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Fluid Mechanics

SIMPLE MANOMETER, PIEZOMETER, U-TUBE MANOMETER

 Introduction

  • There are many techniques for the measurement of pressure and vacuum. Instruments used to measure pressure are called pressure gauges.
  • Manometers are used for the measurement of very low pressures as well as vacuum especially in hydraulic laboratories.

Manometers

  • Manometers are used for measuring pressures by balancing the fluid column of fluid against another column of fluid of known specific gravity. 

Manometers can be classified as:

1. Simple manometers

a.Piezometer

b.U-tube manometer

2. Micro manometers (or single column manometers)

a.Vertical column micro manometer

b. Inclined column micro manometer

3. Differential manometers

a.Upright U-tube differential manometer

b.Inverted  U-tube differential manometer

1.  Simple manometers

  • It consists of a glass tube with one end open to the atmosphere and other end connected to a point at which pressure is to be measured.

a. Piezometer

  • It consists of glass tube connected to a vessel or pipe at which static pressure is to be measured.
  • It is the simplest of all the manometers (Fig.1) It is used to measure very low pressures.

    


  Fig. 1 Piezometer
                                               

The pressure in piezometer is given by the following equation.

 p=ρgh

Where,

ρ = density of liquid

h = height of liquid in the piezometer from the centre of the pipe.

g = acceleration due to gravity.

b.  U-tube manometer

  • The manometer is named so because it consists of a glass tube having the shape of alphabet 'U'. One end is open to the atmosphere and other end connected to a point at which pressure is to be measured.

Let        ρ1 = density of liquid for which pressure has to be determined

             ρ2 = density of manometer liquid (assume mercury)

             ω1 = weight density of liquid for which pressure has to be determined

             ω2 = weight density of manometer liquid

S1 = Specific gravity of liquid for which pressure has to be determined

             S2 = Specific gravity of manometer liquid


Fig.U- tube manometer

  • Let h be the pressure in terms of height of fluid in the pipe.
  • h1is the distance from the datum line XX to the centre of pipe
  • h2 is the height of manometer liquid from the datum line XX in the right limb
  • Pressure in the left limb at XX        = P + ρ1gh1 = P + ω1h1
  • Pressure in the right limb at XX      = ρ2gh2 = ω2h2
  • According to Pascals law, at datum line pressure will be equal
  •           P + ω1h1 = ω2h2
  •           P = ω2h2  - ω1h1.............(i)
  •           P = ρ2gh2 - ρ1gh1 ........ (ii)
  • On dividing equation (ii) by ρg where ρ is the density of the water:
  •         ...........     (iii)

  • Sp. Gravity (s) =  =   .......(iv)

  •           Since P = ρgh where h is head of water
  •           h = S2h2 -S1h1


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