally.

The resultant force on the body, R = (PD2 +PL2 ). 5

Air foil theory: The practical utility of the forces drag and lift is derived in

running sea ships, submarines and aeroplanes. The coefficient of drag and

coefficient of lift depends upon the angle of inclination of the plate with the

vertical. In actual practice the angle of inclination depends upon the geometrical

position of the body, with respect to its motion. In practical aeronautics, we are

always interested in airfoils, in which the resulting force is nearly perpendicular

to the direction of flow. In this case, the lift is great and the drag is small. Since

the lift serves the purpose of supporting the aeroplanes, therefore more the lift

the better it is. Moreover, the drag is a necessary evil, which has to be

compensated for by the propeller thrust. It has been experimentally found that if

a flat plate is inclined at about 4 degree, the ratio of force of lift to the force of

drag is about 6. In order to increase this ratio, the plate is given a light curvature

or camber gives twice the ratio of these forces than the flat plate. This ratio is

further increased by nicely rounding off the front end of the plate and providing

a sharp edge to the tail of plate. In this way it is possible to have lift-drag ratio

of even 20 or more. The above theory is known as air foil theory.

Boundary layer separation: When a body is held immersed in a flowing

liquid, a thin layer of the liquid will behave, as if it is fixed to the boundary of

20

the body. But if the immersed body is a curved or angular one, the boundary

layer does not stick to the whole surface of the body. The boundary layer leaves

the surface and gets separated from it. This phenomenon is known as boundary

layer separation. The point, where the boundary layer gets separated from the

surface of the body, is known as point of separation.

Magnus effect: Consider a liquid having streamline flow from left to right. If

we introduce a cylinder in the path of the streamlines, we shall see that the

boundary layer has adhered to the surface of the cylinder throughout. Now let

the cylinder be rotated about its longitudinal axis. The rotating motion of the

cylinder will deviate the streamlines. This phenomenon of deviating the

streamlines by the rotating cylinder is known as Magnus effect.

Prevention of boundary layer separation: The separation of boundary layer in

a turbulent flow may be prevented in order to have the reduced drag. Many

methods have been suggested to prevent the separation of boundary layer. But

the following are important.

Boundary layer theory: The liquid in the vicinity of the surface of the body

may be divided into the following two portions:

A very thin layer of the fluid, which is in the immediate contact of the body.

This layer of the fluid behaves like a thin coating, as if it is fixed or glued to the

boundary of the body. Since this thin layer of the fluid acts in such a way, as if

its inner surface is fixed to the boundary of the body, therefore velocity of the

fluid at the boundary is zero. Such a thin layer of the fluid is known as boundary

layer.

If we go away from the surface of the body, normal to the flow of the fluid

21

OBJECTIVE QUESTIONS:

1. A perfect gas is one - Which satisfies the relation PV = nRT.

2. An ideal fluid is - Frictionless and incompressible.

3. An ideal flow of any fluid must fulfil - continuity equation.

4. The velocity of fluid particle at the centre of the pipe section is -

Maximum.

5. The stress strain relation of the Newtonian fluid is - Linear.

6. The units of kinematic viscosity are - m2/sec.

7. The units of dynamic viscosity are - Newton-sec/ m2.

8. The units of surface tension are - Energy / unit area. = Joule / m2.

9. Density in terms of viscosity is - Dynamic viscosity / Kinematic

viscosity.

10. Newton's law of viscosity relates - shear stress and rate of angular

deformation in a fluid. τ = µ du / dy

11. SI unit of viscosity is - 10 times poise.

12. Shear stress can never occur in frictionless fluid regardless of its motion.

13. The upper critical Reynolds number is - About 2000.

14. The Reynolds number for pipe flow is given by - pVD/ µ

15. The Reynolds number is defined as Re = inertia force / viscous force.

16. The Weber number is the ratio of ……….. Inertia forces to surface

tension and is given by V/v s/PL

17. Froude number is useful in calculations………. Hydraulic jump.

18. The normal stress is the same in all directions at a point in fluid…………

when there is no motion of one layer relative to an adjacent layer.

19. When a venturimeter is used in an inclined position, it will show………

same reading.

20. The critical depth on a channel is given by…….. h =v2/g

22

21. The bulk modulus of elasticity …….. Is larger when the fluid is more

compressible.

22. One poise is equivalent to ………. 1 dyne sec/cm2.

23. if a barometer carries water instead of mercury, the height of column for a

pressure equivalent to 75 cm of mercury will be ……… 1020 cm ( 75 x

13.6 x9810/9810)

24. Mass density of a liquid is given by…….. ? =mass /volume.

25. In a flowing fluid, a particle may possess ………. Inertia energy, pressure

energy, kinetic energy, elevation or gravitational energy,

26. A barometer is used to measure …… atmospheric pressure.

27. mercury is generally used in barometer because…… of higher density

due to which the height of barometer is less, it has practically zero vapour

pressure, it shines and can be easily read, it does not stick to the tube

walls.

28. One atm. Pressure is equivalent to ………….. 1.01315 x 105N/m2, 700

mm Hg, 1.0133 x 105 kg/m-sec2, 1.0133 x106 gm/cm-sec2.

29. A simple pitot tube is used to measure …. The velocity in a flowing

stream.

30. The flow of water in a pipe of diameter 3000 mm can be measured by

……….. Pitot tube.

31. A fluid is a substance that ……………. Cannot remain at rest under

action of any shear force.

32. An ideal flow of any liquid must fulfil ………… Bernoulli's equation.

33. The continuity equation ….. relates the mass rate of flow along a stream

line.

34. The equation of continuity of flow is applicable when ….. the flow is one

dimensional, the flow is steady, the flow is compressive, the velocity is

uniform over the cross section .

23

35. One dimensional flow is … flow which neglects changes in a transverse

direction.

36. Uniform flow occurs when ……… at every point the velocity vector is

identical in magnitude and direction for any given instant.

37. Steady flow occurs when …. Conditions do not change with time at any

point.

38. If the particles of a fluid attain such velocities that vary from point to

point in magnitude and direction as well as from instant to instant, the

flow is said to be…….turbulent flow.

39. The equation of continuity of flow is based on the principle of

conservation of ……… mass.

40. The general energy equation is applicable to …………….. Steady flow.

41. If the Mach number of a flow is 3 the flow is known as ….supersonic.

42. A control volume refers to ……. A fixed region in space.

43. For smooth turbulent flow the friction factor varies as ……….. NR1/4

44. The pressure centre is ….. a point on the line of action of the resultant

force.

45. The hydraulic gradient is equal to ………. Head loss due to friction/ total

length of channel.

46. The hydraulic mean depth of a pipe, not running full, is given by…m

=r2(?-sin ?)/2 r ?

47. A fluid, in which resistance to deformation is independent of the shear

stress, is known as….. Newtonian fluid.

48. Steady flow is motion in which …………… velocity is independent of

time.

49. Uniform flow is motion whose… velocity is the same at every point.

50. The principle, "the buoyancy is equal to the weight of the fluid displaced

and the line of action is through the centroid of the displaced mass is

known as ………. Archimedes principle.

24

51. If a centrifugal pump takes too much power, the cause may be …….

Heavy liquid.

52. In a centrifugal pump the pressure energy of water is increased because of

………Centrifugal force.

53. A Kaplan turbine is suitable for ………….low head high discharge.

54. Input to a reciprocating pump may be calculated from (H) head, and

discharge Q m3/sec as …..WQH/75

55. In case of forced vortex ………. Velocity increases with radius.

56. 105 N/m2 pressure is equivalent to …. ***101

57. The distance r from the centre of a tube of radious r0 where the average

velocity occurs in laminar flow is …………. .707 r0.

58. In a turbulent flow in a pipe we know the ……shear stress varies linearly

with the flow rate.

59. Minor loss in a piping system are ………. Found by using loss

coefficient.

60. The head loss in a pipe flow can be calculated by using……. The Darcy

Weisbach equation.

61. Pressure drag results from ………….. Occurrence of a wake.

62. A surge wave is an example of …………. Unsteady non uniform flow.

63. The velocity distribution in a turbulent flow in a pipe is often assumed to

…… vary according to the 1/7th power law.

64. The parameters which determine the friction factor of turbulent flow in a

rough pipe are…… Reynolds number and relative roughness.

65. Viscosity has dimension of …………. M/LT

66. Water turbine may be put in the decreasing order of specific

speed………… propeller turbine, reaction turbine, impulse turbine.

67. in Hagen-Poiseuille flow of viscous liquid, one of the following pairs of

forces strike a balance ……….inertia and viscous forces.

25

68. Reynolds number = inertia force / viscous force, weber number = inertia

force /surface tension force, Mach number = inertia force /elastic force,

Froude number = inertia force/ gravity.

69. mouthpieces are used to measure ….. Rate of flow.

70. The rate of flow through a venturimeter varies as……….v H.

71. Total drag on a body is the sum of ……… friction drag and velocity drag.

72. The pressure gradient in a developed turbulent flow in a horizontal pipe

….. is constant.

73. In an isothermal atmosphere the pressure ……….. Decreases

exponentially with elevation.

74. The viscosity of a fluid varies with ……….. Temperature.

75. The shear stress in a turbulent pipe flow………. Is zero at the centre and

increases as linearly to the wall.

76. If the Froude number in open channel flow is equal to 1, the flow is

known as …… streaming flow.

77. Model analysis of aeroplanes and projectiles moving at supersonic speed

are based on …… Mach number.

78. Water hammer in pipes takes place when... flowing fluid is * * *

79. Find the odd man out…………. Pressure, unit shear stress, energy,

modulus of elasticity.

80. A stream line ………… is fixed in space in space flow.

81. To determine the reservoir storage capacity for a given uniform demand,

one of the following data is most useful… mass curve of the flow volume

for several consecutive years.

82. Stanton diagram is a plot of ………. Log of factor against log of

Reynolds number.

83. Drag force is not a function of ……… mass density of the body.

84. Dynamic viscosity: Poise: Kinematic viscosity: stroke.

26

85. Using pressure P, flow rate Q, diameter D, and density d, which of the

following represents a dimensionless group? …….. PD4/dQ3

86. As the temperature increases, the viscosity of a gas ….. Increases, and

that of a liquid decreases.

87. The locus of elevations that water will rise in a series of pitot tubes is

called……. The energy grade line.

88. The flow of a fluid in a pipe takes place from…….. Higher energy to

lower energy.

89. When the fluid is at rest, the shear stress is …………zero.

90. Bluff body ………. Surface does not coincide with streamlines.

91. In a completely turbulent flow the head loss………..increases with the

velocity squared.

92. For a supersonic flow, velocity……….. Increases with increase in area of

flow.

93. The maximum velocity through a circular channel takes place when the

depth of flow is equal to …… .81 times the diameter.

94. In an open channel, under critical depth …….. Specific energy is

minimum.

95. In an open channels, under critical flow conditions, the velocity head is

equal to ……half the depth of flow.

96. a hydraulic jump is classified on the basis of initial………. Froude

number.

97. In a mixed flow turbine water enters ……. Radially and leaves axially.

98. A draft tube converts……. Kinetic energy into mechanical energy.

99. Priming is required in ……………..centrifugal pumps.

100. In case the velocity vector at different points along a stream line remains

unchanged then the flow is termed as……. Uniform flow.

101. The existence of velocity potential in fluid indicates that………

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102. In the case of laminar flow, the friction factor f is independent of the

relative roughness and is only a function of the Reynolds number Re. f is

equal to …. 64/ R

103. In the case of Penton wheel turbine installed in a hydraulic power plant,

the gross head available is the vertical distance between…. Reservoir

level and turbine inlet.

104. For pumping molasses, it is preferable to employ…. Open impeller pump.

105. In the case of a centrifugal pump, cavitation will occur if…. It operates

below the minimum net positive suction head.

106. A simple pitot tube can be used to measure which of the following

quantities… Static head, Dynamic head, Total head.

107. For flow through a horizontal pipe, the Pressure gradient dp/ dx in the

flow direction is …. - Ve.

108. Which of the following sets of conditions clearly apply to an ideal fluid…

nonviscous and incompressible fluid.

109. In the region of the boundary layer nearest to the wall where velocity is

not zero, the viscous forces…..are less than inertia forces.

110. The realization of velocity potential in fluid flow indicates that the …

flow must be irrotational.

111. Chances of occurrence of cavitation are high if the …. Local pressure

falls below the vapour pressure.

112. A fully developed laminar viscous flow through a circular tube has the

ratio of maximum velocity to average velocity as…2.

113. The Euler's equations of motion for the flow of an ideal fluid is derived

considering the principle of conservation of …. Mass and the fluid as

incompressible and inviscid.

114. Flow separation at a solid surface takes place due to … decrease in

pressure along the flow direction.

28

115. For attaining a non-overloading characteristic in centrifugal pumps…

backward bent vanes are preferred over forward bent vanes.

116. Cavitation in hydraulic machines occurs at the ….. Exit of the pump and

exit of a turbine.

117. During the flow over a circular cylinder, the drag co-efficient drops

significantly at a critical Reynolds number of 2 x 10 5. This is due to….

Excessive momentum loss in the boundary layer.

Objective Question-2:

1. In Red wood viscometer – comparison of viscosity is done.

2. A fluid is a substance that – has the same shear stress at a point regardless

of its motion.

3. Centre of buoyancy is – Centroid of displaced volume fluid.

4. Length of mercury column at a place at an altitude will vary with respect

to that at ground in a – manner first slowly and then steeply.

5. In isentropic flow, the temperature – cannot exceed the reservoir

temperature.

6. When power is transmitted through a considerable distance by means of

water under pressure, the maximum power is transmitted when friction

loss of head is – one third of the total head supplied.

7. A stream line is – Fixed in space in steady flow.

8. A rotameter is a device used to measure –flow of fluids.

9. An ideal fluid – Frictionless and incompressible.

10. The speed of sound in a perfect gas having temperature -T, is given by √

KRT.***, √kR/T, where, k = ratio of specific heat capacities, R = Gas

constant, T = absolute temperature.

11. Reynolds number for pipe flow is given by – pvD / μ.

29

12. With rise in gas temperature, dynamic viscosity of most of the gases –

increases.

13. The flow of water in a pipe of diameter 3000 mm can be measured by –

Pitot tube.

14. The continuity equation – relates the mass rate of flow along a stream

line.

15. Apparent shear forces – can never occur in frictionless fluid regardless of

its motion, can never occur when the fluid is at rest, and depends upon

cohesive forces.

16. Of the following dimensionless parameter is – Pressure coefficient,

Froude number, Darcy Weisbach friction factor.

17. Weber number is the ratio of – inertia forces to surface tension.

18. One dimensional flow – neglects changes in a transverse direction.

19. Steady flow occurs when – conditions don’t change with time at any

point.

20. A flow in which each liquid particle has a definite path and their paths do

not cross each other is called – Streamline flow.

21. Equation of continuity of fluid is applicable only when the flow is –

steady, one dimensional, compressive.

22. Buoyant force is – equal to the volume of liquid displaced by the body.

23. In a rectangular notch, the ratio of percentage error in

discharge/measurement of head is – 3/2.

24. Cavitations is caused by – Low pressure.

25. If the particles of a fluid attain such velocities that vary from point to

point in magnitude and direction as well as from instant, the flow is –

Turbulent flow.

26. The general energy equation is applicable to - Steady flow.

27. In a turbulent flow in a pipe – shear stress varies linearly with radius.

30

28. The friction resistance in pipe is proportional to v 2 according to - Froude

number.

29. In laminar flow, maximum velocity at the centre of pipe is how many

times to the average velocity – Two.

30. Pitot tube is used to measure the velocity head of –flowing fluid.

31. A sharp edged obstruction over which the flow of a fluid takes place is –

Orifice.

32. In equilibrium condition, fluids are not able to sustain – Surface tension.

33. If V1 and V2be the velocity at inlet and outlet, then loss of head due to

sudden enlargement is proportional to – (V1- V2) 2.

34. The pressure coefficient may take the form – ∆ P/(σ v2/2).

35. Flow occurring in a pipeline when a valve is being opened is – Unsteady.

36. The non dimensional number governing frictional resistance is – Mach

number.

37. Total pressure on 1m x1m gate immersed vertically at a depth of 2 m

below the free surface will be – 1000 kg.

38. The general equation of continuity for three dimensional flow of a

compressible fluid for steady flow is – du/dx + dv/dy + dw/dz = 0.

39. A large Reynolds number is indication of – Highly turbulent flow.

40. Non uniform flow occurs when –velocity, depth, pressure, etc. changes

point to point in the fluid flow.

41. In steady flow of a fluid, the acceleration of any fluid particle is – Zero.

42. For measuring flow by a venturimeter, it should be installed in – any

direction and in any location.

43. Froude number is significant in – Simultaneous motion through two

fluids where there is a surface of discontinuity, gravity forces, and wave

making effect, as with ship’s hulls.

44. The fluid forces considered in the Navier Stokes equation are – Gravity,

pressure and viscous.

31

45. The flow in venturiflume takes place at – atmospheric pressure.

46. The depth of the centre of pressure in rectangular lamina of height h with

one side in the liquid surface is at – 2h/3.

47. Maximum discharge over a broad crested weir is – 1.71 CdLH3/2.

48. Reynolds number is significant in – Full immersion or completely

enclosed flow, as with pipes, aircraft wings, nozzles etc.

49. Two dimensional flow occurs when the – fluid particles move in a plane

or parallel planes and the streamline patterns are identical in each plane.

50. A streamline is defined as the line – of equal velocity in a flow.

51. Mach number is significant in – supersonics, as with projectiles and jet

propulsion.

52. A piece of wood having weight 5 kg floats in water with 60% of its

volume under the liquid. The specific gravity of wood is - .6.

53. A piece of metal of specific gravity 7 floats in mercury of specific gravity

of 13.6. What fraction of its volume is under mercury - .515. (If V is the

volume of metal and x is fraction under mercury, then x V / V = 7 / 13.6.

54. For an irrotational flow the equation ∂ 2 /∂ x2 + ∂ 2 /∂ y2 is known as –

Laplace Equation.

55. Separation of flow occurs due to reduction of pressure gradient to – the

extent such that vapour formation starts.

56. The magnitude of water hammer depends on the – length of pipeline,

speed at which the valve is closed, elastic properties of the liquid flowing

through the pipe and pipe material.

57. Mercury is suitable for manometers because it- is generally not used in

manometers.

58. A critical depth meter is always associated with – Hydraulic jump.

59. Motion of a fluid in which the fluid mass rotates without the external

force is known as – Free vortex motion.

32

60. In parallel pipe problems, - head losses through each pipe are added to

obtain the total head loss.

61. The continuity equation of flow is based on the principle of conservation

of – energy.

62. A simple pitot tube is used to measure – Velocity is a flowing stream.

63. A right circular cylinder open at the top is filled with liquid (specific

gravity 1.2) and rotated about its vertical axis at such speed that half the

liquid spills out. Pressure at the centre of the bottom is - one fourth of its

value when cylinder was full.

64. Head loss in turbulent flow in pipe varies directly as the – square root of

velocity.

65. Velocity of fluid particle at the centre fo pipe section is – average.

66. Froude number is useful in the calculation of – Water Hammer.

67. Hammer blow in pipe occurs when – Flow of fluid through pipe is

gradually brought to rest by the closing the valve.

68. Tranquil flow must always occur – above critical depth.

69. The flow of any fluid, real or ideal satisfies – Newton’s Second law of

motion, τ = (μ + η) du/dy and fluid cannot generate a boundary.

70. Boundary layer separation is caused by – reduction of pressure gradient

to zero.

71. In laminar flow – Newton’s law of viscosity applies.

72. The purpose of surge tank in a pipe line is to minimize friction losses in

pipe.

73. An air vessel is provided at the summit in a siphon – to avoid an

interruption in the flow.

74. 1 N/m2 pressure is equivalent to – 1 Pascal, 10-5bar, 10-2 kg/m sec2.

75. Mach number is defined as – it is the ratio of inertia force to pressure

force.

33

76. Process of diffusion of one liquid into other through a semi-permeable

membrane is called – Osmosis.

77. Dynamic viscosity of most of the gases with rise in temperature –

Decreases.

78. Correct statement: Centre of buoyancy is located at the centre of gravity

of the displaced liquid, For stability of a submerged body, centre of

gravity of the body must lie directly below the centre of buoyancy, If c.g.

and centre of buoyancy coincide, the submerged body must lie at neutral

equilibrium for all positions.

79. To replace a compound pipe by a new pipe, the pipes will be equivalent

when both the pipes have same – length and loss of head.

80. if the pressure at the inlet of a pipe is 90 kg/cm2 and the pressure drop

over the pipe line is 10 kg/cm2, the efficiency of transmission is – 55.5%

81. The resultant upward pressure of a fluid on a floating body is equal to the

weight of fluid displaced by the body. This definition is according to –

Buoyancy.

82. Free surface of a liquid behaves like a sheet and tends to contract to

smallest possible area due to the force of – Friction.

83. Reynolds number for non circular cross section is – 2V.P/4 ν.

84. The point in the immerse body through which the resultant pressure of the

liquid may be taken to act is known as – Metacentre.

85. For pipe flows, at constant diameter, head is proportional to – (flow)2.

86. Value of coefficient of compressibility for water at ordinary pressure and

temperature is – 21000 kg/cm3.

87. A balloon lifting in air follows the – Archimedes Principle.

88. Surface tension – decreases with fall in temperature.

89. Viscosity of water in comparison with mercury is – Higher.

90. Hydraulic grade line as compared to the centre line of conduit – Should

always above.

34

91. Speed of a submarine can be measured by – Pirani gauge.

92. Thickness of laminar boundary layer at a distance x from the leading edge

over flat plate varies as – x.

93. Thickness of turbulent boundary layer at a distance x from the leading

edge over a flat plate varies as – x 4/5.

94. The shear stress in a turbulent pipe flow – is zero at the centre and

increased linearly to the wall.

95. The viscosity of a fluid varies with – temperature and for gases it

decreases with increase in temperature. for gases it increases with

temperature.

96. The generation capacity of world’s largest capacity hydroelectric plant is

of the order of – 5000 MW.

97. The turbine that cannot be installed in high plant is – Kaplan turbine,

Francis turbine (Horizontal), Pelton wheel (horizontal and vertical).

98. A fluid is a substance that – always moves when subjected to a shearing

stress.

99. When the relationship between Reynolds number and the friction factor is

represented by a straight line, the flow is said to be – laminar.

100. A piezometer cannot be used for pressure measurement in pipes when –

Fluid in the pipe is a gas.

101. Most economical section of a triangular channel is an isosceles triangle

with vertex angle of – 90 degree.

102. The pressure in meters of oil (specific gravity .85) equivalent to 42.5 m of

water is – 50 m.

103. The line traced by a single fluid particle as it moves over a period of time

is called – Path line.

104. For a given cross- section area, most economical channel section has

maximum – discharge.

105. A hot wire anemometer is used for the measurement of – velocity of gas.

35

106. Drag force on a 40:1 scale model of a ship is measured to be 10 N.

Force expected on the ship will be – 640 kN.

107. The coefficient of discharge of an orifice varies with – Reynolds’s

number.

108. The shear stress distribution for a fluid flowing in between the parallel

plates, both at rest is – zero at the mid point and varies linearly with

distance from mid plane.

109. Friction drag is generally larger than the pressure drag in – Flow past a

cylinder.

110. An imaginary curve drawn through a flowing fluid in such a way that the

tangent to it at any point gives the direction of velocity of flow at that

point is known as – Stream line.

111. Capillarity is due to – Adhesion and cohesion.

112. The losses are maximum in – Turbulent flow.

113. in a venturieter, length of divergent cone as compared to the length of

convergent cone is – Half.

114. Principle of similitude forms the basis of –designing models so that the

result can be converted to prototypes.

115. If V is the mean velocity of flow, then according to Darcy-Weisbach

equation for pipe flow, energy loss over a length of pipe is proportional to

– 1/V.

116. The equation of continuity holds good when the flow – velocity is

uniform at all the cross section. It is based on Bernoulli’s theorym.

117. Cavitation will begin when – Pressure is increased.

118. Head loss in turbulent flow in a pipe – varies inversely as velocity.

119. A block of ice floating over water in a vessel slowly melts in it. Water

level in the vessel will – remains same.

120. Total pressure on the top of a closed cylindrical vessel of radius r filled

with liquid is proportional to – r2.

36

121. The drag coefficient for laminar flow varies as – Re -1/2.

122. The magnitude of water hammer depends on – Length of pipe, elastic

properties of pipe material, rate of stoppage of flow.

123. In Series pipe applications- flow increases.

124. For no shock wave to develop, when flow taking place through a

converging diverging tube, mach number at exit should be – 1.

125. The velocity distribution for flow between fixed parallel plates – is

constant over the cross section.

126. The most economical section o a rectangular channel for maximum

discharge is obtained when its depth is equal to – the breadth .

127. When a fluid flows in concentric circles, it is known as – Free circular

motion.

128. Region downstream from the streamline where separation takes place

from the boundary is known as – cavitation.

129. The river flow during floods can be classified as – unsteady non uniform

flow.

130. Separation is caused by – the boundary layer thickness reducing to zero.

131. Wake always occurs – after a separation point.

132. In a flow field, at the stagnation point – Total energy is zero.

133. Total drag on a body is the sum of –friction drag and pressure drag.

134. The turbulent boundary layer thickness varies as – x1/5.

135. In a free vortex flow the tangential velocity is – directly proportional to

the square of the radial distance.

136. The radial component of velocity in a free vortex is – inversely

proportional to the square of the radial distance.

137. The upper surface of the weir over which water flows is known as –

Crest.

138. Fire hose is generally made of – cylindrical shape.

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139. Choking in pipe flow implies – negative flow takes place due to water

hammer.

140. Friction factor for pipes depends on – rate of flow, fluid density,

viscosity, pipe roughness.

141. In the case of flow through parallel pipes – head loss in each pipe is same.

142. To replace a pipe of diameter D by n parallel pipes of diameter d, the

formula used is – D/ n2/5.

143. Power transmitted through a pipe is maximum when the loss of head due

to friction is – One third of the total head supplied.

144. Loss of head due to friction in a pipe of uniform diameter with viscous

flow is equal to – 16/Re.

145. Hydraulic grade line for any flow system as compared to energy line is –

Below.

146. A fluid in which resistance to deformation is independent of the shear

stress, is known as – Newtonian fluid.

147. Pressure drag results from – occurrence of a wake.

148. Model analysis of aeroplanes and projectiles moving at supersonic speed

are based on – Mach number.

149. Buff body surface – does not coincide with stream line.

150. Centre of pressure on an inclined pane is – below the centroid.

151. Separation of flow occurs when pressure gradient – changes abruptly.

152. The Friction head lost due to the flow of a viscous fluid through a circular

pipe of length L and diameter d with a velocity v, and pipe friction factor

f is – 4 f L v 2 / d.2 g.

153. Pressure coefficient is the ratio of pressure force to – inertia force.

154. Component of the force of fluid on the body (which is generally inclined

to the direction of motion of the body) parallel to the direction of motion

is called – drag.

155. Weber number is the ratio of Inertia force to – Surface tension.

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156. Critical velocity is – Terminal velocity.

157. The function of surge tank is to – Relieve the pipe line from excessive

pressure produced by water hammer.

158. Units of Kinematic viscosity are – m2/sec. it is given by dynamic

viscosity/ density.

159. With increase in pressure the bulk modulus of elasticity – Increases.

160. Head loss due to a sudden enlargement in a pipe is – (v1- v2) 2 / 2g. * *

161. The metacentre is – point of intersection of buoyant force and centre line

of body.

162. The loss of head due to sudden contraction is given by –

163. The units of dynamic or absolute viscosity is – Newton-sec/m2.

164. A body floats in stable equilibrium – when Metacentre is above c.g.

165. Speed of sound in water is equal to (K is bulk modulus and p is density) –

√k/p.

166. Ratio between inertia forces and the square root of pressure force is

known as – Euler number.

167. The laminar boundary layer thickness varies as – x1/2.

168. In a flow field, stagnation point is a point where the – velocity is zero.

169. Euler’s equation in the differential flow of motion of liquids is given by –

dp /p + g dz +v dv.

1. Hyraulic jump occurs when – flow is supercritical and adequate down

stream depth is available.

2. Hydraulic jump is used for – reducing the energy of flow.

3. The unit of specific speed is – R.P.M.

4. A draft tube converts – Kinetic energy into mechanical energy.

5. the Hydraulic radius is given by – area divided by wetted perimeter.

6. Running away speed of a pelton wheel is – no load speed when governor

mechanism fails.

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7. Priming is required in – Centrifugal pumps.

8. Spouting velocity is – ideal velocity of jet.

9. Multistage centrifugal pumps are used to obtain – high head.

10.High specific speed of a a pump implies that it is a – axial flow pump.

11.A plot between power generated in MW and time is known as – Load

curve.

12.In centrifugal pumps, maximum efficiency is obtained when the blades

are - Bent backwards.

13.Indicator diagram of a reciprocating pump is a graph between – Flow vs

swept volume.

14.A hydraulic accumulator normally consists of - a cylinder and a ram.

15.For hydraulic turbines – P = K N 3.

16.A draft tube is used with – Reaction turbine.

17.Load factor is equal to – average load over a certain period/maximum

load occurring during the same period.

18.The angle of draft tube is – less than 8 degree.

19.The percentage slip for a reciprocating pump is defined as the percentage

of – (theoretical discharge – actual discharge) / theoretical

discharge.

20.Oerall efficiency of a centrifugal pump is equal to – volumetric efficiency

x manometric efficiency x mechanical efficiency.

21.To avoid cavitation in centrifugal pumps – suction pressure should be

high.

22.Ratio of work done on the wheel to the energy supplied to the turbine is

called – Hydraulic efficiency.

23.

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τ ∂ ∂

% & + < = > ± µ ¼ ½ ¾ Π Σ η α λ μ

ν ξ π

τ τ τ ρ σ υ Ώ ≤ ≥ √ ∞ ← ↑

→ θ ↓

∂ ∆ ≈ ≠ β γ δ ε ζ

Ф ω

jdkjdljdkjjdj

41