Wednesday, May 23, 2018

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Fluid Mechanics - Systems of Pressure Measurement

Pressure measurement is often a relative thing. What we mean when we say there is 35 PSI of air pressure in an inflated car tire is that the pressure inside the tire is 35 pounds per square inch greater than the surrounding, ambient air pressure. It is a fact that we live and breathe in a pressurized environment. Just as a vertical column of liquid generates a hydrostatic pressure, so does a vertical column of gas. If the column of gas is very tall, the pressure generated by it will be substantial enough to measure. Such is the case with Earth’s atmosphere, the pressure at sea level caused by the weight of the atmosphere is approximately 14.7 PSI.

You and I do not perceive this constant air pressure around us because the pressure inside our bodies is equal to the pressure outside our bodies. Thus our skin, which serves as a differential pressure-sensing diaphragm, detects no difference of pressure between the inside and outside of our bodies. The only time the Earth’s air pressure becomes perceptible to us is if we rapidly ascend or descend in a vehicle, where the pressure inside our bodies does not have time to equalize with the pressure outside, and we feel the force of that differential pressure on our eardrums.

If we wish to speak of a fluid pressure in terms of how it compares to a perfect vacuum (absolute zero pressure), we specify it in terms of absolute units. For example, when I said earlier that the atmospheric pressure at sea level was 14.7 PSI, what I really meant is it is 14.7 PSIA (pounds per square inch absolute), meaning 14.7 pounds per square inch greater than a perfect vacuum. When I said earlier that the air pressure inside an inflated car tire was 35 PSI, what I really meant is it was 35 PSIG (pounds per square inch gauge), meaning 35 pounds per square inch greater than ambient air pressure. When units of pressure measurement are specified without a “G” or “A” suffix, it is usually (but not always!) assumed that gauge pressure (relative to ambient pressure) is meant. This offset of 14.7 PSI between absolute and gauge pressures can be confusing if we must convert between different pressure units. Suppose we wished to express the tire pressure of 35 PSIG in units of inches of water column (”W.C.). If we stay in the gauge-pressure scale, all we have to do is multiply by 27.68:


Note how the fractions have been arranged to facilitate cancellation of units. The “PSI” unit in the numerator of the first fraction cancels with the “PSI” unit in the denominator of the second fraction, leaving inches of water column (”W.C.) as the only unit standing. Multiplying the first fraction (35 PSI over 1) by the second fraction (27.68 ”W.C. over 1 PSI) is “legal” to do since the second fraction has a physical value of unity (1): being that 27.68 inches of water column is the same physical pressure as 1 PSI, the second fraction is really the number “1” in disguise. As we know, multiplying any quantity by unity does not change its value, so the result of 968.8 ”W.C. we get has the exact same physical meaning as the original figure of 35 PSI. This technique of unit conversion is sometimes known as unity fractions, and it is discussed in more general terms in another section of this book (refer to Unit Conversions and Physical Constants).

If, however, we wished to express the car’s tire pressure in terms of inches of water column absolute (in reference to a perfect vacuum), we would have to include the 14.7 PSI offset in our calculation, and do the conversion in two steps:



The proportion between inches of water column and pounds per square inch is still the same (27.68) in the absolute scale as it is in the gauge scale. The only difference is that we included the 14.7 PSI offset in the very beginning to express the tire’s pressure on the absolute scale rather than on the gauge scale. From then on, all conversions were in absolute units.

There are some pressure units that are always in absolute terms. One is the unit of atmospheres, 1 atmosphere being 14.7 PSIA. There is no such thing as “atmospheres gauge” pressure. For example, if we were given a pressure as being 4.5 atmospheres and we wanted to convert that into pounds per square inch gauge (PSIG), the conversion would be a two-step process:


Another unit of pressure measurement that is always absolute is the torr, equal to 1 millimeter of mercury column absolute (mmHgA). 0 torr is absolute zero, equal to 0 atmospheres, 0 PSIA, or -14.7 PSIG. Atmospheric pressure at sea level is 760 torr, equal to 1 atmosphere, 14.7 PSIA, or 0 PSIG.

If we wished to convert the car tire’s pressure of 35 PSIG into torr, we would once again have to offset the initial value to get everything into absolute terms.


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