Short Notes: Manometry and Buoyancy | Short Notes for Mechanical Engineering PDF Download

 Page 1


Manometry and Buoyancy  
Manometers use the relationship between pressure and head to measure pressure. 
This relation is highly used making this section of Fluid mechanics important in 
terms of GATE, ESE and other various other psu exams.
Pressure And Head
We have the vertical pressure relationship
p = pgz + constant
measuring z from the free surface so that z = -h
¦t
j
x
p = pgh + constant
surface pressure is atmospheric,patm osph e ric
A itm o sp h e ric — constant
so
P ~ + P atm osp h eric
We generally assume atmospheric pressure as the datum , 
Gauge pressure, pg = pgh
Page 2


Manometry and Buoyancy  
Manometers use the relationship between pressure and head to measure pressure. 
This relation is highly used making this section of Fluid mechanics important in 
terms of GATE, ESE and other various other psu exams.
Pressure And Head
We have the vertical pressure relationship
p = pgz + constant
measuring z from the free surface so that z = -h
¦t
j
x
p = pgh + constant
surface pressure is atmospheric,patm osph e ric
A itm o sp h e ric — constant
so
P ~ + P atm osp h eric
We generally assume atmospheric pressure as the datum , 
Gauge pressure, pg = pgh
The lower limit of any pressure is the pressure in a perfect vacuum.Pressure 
measured above a perfect vacuum (zero) is known as absolute pressure.
Absolute pressure, pa = pgh+ patm ospheric
Absolute pressure = Gauge pressure + Atmospheric
Manometry
• Pressure is proportional to the height of a column of fluid.
• Manometry is the field of science which deals with the evaluation of the 
pressure of the fluid.
• The instrument used to carry out the complete process is termed as 
Manometer.
• Types of Manometers: Barometer, Piezometer and U-tube Manometer.
• Manometers use the relationship between pressure and head to measure 
pressure
Piezometer Tube Manometer:
• 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.
• Pressure at A = pressure due to column of liquid hi
P a = pghi
• Pressure at B = pressure due to column of liquid h2
Pb = pgh2
Limitations of Piezometer:
• Can only be used for liquids
• Pressure must above atmospheric
• Liquid height must be convenient i.e. not be too small or too large
U-tube Manometer:
Page 3


Manometry and Buoyancy  
Manometers use the relationship between pressure and head to measure pressure. 
This relation is highly used making this section of Fluid mechanics important in 
terms of GATE, ESE and other various other psu exams.
Pressure And Head
We have the vertical pressure relationship
p = pgz + constant
measuring z from the free surface so that z = -h
¦t
j
x
p = pgh + constant
surface pressure is atmospheric,patm osph e ric
A itm o sp h e ric — constant
so
P ~ + P atm osp h eric
We generally assume atmospheric pressure as the datum , 
Gauge pressure, pg = pgh
The lower limit of any pressure is the pressure in a perfect vacuum.Pressure 
measured above a perfect vacuum (zero) is known as absolute pressure.
Absolute pressure, pa = pgh+ patm ospheric
Absolute pressure = Gauge pressure + Atmospheric
Manometry
• Pressure is proportional to the height of a column of fluid.
• Manometry is the field of science which deals with the evaluation of the 
pressure of the fluid.
• The instrument used to carry out the complete process is termed as 
Manometer.
• Types of Manometers: Barometer, Piezometer and U-tube Manometer.
• Manometers use the relationship between pressure and head to measure 
pressure
Piezometer Tube Manometer:
• 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.
• Pressure at A = pressure due to column of liquid hi
P a = pghi
• Pressure at B = pressure due to column of liquid h2
Pb = pgh2
Limitations of Piezometer:
• Can only be used for liquids
• Pressure must above atmospheric
• Liquid height must be convenient i.e. not be too small or too large
U-tube Manometer:
• It consist a U shaped bend whose one end is attached to the gauge point 'A' 
and 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" 
connected as shown and filled with manometric fluid.
Note:
• The manometric fluid density should be greater than of the fluid measured, 
Pman > P
• 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
• Pb = Pc
• For the left hand arm pressure at B
° pressure at A + pressure of height of liquid being measured
Pb = PA + pgh-i
• For the right hand arm pressure at C =
° pressure at D + pressure of height of manometric liquid
Pc = Patmos + Pmano9^2
We are measuring gauge pressure we can subtract Patmospheric {Jiving
Pb= Pc
Pa = Pmanofji12" P9^1 
Differential U-Tube Manometer: •
• A U-Tube manometric liquid heavier than the liquid for which the pressure 
difference is to be measured and is not immiscible with it.
Page 4


Manometry and Buoyancy  
Manometers use the relationship between pressure and head to measure pressure. 
This relation is highly used making this section of Fluid mechanics important in 
terms of GATE, ESE and other various other psu exams.
Pressure And Head
We have the vertical pressure relationship
p = pgz + constant
measuring z from the free surface so that z = -h
¦t
j
x
p = pgh + constant
surface pressure is atmospheric,patm osph e ric
A itm o sp h e ric — constant
so
P ~ + P atm osp h eric
We generally assume atmospheric pressure as the datum , 
Gauge pressure, pg = pgh
The lower limit of any pressure is the pressure in a perfect vacuum.Pressure 
measured above a perfect vacuum (zero) is known as absolute pressure.
Absolute pressure, pa = pgh+ patm ospheric
Absolute pressure = Gauge pressure + Atmospheric
Manometry
• Pressure is proportional to the height of a column of fluid.
• Manometry is the field of science which deals with the evaluation of the 
pressure of the fluid.
• The instrument used to carry out the complete process is termed as 
Manometer.
• Types of Manometers: Barometer, Piezometer and U-tube Manometer.
• Manometers use the relationship between pressure and head to measure 
pressure
Piezometer Tube Manometer:
• 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.
• Pressure at A = pressure due to column of liquid hi
P a = pghi
• Pressure at B = pressure due to column of liquid h2
Pb = pgh2
Limitations of Piezometer:
• Can only be used for liquids
• Pressure must above atmospheric
• Liquid height must be convenient i.e. not be too small or too large
U-tube Manometer:
• It consist a U shaped bend whose one end is attached to the gauge point 'A' 
and 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" 
connected as shown and filled with manometric fluid.
Note:
• The manometric fluid density should be greater than of the fluid measured, 
Pman > P
• 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
• Pb = Pc
• For the left hand arm pressure at B
° pressure at A + pressure of height of liquid being measured
Pb = PA + pgh-i
• For the right hand arm pressure at C =
° pressure at D + pressure of height of manometric liquid
Pc = Patmos + Pmano9^2
We are measuring gauge pressure we can subtract Patmospheric {Jiving
Pb= Pc
Pa = Pmanofji12" P9^1 
Differential U-Tube Manometer: •
• A U-Tube manometric liquid heavier than the liquid for which the pressure 
difference is to be measured and is not immiscible with it.
Differential U - Tube Manometer
• Pressure difference between A and B is given by equation
Pa - Pb = P2h2 + P3^3 - Pi hi 
Inverted U-Tube Manometer:
• 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.
• It generally consists of an air cock at top of manometric fluid type.
Pressure difference can be calculated from equation:
P i - P igH 2 - p m g(Hi- h2 )=p2 - p 2g H i
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.
Page 5


Manometry and Buoyancy  
Manometers use the relationship between pressure and head to measure pressure. 
This relation is highly used making this section of Fluid mechanics important in 
terms of GATE, ESE and other various other psu exams.
Pressure And Head
We have the vertical pressure relationship
p = pgz + constant
measuring z from the free surface so that z = -h
¦t
j
x
p = pgh + constant
surface pressure is atmospheric,patm osph e ric
A itm o sp h e ric — constant
so
P ~ + P atm osp h eric
We generally assume atmospheric pressure as the datum , 
Gauge pressure, pg = pgh
The lower limit of any pressure is the pressure in a perfect vacuum.Pressure 
measured above a perfect vacuum (zero) is known as absolute pressure.
Absolute pressure, pa = pgh+ patm ospheric
Absolute pressure = Gauge pressure + Atmospheric
Manometry
• Pressure is proportional to the height of a column of fluid.
• Manometry is the field of science which deals with the evaluation of the 
pressure of the fluid.
• The instrument used to carry out the complete process is termed as 
Manometer.
• Types of Manometers: Barometer, Piezometer and U-tube Manometer.
• Manometers use the relationship between pressure and head to measure 
pressure
Piezometer Tube Manometer:
• 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.
• Pressure at A = pressure due to column of liquid hi
P a = pghi
• Pressure at B = pressure due to column of liquid h2
Pb = pgh2
Limitations of Piezometer:
• Can only be used for liquids
• Pressure must above atmospheric
• Liquid height must be convenient i.e. not be too small or too large
U-tube Manometer:
• It consist a U shaped bend whose one end is attached to the gauge point 'A' 
and 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" 
connected as shown and filled with manometric fluid.
Note:
• The manometric fluid density should be greater than of the fluid measured, 
Pman > P
• 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
• Pb = Pc
• For the left hand arm pressure at B
° pressure at A + pressure of height of liquid being measured
Pb = PA + pgh-i
• For the right hand arm pressure at C =
° pressure at D + pressure of height of manometric liquid
Pc = Patmos + Pmano9^2
We are measuring gauge pressure we can subtract Patmospheric {Jiving
Pb= Pc
Pa = Pmanofji12" P9^1 
Differential U-Tube Manometer: •
• A U-Tube manometric liquid heavier than the liquid for which the pressure 
difference is to be measured and is not immiscible with it.
Differential U - Tube Manometer
• Pressure difference between A and B is given by equation
Pa - Pb = P2h2 + P3^3 - Pi hi 
Inverted U-Tube Manometer:
• 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.
• It generally consists of an air cock at top of manometric fluid type.
Pressure difference can be calculated from equation:
P i - P igH 2 - p m g(Hi- h2 )=p2 - p 2g H i
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.
Micro Mamometer
Let 'a' = area of the tube, A = area of the reservoir, h3 = Falling liquid level reservoir, 
h2 = Rise of the liquid in the tube,
• By conversation of mass, Ah3 = ah2
• Equating pressure heads at datum,
Pi = (Pm - Pi)gh3 + pmgh2 - Pighi
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 manometer is more. •
In d in e a M a n o m e te r
• Pressure difference between A and B is given by equation 
PA “ Pb = P2Lsin0 + P3^2 “ Pi hi
Buoyancy
Buoyancy is also known as buoyant force. It is the force exerted on an object that 
is wholly or partly immersed in a fluid.
Concept of Buoyancy: When a body is immersed in a fluid, an upward force is 
exerted by fluid on the body which is equal to weight of fluid displaced by body.
This acts as upward.
Archimedes’ Principle: It states, when a body is immersed completely or partially in 
a fluid, it is lifted up by a force equal to weight of fluid displaced by the body.