or
.
"Pressure" is the ratio of a normal force to the area on which the force acts. Units are
thus or
.
Think of a column of fluid of height h and cross sectional area A. The fluid has a density rho. The pressure P at the base of the column is by definition the force exerted on the base divided by the area A; that force is the weight of the column plus any force acting on the top.
EXAMPLE: What is the hydrostatic pressure exerted by the water in a 6.00 ft diameter cylindrical tank which contains 90.0 gal?
If we look at the hydrostatic pressure formula, we see that we need the pressure at the top of the column, the density of the fluid, and the height of the column.
The density we look up: 62.4 lbm/ft3 for water
We aren't given the height of the column, but we do have dimensions on the tank. Since the volume is the product of the area and the height, we should be able to back out the desired number.
Assume: tank has constant cross-section
Air is a fluid -- so the air above the earth exerts a hydrostatic pressure on the surface. This is atmospheric pressure. If you look at the hydrostatic pressure equation, you can see that the pressure exerted will depend on the height of the column and the density of the air. At sea level the pressure is
For many calculations, it is useful to have a fixed reference value for atmospheric pressure. The sea-level value is used. It is called the "standard atmosphere". This value is also used as a unit of pressure measurement (atm). It may be used in homework problems, etc., if there is no other information given about atmospheric conditions.
In your chemistry classes, you've probably seen pressures measured in mm Hg (a.k.a. Torr). These aren't "natural" pressure units (force/area) -- so where did they come from? We just observed that a column of fluid produces a pressure, so that the height of the column is an indicator of the pressure produced. This principle is the basis of one of the traditional methods of measuring pressure: the manometer. When pressure is expressed in terms of a height of fluid, it is called fluid "head". Usually, water or mercury is used.
Converting between force/are and head units is simple. You use the fluid weight term from the hydrostatic pressure equation:
EXAMPLE: Take the result from above and express it in "head".
An old, simple way of measuring pressure is with a "manometer". A u-shaped tube is partially filled with liquid, usually water or mercury. Each end is connected to a pressure source, and the difference in liquid height corresponds to the difference in pressure.
At the bottom of the manometer, the force exerted by one leg balances against the force exerted by the other. The force balance equation can be written:
Often, a manometer is connected so that the same fluid is present at the tops of both legs. In this case, and if only a single manometer fluid is used, there are only two densities, and the terms can be lumped together. You can also group the two height terms and express them as a difference. This gives the "differential manometer equation":
The differential manometer equation is frequently used to help determine a flow rate. If a restriction (an orifice, valve, etc.) is placed in a line carrying a flowing fluid, it will produce a pressure drop. A manometer can then be used to measure the pressure drop. The pressure difference is proportional to the flow rate squared.
If you look at the manometer, you'll see that it doesn't really measure a pressure, but instead detects the difference in pressure between the taps. Almost all pressure measurement devices have the same limitation. Thus, most pressures are measured with reference to some known value.
Getting "zero" pressure can be complicated and expensive. For most measurements, it is more practical to measure with respect to atmospheric pressure. For example, to use a manometer, you may attach one end to the pressure source to be measured and leave the other open to the atmosphere. This is so common that pressures measured in this way are designated gage pressure. If absolute pressure is to be measured, it is necessary to evacuate one end of the manometer so that the fluid works against vacuum.
Thus, a "closed end" manometer measures absolute pressure, while an "open end" manometer measures gage pressure. A "barometer" measures atmospheric pressure.
Pressures less than atmospheric are "vacuums". Common practice is to state negative gage pressures as positive vacuum. Vacuums are frequently listed in head units.
The chart below may help keep track of things.
References:
R.M. Price
Original: 6/3/94
Modified: 9/1/94,6/21/96,7/13/98, 9/1/98; 5/25/2004
Copyright 1998, 2004 by R.M. Price -- All Rights Reserved