PROCESS VARIABLES: PRESSURE

Pressure is the ratio of a normal (perpendicular) force to the area on which the force acts.

Fluid Pressure

Suppose a fluid is flowing through a horizontal pipe and a leak develops. To stop the leak a force must be applied over the area of the hole that causes the leak. This pressure is called the fluid pressure (the force that must be applied divided by the area of the hole).

Hydrostatic Pressure

A column of fluid of density has height h and cross sectional area A.

pressure P at base of the column = the force exerted on the base divided by the area A = the weight of the column (W) plus any force acting on the top (Fo).

P=Fbase

A= 1

A( Fo+W )= 1

A (Fo+mggc )

¿Fo

A+ ρh g

gc

=Po+ρhggc

=Po+ ρgh

formula for pressure due to a column of fluid, or hydrostatic pressure.

Atmospheric Pressure

Air is a fluid -- the air above the earth exerts a hydrostatic pressure on the surface - atmospheric pressure. Pressure exerted will depend on the height of the column and the density of the air.

At sea level the pressure is 1 atm = 14.696 psi = 101.325 kPaDecreases as altitude increases - reduced pressure is why breathing is more difficult sea-level value used as a fixed reference value - called the "standard atmosphere" - also used as a unit of pressure measurement (atm).

EXAMPLE: What is the hydrostatic pressure exerted at the base by the water in a 6.00 ft diameter cylindrical tank which contains 90.0 gal?

If atmospheric pressure (pressure at the surface) is 14.7 psi, then pressure at the base = psiHead

pressures also measured in mm Hg (Torr). These are not "natural" pressure units (force/area)

A column of fluid produces a pressure - so 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.

Head units are mostly used for very low pressures and expressed as "mm Hg" or "in H2O".

For converting between force/area and head units use the fluid weight term from the hydrostatic pressure equation:

P( force

area )=ρ fluid g P( head )

EXAMPLE: For the example earlier, express the hydrostatic pressure as head of water and mercury.

Fluid Pressure Measurement

Pressure Sensing Devices

Some Pressure sensing devices are- Bourdon gauge- Diaphragm capsule- Capacitance sensor- Column of fluid- Manometer- Barometer Bourdon gauge

Manometers

A manometer is a U-shaped tube 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:

P1+ρ1 gh1=P2+ ρ2 g h2+ρl gh

Often manometer connected so that the same fluid is present at the tops of both legs (ρ1= ρ2=ρ) and only a single manometer fluid (ρl) is usedThis gives the "differential manometer equation":

P1−P2= ( ρ1−ρ ) gh

frequently used to determine flow rate. A restriction (e.g. orifice) is placed in a line carrying a flowing fluid - produces a pressure drop. Manometer used to measure the pressure drop. The pressure difference is proportional to the flow rate squared.

Absolute vs. Gage Pressure

Most pressures are measured with reference to some known value. Getting "zero" pressure complicated and expensive - more practical to measure w.r.t. atmospheric pressure. e.g. one end of a manometer is attached to the pressure source to be measured the other open to atmosphere.

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.

Two mercury manometers, one open-end and the other sealed-end, are attached to an air duct. The reading on the open-end manometer is 25 mm and that on the sealed-end manometer is 800 mm. Determine the absolute pressure in the duct, the gauge pressure in the duct, and the atmospheric pressure, all in mm Hg.

A fluid of unknown density is used in two manometers—one sealed-end, the other across an orifice in a water pipeline. The readings shown here are obtained on a day when barometric pressure is756 mm Hg.

What is the pressure drop (mm Hg) from point (a) to point (b)?