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Manometers

In this Demonstration, the pressure on a fluid is measured using a piezometer, a U-tube manometer and an inclined-tube manometer. Use the buttons to select the type of manometer and the manometer fluid (water, oil or mercury). You can change the pressure on the manometer fluid and the angle of the inclined manometer with the sliders.

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A piezometer tube consists of a vertical tube that is open to atmospheric pressure at one end. A sphygmomanometer is a type of piezometer that is used to measure blood pressure. A force balance determines the height of the manometer fluid:
,
where is the hydrostatic pressure of the manometer fluid, is specific weight, is specific gravity, is the density of water, is acceleration due to gravity, and is fluid height.
In a simple U-tube manometer, fluid can be a gas or a liquid. A force balance is used to calculate the fluid height:
.
If fluid is air, the specific weight is negligible, so the force balance simplifies to:
.
The advantage of using an inclined tube manometer is that slight changes in the pressure of the manometer fluid give significant readings along the incline. For an inclined manometer open to atmospheric pressure at one end:
,
the vertical height of the fluid in terms of the length and angle is given by:
,
and the change in pressures is:
.
If the inclined manometer is closed at both ends:
.
View the screencast video [2] for an example problem using this type of inclined manometer.
The screencast video [3] shows another worked example problem.
References
[1] B. R. Munson, T. H. Okiishi and W. W. Huebsch, Fundamentals of Fluid Mechanics, 6th ed., Hoboken, NJ: John Wiley & Sons, 2009.
[2] Cal Poly Pomona. Force Balance on Inclined Manometer [Video]. (Mar 28, 2017) www.youtube.com/watch?v=wHGUJTSMjOo&t=468s.
[3] University of Colorado Boulder. Manometer Example [Video]. (Mar 28, 2017) www.youtube.com/watch?v=Q1opScBlMkA.
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