Fluid Dynamics II

7/27/2019 Fluid Dynamics II

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FLUIDDYNAMICS


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Energy of A Flowing Fluid

A liquid may possess three forms of energy:

Potential energy

If a liquid of weight W is at a height of z above

datum line.

Potential energy = Wz

Potential energy per unit weight = zUnit : Nm/N can be called the po tent ial head.


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Pressure energy

When a fluid flows in a continuous stream under

pressure it can do work. If the area of cross-section of

the stream of fluid is a, then force due to pressure p oncross-section ispa.

Similarly the pressure energy per unit weightp/W is

equivalent to a head and is referred to as the pressure

head.


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Kinetic energy

The kinetic energy per unit weight

Referred to as the velocity head.


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Bernoullis Equation

Bernoullis Theorem states that the total

energy of each particle of a body of fluid is the

same provided that no energy enters or leaves

the system at any point. The division of this

energy between potential, pressure and kineticenergy may vary, but the total remains

constant.


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Bernoullis Equation


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Limitation Bernoullis

Equation

Bernoullis Equation has some restrictions in its

applicability, they are :

The flow is steady

The density is constant (which also means the fluid is

compressible)

Friction losses are negligible

The equation relates the state at two points along a single

streamline (not conditions on two different streamlines).


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Application of Bernoullis

Equation

Horizontal Pipe


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Equation


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Equation

Horizontal Venturi Meter

It is a device used for measuring the rate of flow of non-

viscous, incompressible fluid in non-rotational and steady-

stream lined flow.

Although venturi meters can be applied to the

measurement of gas, they are most commonly used for

liquids.

The following treatment is limited to incompressible fluids.


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Equation


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Equation

Advantage & Disadvantages

The Venturi Meter described earlier is a reliable flow

measuring device.

It causes little pressure loss. For these reasons it iswidely used, particularly for large-volume liquid and gasflows.

This meter is relatively complex to construct and hence

expensive especially for small pipelines.


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Equation


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Equation


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Equation


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Equation

Inclined Venturi Meter

This will show that the U-type of gauge is used to

measure the pressure difference.

The gauge reading will be the same for a given

discharge irrespective of the inclination of the

meter.


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Equation


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Equation

OR

WHERE


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EXAMPLE


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EXAMPLE

The water supply to a gas water heater contracts from 10mm in

diameter at A to 7 mm in diameter at B. If the pipe is horizontal,

calculate the difference in pressure between A and B when the

velocity of water at A is 4.5 m/s. The pressure difference operates

the gas control through connections which is taken to a horizontal

cylinder in which a piston of 20 mm diameter moves. Ignoringfriction and the area of the piston connecting rod, what is the force

on the piston?


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Equation

Small orifice

The principle of the orifice meter is identical

with that of the venturi meter. The reduction at

the cross section of the flowing stream inpassing through the orifice increases the

velocity head at the expense of the pressure

head, and the reduction in pressure between

the taps is measured by a manometer.

Bernoulli's equation provides a basis for

correlating the increase in velocity head with

the decrease in pressure head.


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There are Section 1 (entrance of the orifice) and Section 2

(exit of the orifice also known as vena contracta).

Vena contracta is the point in a fluid stream where the

diameter of the stream is the least, and fluid velocity is at its

maximum, such as in the case of a stream issuing out.


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Equation

WHERE,


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TYPES OF ORIFICE


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EXAMPLE

A meter orifice has a 100 mm diameter

rectangular hole in the pipe. Diameter of the pipe

is 250 mm. Coefficient of discharge, Cd = 0.65

and specific gravity of oil in the pipe is 0.9. Thepressure difference that is measured by the

manometer is 750 mm. Calculate the flow rate of

the oil through the pipe.


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Fluid Dynamics II

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