Study Notes: Manometry | Fluid Mechanics for Mechanical Engineering PDF Download

Manometers

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

• Pressure is proportional to the height of a column of fluid.
• The instrument used to carry out the complete process is termed a Manometer.
• Types of Manometers: Barometer, Piezometer and U-tube Manometer.
• Manometers use the relationship between pressure and head to measure pressure 

Piezometer

• The simplest manometer is an open tube. This is attached to the top of a container with liquid at pressure. containing liquid at a pressure.
• The tube is open to the atmosphere, the pressure measured is relative to atmospheric so it measures gauge pressure.
  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.
  Limitations of Piezometer -
  (i) Can only be used for liquids.
  (ii) Pressure must above atmospheric.
  (iii) Liquid height must be convenient i.e. not be too small or too large.

U-tube Manometer

• It consists of a U shaped bend whose one end is attached to the gauge point ‘A’ and the other end is open to the atmosphere.
• It can measure both positive and negative (suction) pressures.
• U-Tube enables the pressure of both liquids and gases to be measured U is connected as shown and filled with manometric fluid.

Note

• The manometric fluid density should be greater than of the fluid measured, ρ_mano. > ρ
• The two fluids should not be able to mix they must be immiscible.
  
• Pressure in a continuous static fluid is the same at any horizontal level,
  Pressure at B = Pressure at C
  P_B = P_C
  For the left-hand arm pressure at B,
  P_B = Pressure at A + Pressure of height of liquid being measured
  P_B = P_A + ρgh₁
• For the right-hand arm pressure at C:

  P_C = Pressure at D + Pressure of height of manometric liquid.
  P_C = ρ_mano gh₂
  We are measuring gauge pressure we can subtract
  P_atmospheric giving:
  P_B = P_C
  P_A  = ρ_manogh₂ – ρgh₁

Differential U-Tube Manometer:

• A U-Tube manometric liquid is heavier than the liquid for which the pressure difference is to be measured and is not immiscible with it.
  

Pressure difference between A and B is given by equation
P_A + ρ₁g(h₁ + h) = P_B + ρ₂h₂ + ρ_Hggh
P_A - P_B = ρ₂gh₂ + ρ_Hggh - ρ₁gh₁ - ρ₁gh
P_A - P_B = ρ₂gh₂ + (ρ_Hg - ρ₁)gh - ρ₁gh₁ 

Inverted U-Tube Manometer

• An inverted U-tube manometer consists of an inverted U-tube containing a light liquid.
• This is used to measure the differences of low pressures between two points where better accuracy is required.
  
  Inverted U-Tube Manometer

The pressure difference can be calculated from equation,
P_A - ρ₁gh₁ = P_B - ρ₂gh₂ - ρgh
P_A - P_B = ρ₁gh₁ - ρ₂gh₂ - ρgh
When both the pipes are the same level i.e. h₁ = h₂ 
P_A - P_B = (ρ₁ - ρ₂)gh₁ - ρgh

Micro Manometer

• Micro Manometer is the modified form of a simple manometer whose one limb is made of larger cross-sectional area.
• It measures very small pressure differences with high precision.

Inclined Manometer

• An inclined manometer is used for the measurement of small pressures and is to measure more accurately than the vertical tube type manometer.
• Due to inclination, the distance moved by the fluid in the manometer is more.
• The sensitivity of simple manometers can be enhanced by using inclined tubes. It is due to increase in length by (1/sin θ), where θ is the angle of inclination with the horizontal.