MANOMETERMANOMETER

Bulacan Agricultural State CollegeBulacan Agricultural State College

(BASC)(BASC)

Preferred By: Erwin BlasPreferred By: Erwin Blas

BSIT-2BBSIT-2B

ManometerManometer

• A A manometermanometer is an device is an device employed to measure pressure. employed to measure pressure.

Variety of manometer Variety of manometer designsdesigns• simple, common design is to seal a simple, common design is to seal a

length of glass tubing and bend the length of glass tubing and bend the glass tube into a U-shape. The glass glass tube into a U-shape. The glass tube is then filled with a liquid, tube is then filled with a liquid, typically mercury, so that all trapped typically mercury, so that all trapped air is removed from the sealed end of air is removed from the sealed end of the tube. The glass tube is then the tube. The glass tube is then positioned with the curved region at positioned with the curved region at the bottom. the bottom.

• After the mercury settles to the After the mercury settles to the bottom of the manometer, a vacuum bottom of the manometer, a vacuum is produced in the sealed tube (the is produced in the sealed tube (the left tube in the picture). The open left tube in the picture). The open tube is connected to the system tube is connected to the system whose pressure is being measured. whose pressure is being measured. In the sealed tube, there is no gas to In the sealed tube, there is no gas to exert a force on the mercury (except exert a force on the mercury (except for some mercury vapor). for some mercury vapor).

• In the tube connected to the system, In the tube connected to the system, the gas in the system exerts a force the gas in the system exerts a force on the mercury. The net result is that on the mercury. The net result is that the column of mercury in the left the column of mercury in the left (sealed) tube is higher than that in (sealed) tube is higher than that in the right (unsealed) tube. The the right (unsealed) tube. The difference in the heights of the difference in the heights of the columns of mercury is a measure of columns of mercury is a measure of the pressure of gas in the system.the pressure of gas in the system.

• In the example at the left, the top of In the example at the left, the top of the left column of mercury the left column of mercury corresponds to 875 mm on the scale. corresponds to 875 mm on the scale. The top of the right column of The top of the right column of mercury corresponds to 115 mm. mercury corresponds to 115 mm. The difference in heights is 875 mm - The difference in heights is 875 mm - 115 mm = 760. mm, which indicates 115 mm = 760. mm, which indicates that the pressure is 760. mm Hg or that the pressure is 760. mm Hg or 760. torr.760. torr.

• This method for measuring pressure This method for measuring pressure led to the use of millimeters of led to the use of millimeters of mercury (mm Hg) as a unit of mercury (mm Hg) as a unit of pressure. Today 1 mm Hg is called 1 pressure. Today 1 mm Hg is called 1 torr. A pressure of 1 torr or 1 mm Hg torr. A pressure of 1 torr or 1 mm Hg is literally the pressure that produces is literally the pressure that produces a 1 mm difference in the heights of a 1 mm difference in the heights of the two columns of mercury in a the two columns of mercury in a manometer.manometer.

F = m gF = m g• In this equation, m is the mass of In this equation, m is the mass of

mercury in the column and g = mercury in the column and g = 9.80665 m/sec2 is the gravitational 9.80665 m/sec2 is the gravitational acceleration. This force is distributed acceleration. This force is distributed over the cross-sectional area of the over the cross-sectional area of the column ( A ). The pressure resulting column ( A ). The pressure resulting from the column of mercury is thusfrom the column of mercury is thus

P= mg/ AP= mg/ A

• The mass of mercury is given by the The mass of mercury is given by the product of the density of mercury ( product of the density of mercury ( dHgdHg ) and the volume of mercury ( ) and the volume of mercury ( VV ). For a ). For a cylindrical column of mercury, the cylindrical column of mercury, the volume of mercury is the product of the volume of mercury is the product of the cross-sectional area and the height of cross-sectional area and the height of the column ( the column ( hh ). These relationships ). These relationships product the following equation.product the following equation.

• P= mg/ A= dHgVg/ P= mg/ A= dHgVg/ A=dHgAhg/A=dHghgA=dHgAhg/A=dHghg

Vertical U-Tube Vertical U-Tube ManometerManometer

The pressure difference in a vertical U-The pressure difference in a vertical U-Tube manometer can be expressed asTube manometer can be expressed as

pd = γ h         (1)pd = γ h         (1)

wherewhere

pd = pd = pressurepressure

γ = γ = specific weightspecific weight of the fluid in the tube of the fluid in the tube (kN/m3, lb/ft3(kN/m3, lb/ft3

h = liquid height (m, ft)h = liquid height (m, ft)

The specific weight of water, which is the The specific weight of water, which is the most commonly used fluid in u-tube most commonly used fluid in u-tube manometers, is manometers, is 9.8 kN/m39.8 kN/m3 or or 62.4 lb/ft362.4 lb/ft3..

Inclined U-Tube Inclined U-Tube ManometerManometer

• The pressure difference in a inclined The pressure difference in a inclined u-tube can be expressed asu-tube can be expressed as

pd = γ h sin(θ)         (2)pd = γ h sin(θ)         (2)

wherewhere

θ = angle of column relative the θ = angle of column relative the horizontal planehorizontal plane

Inclining the tube manometer will Inclining the tube manometer will increase the accuracy of the increase the accuracy of the measurement.measurement.

Example - Differential Example - Differential Pressure Measurement in Pressure Measurement in an Orificean Orifice

• A water manometer connects the upstream and A water manometer connects the upstream and downstream of an orifice located in an air flow. The downstream of an orifice located in an air flow. The difference height of the water column is difference height of the water column is 10 mm10 mm..

The pressure difference head can then be expressed The pressure difference head can then be expressed as:as:

pd = (9.8 kN/m3) (103 N/kN) (10 mm) (10-3 m/mm) pd = (9.8 kN/m3) (103 N/kN) (10 mm) (10-3 m/mm)         = = 9898 N/m2 (Pa) N/m2 (Pa)wherewhere9.8 (kN/m3) is the specific weight of water in SI-units.9.8 (kN/m3) is the specific weight of water in SI-units.

Example - Differential Pressure Example - Differential Pressure Measurement with an Inclined U- Measurement with an Inclined U-Tube manometerTube manometer

We use the same data as in the We use the same data as in the example above, except that the U-example above, except that the U-Tube is inclined to Tube is inclined to 45o45o..

The pressure difference head can then The pressure difference head can then be expressed as:be expressed as:

pd = (9.8 kN/m3) (103 N/kN) (10 mm) pd = (9.8 kN/m3) (103 N/kN) (10 mm) (10- 3 m/mm) sin(45)(10- 3 m/mm) sin(45)

        = = 69.369.3 N/m2 (Pa) N/m2 (Pa)