Hydraulics BE8203 Hydraulics

School of Architecture & the Built Environment 1 Diploma in Civil Engineering with Business

CHAPTER 1 - HYDRAULICS

This chapter introduces some very important and fundamental properties of fluids such as pressure, force, weight, mass density, relative density etc.

1.1 Fluid Properties:

Mass Density, - mass of substance per unit volume (kg/m3)

Weight Density, w - weight of substance per unit volume (N/m3)

Relative Density or Specific Gravity r.d. - the ratio of the mass density of a substance to that of water (dimensionless)

Dynamic Viscosity - shear force per unit area required to drag one layer of fluid with unit velocity passes another layer an unit distance away from it (kg/m.s)

Kinematic Viscosity - the ratio of dynamic viscosity to mass density (m2 /s)

1.2 Pressure:

The pressure or the intensity of pressure is the force per unit area exerted by the fluid any location i.e.

p =F/A (unit: N/m2 )

In a region like outer space which is devoid of gases, the pressure is zero which is called __________________________________.

On the surface of the earth, pressure is exerted by the mass of gases above the earth which is known as __________________________________.

Gauge pressure is the pressure measured taking atmospheric pressure as _______. The gauge pressure can be positive or negative. Positive gauge pressure means the pressure is __________ than atmospheric pressure and negative gauge pressure means that the pressure is __________ than atmospheric pressure.

Absolute pressure = _______________________ + _________________________

A typical pressure

Atmospheric pressure

Absolute zero

Gauge Pressure

Another typical pressure

Vacuum or negative gauge pressure

Absolute pressure

Fig 1: Pressure Scale

Hydraulics BE8203 Hydraulics

School of Architecture & the Built Environment 2 Diploma in Civil Engineering with Business

Pressure exerted by fluids at rest:

Pressure increases with increasing depth.

where h = depth (m) (depth is always measured vertically) = density of water (kg/m3 )

g = acceleration due to gravity (9.81 m/s2 )

(Pressure unit: N/m2 or Pa)

Some facts about hydrostatic pressure:

i. The pressure depends only on the depth of water above the point. ii. The pressure increases in direct proportion to the depth. iii. It acts at _______________ to any surface in contact with the fluid. iv. Pressure at any point is the same in all directions. v. Pressure is _______________ at a horizontal level in a continuous fluid mass.

1.3 Pressure Head:

Pressure head (in m) is a convenient engineering term commonly used in practice. The pressure head expresses the pressure in term of the height of the column of liquid causing the pressure.

gPh

ghP

=

=

1.4 Manometry:

Manometry is the technique of using vertical columns of fluid for the measurement of pressure. Manometry can be very accurate and convenient.

At the tapping point, the manometer tube must enter at right angle to the flow.

1.4.1 Piezometer:

Open top transparent tube Attached directly to the point where pressure is measured

Fig 2: Hydrostatic Pressure Distribution / Profile

h = 0 Therefore P = 0 Pa

5 m

h = 5 m Therefore P = 1000 x 9.81 x 5 = 49050 Pa

P = gh

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School of Architecture & the Built Environment 3 Diploma in Civil Engineering with Business

Filled with same liquid

1.4.2 U-tube Manometer:

The U-tube manometer is essentially a piezometer with its tube bent into a U - shape. It enables the use of another fluid (often denser such as mercury) to widen the scope of measurement. It may be used for gases, which is trapped by the liquid in the U bend. The U-tube manometer is used to measure the pressure difference between two points i.e. (PA - PB ). If one of the arms is open to the atmosphere, then the guage pressure at the tapping can be measured.

1.4.3 Inverted U-tube Manometer:

An inverted U-tube manometer is essentially a U-tube manometer in an inverted position. It has either no manometer fluid or the manometer fluid has a lighter density than the fluid being measured.

Fig 5: Inverted U-tube Manometer

P1 - P2 = gH N/m2

H

1 2

H1

H2

Fig 3: Piezometers

Fig 4: U-tube Manometer

2

1

2

h

1

P1-P2 = gh (2-1) N/m2

H

1

2

()

P1-P2 = gH N/m2

Hydraulics BE8203 Hydraulics

School of Architecture & the Built Environment 4 Diploma in Civil Engineering with Business

Example 1

A U-tube manometer connects two pipes A and B as shown in Fig 6. If both pipes are carrying water, calculate the pressure difference between pipes A and B.

Example 2

A Hydraulic Press is shown in Fig 7 which uses oil of r.d.= 0.86 as its transmission fluid. The smaller piston under W1 has a diameter of 250 mm. The larger piston under W2 has an area of 3.0 mx1.0 m. If the force W1=500 N, calculate the force W2 acting on the larger piston.

Updated by Elizabeth Chow May 05 Mar 06 Mar 07 Mar 09

Updated by Tracy Law Sep 09 Apr 10 Sep 10 Apr 11

W1

W2 1.8 m

Fig 7

A Water

Mercury, r.d = 13.6

150 mm

h

a

B

Fig 6