For a COMPRESSIBLE FLUID:

The density of a gas may change significantly with changes in

pressure and temperature, however since the density of gases

is small, the pressure gradient in the vertical direction is

correspondingly small.

But for situations in which the variations in heights are large,

attention must be given to changes in specific weight, .

If the ideal gas assumption is made,

For a COMPRESSIBLE FLUID:

By separating variables:

If temperature is constant (i.e. T=T0):

MEASUREMENT OF FLUID PRESSURE:

A standard technique for measuring pressure involves the use of liquid columns in vertical or inclined tubes, which are called manometers.

PIEZOMETER TUBE:

The simplest type of manometer consists of a vertical tube, open at the top, and attached to the contained in which the pressure is measured.

The equation p=h+p0 gives the absolute pressure.

The major disadvantages are:It is only usable for liquidsSuction pressures can not be measuredPressure to be measured must be relatively small, so that the required height of the column is reasonable.

h

p

p0

U TUBE MANOMETER:

A widely used manometer type consists of a tube formed into a U-shape

The fluid in the manometer is called gage fluid.

The pressure is evaluated in a summation process in which if one travels downward in the fluid, the pressure increases, otherwise it decreases by h

The major advantage is that the gage fluid can be different from the fluid in the container in which the pressure is measured. Depending on the pressure values to be measured a heavy or a light gage fluid may be used. It should be noted that the pressures at equal elevations in a continuous mass of fluid at rest must be the same

6

The basic manometer.

P1gas=P2=Patm+fluidgh

The Manometer

f

Patm

The tube is open to atmospheric air

the pressures at equal elevations in a continuous mass of fluid at rest must be the same so P1gas=P2

The Manometer

In stacked-up fluid layers, the pressure change across a fluid layer of density and height h is gh.

It is commonly used to measure small and moderate pressure differences. A manometer contains one or more fluids such as mercury, water, alcohol, or oil.

Measuring the pressure drop across a flow

section or a flow device by a differential

manometer.

The Manometer

Differential manometers are employed to measure the difference in pressure between two containers or two points in a given system.

Example

Inclined manometer