# 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.

In the figure bellow illustrates the water levels in an u-tube where the left tube is connected to a point with higher pressure than the right tube - example: the left tube may be connected to a pressurized air duct when the right tube is open to the ambient air.

### 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 figure bellow indicates a u-tube where the left tube is connected to a higher pressure than the right tube. Note that the left and the right tube must in the same declined plane for the angle to the horizontal plane to be correct.

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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