# U-Tube Manometer

## The inclined and vertical u-tube manometers are inexpensive and common in the differential pressure measurement with flow meters like pitot tubes, orifices and nozzles

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Pressure measuring devices using liquid columns in vertical or inclined tubes are called manometers. One of the most common is the water filled u-tube manometer used to measure pressure difference in pitot or orifices located in the airflow in air handling or ventilation system.

### Vertical U-Tube Manometer

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

p_{d}= γ h

=ρ g h(1)

where

p_{d}= pressure

γ= specific weight of the fluid in the tube (kN/m^{3}, lb/ft^{3})

ρ = density (kg/m^{3}, lb/ft^{3})

g = acceleration of gravity (9.81 m/s^{2},32.174 ft/s^{2})

h= liquid height (m, ft)

The specific weight of water, which is the most commonly used fluid in u-tube manometers, is *9.81 kN/m ^{3}* or

*62.4 lb/ft*.

^{3}#### Example - Differential Pressure Measurement in an Orifice

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

The pressure difference head can then be expressed as:

p_{d}=(9.8 kN/m^{3}) (10^{3}N/kN) (10 mm) (10^{-3}m/mm)

= 98 N/m^{2}(Pa)

where

9.8 (kN/m^{3}) is the specific weight of water in SI-units.

### Inclined U-Tube Manometer

A common problem when measuring pressure difference in a low velocity system - like an air ventilation system - is a low column height and accuracy. Accuracy can be improved by inclining the u-tube manometer.

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

p_{d}= γ h sin(θ)(2)

where

h = length, difference in position of the liquid column along the tube (mm, ft)

θ= angle of column relative the horizontal plane

Inclining the tube manometer increases the accuracy of the measurement.

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

We use the same data as in the example above, except that the U-Tube is inclined *45 ^{o}*.

The pressure difference head can then be expressed as:

p_{d}=(9.8 kN/m^{3}) (10^{3}N/kN) (10 mm) (10^{-3}m/mm) sin(45^{o})

= 69.3 N/m^{2}(Pa)

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