Mechanical Engineering Principles

HYDROSTATICS 235

1000 kg/m^3. If the depth of the box in

the water is 280 mm, what is its weight?

[2.47 kN]

6. A body weighs 18 N in air and 13.7 N
   when completely immersed in water of
   density 1000 kg/m^3. What is the density
   and relative density of the body?
   [4.186 tonne/m^3 , 4.186]


7. A watertight rectangular box is 660 mm
   long and 320 mm wide. Its weight is
   336 N. If it floats with its sides and ends
   vertical in water of density 1020 kg/m^3 ,
   what will be its depth in the water?
   [159 mm]


8. A watertight drum has a volume of
   0.165 m^3 and a weight of 115 N. It is
   completely submerged in water of density
   1030 kg/m^3 , held in position by a single
   vertical chain attached to the underside of
   the drum. What is the force in the chain?
   [1.551 kN]

21.5 Measurement of pressure

As stated earlier, pressure is the force exerted by
a fluid per unit area. A fluid (i.e. liquid, vapour or
gas) has a negligible resistance to a shear force, so
that the force it exerts always acts at right angles to
its containing surface.
The SI unit of pressure is thePascal,Pa,which
is unit force per unit area, i.e.1Pa=1N/m^2 .The
Pascal is a very small unit and a commonly used
larger unit is the bar, where

1bar= 105 Pa

Atmospheric pressure is due to the mass of the
air above the Earth’s surface. Atmospheric pressure
changes continuously. A standard value of atmo-
spheric pressure, called ‘standard atmospheric pres-
sure’, is often used, having a value of 101325 Pa
or 1.01325 bars or 1013.25 millibars. This latter
unit, the millibar, is usually used in the measure-
ment of meteorological pressures. (Note that when
atmospheric pressure varies from 101325 Pa it is no
longer standard.)
Pressure indicating instruments are made in a
wide variety of forms because of their many dif-
ferent applications. Apart from the obvious criteria

such as pressure range, accuracy and response, many

measurements also require special attention to mate-

rial, sealing and temperature effects. The fluid whose

pressure is being measured may be corrosive or may

be at high temperatures. Pressure indicating devices

used in science and industry include:

(i) barometers (see Section 21.6),

(ii) manometers (see Section 21.8),

(iii) Bourdon pressure gauge (see Section 21.9),

and

(iv) McLeod and Pirani gauges (see Sec-

tion 21.10).

21.6 Barometers

Introduction

A barometer is an instrument for measuring atmo-

spheric pressure. It is affected by seasonal changes

of temperature. Barometers are therefore also used

for the measurement of altitude and also as one

of the aids in weather forecasting. The value of

atmospheric pressure will thus vary with climatic

conditions, although not usually by more than about

10% of standard atmospheric pressure.

Construction and principle of operation

A simple barometer consists of a glass tube, just less

than 1 m in length, sealed at one end, filled with

mercury and then inverted into a trough containing

more mercury. Care must be taken to ensure that

no air enters the tube during this latter process.

Such a barometer is shown in Figure 21.3(a) and

it is seen that the level of the mercury column

falls, leaving an empty space, called a vacuum.

Atmospheric pressure acts on the surface of the

mercury in the trough as shown and this pressure

is equal to the pressure at the base of the column of

mercury in the inverted tube, i.e. the pressure of the

atmosphere is supporting the column of mercury. If

the atmospheric pressure falls the barometer height

hdecreases. Similarly, if the atmospheric pressure

rises thenhincreases. Thus atmospheric pressure

can be measured in terms of the height of the

mercury column. It may be shown that for mercury

the height his 760 mm at standard atmospheric

pressure, i.e. a vertical column of mercury 760 mm