FLUID MECHANICS  THEORY



The concept of absolute and gage pressure
is discussed in this section. Several common pressure measurement
devices and techniques are also introduced.

Gage Pressure
Vacuum
Pressure




Absolute and Gage Pressure 

When pressure is measured relative to absolute zero pressure, it is called absolute pressure. On the other hand, pressure measuring devices often use gage pressure, which is measured relative to atmospheric pressure. Standard atmospheric pressure at sea level is 101.3 kPa or 14.7 psi. Gage pressure is referred to as vacuum or suction pressure when it is negative.
Gage Pressure: p_{gage}
= p_{absolute}  p_{atm}
Vacuum Pressure: p_{vacuum} = p_{atm}  p_{absolute}
For example, when the driver's manual for your car suggests that you
keep your tires at a pressure of 30 psi, it is refering to the gage pressure. This is equivalent to 44.7 psi absolute pressure.






Barometer 
Mercury Barometer 

Atmospheric pressure can be measured through
a mercury barometer. A simple barometer consists of an inverted glass
tube filled with mercury with its open end submerged in a mercury container.
According to the hydrostatic pressure distribution derived
in the last section, the atmospheric pressure is given by
p_{atm} = ρgh
+ p_{vapor}
The vapor pressure in the glass tube is negligibly small, hence the atmospheric
pressure is simply given by the height of the mercury column:
p_{atm} = ρgh
For example, a column height of 760 mm Hg corresponds to the standard
atmospheric pressure of 101.3 kPa (14.7 psi) at sea level. If water is substituted
for mercury, then a column height of 10.3 m H_{2}O is needed
for atmospheric pressure.



Piezometer

Piezometer


A piezometer is the simplest form of a pressure
measuring device. It has a vertical tube connected to the container in
which the
pressure is needed. The pressure head of the fluid column indicates the
pressure of the container:
p_{A} = ρgh
where p_{A} is the gage pressure at point A within the container.
The disadvantages of piezometers are:
(1) Cannot measure vacuum pressure since air would be sucked into
the container through the tube.
(2) The measured pressure should be reasonably low, otherwise a very
long vertical tube is needed.






Manometer 


Another pressure measuring device is the manometer.
It consists of a Utube with one end connected to the container with
an unknown pressure and the other end open to the
known atmospheric pressure. The fluid in the Utube manometer (gage
fluid) can be different from the fluid in the container.
The procedure for determining the pressure inside the container is:
(1) Start from one end, and work from one fluid level to another,
up to the open end of the manometer.
(2) Remember that pressure increases linearly with depth for a fluid at
rest. 



UTube Manometer


Consider the Utube manometer shown. The pressure at point A inside
the tank is calculated as:
p_{A} + ρ_{1}gh_{1}  ρ_{2}gh_{2} = 0
which gives:
p_{A} = ρ_{2}gh_{2}  ρ_{1}gh_{1}
Once again, gage pressure is used in the above equation (i.e., theatmospheric pressure at the open end is zero gage). If the fluid in the tank is a gas, then the pressure between point 1 and 2 is negligible, hence
p_{A} = ρ_{2}gh_{2} 



Differential UTube Manometer 

The Utube manometer also can be used to determine the pressure difference
between two systems. This type of manometer is called a differential
Utube manometer. Consider the differential manometer connected between tanks
A and B, as shown in the figure. The pressure will be determined by moving from point A to point B:
p_{A} + ρ_{1}gh_{1}  ρ_{2}gh_{2}  ρ_{3}gh_{3} = p_{B}
The pressure difference is given by
p_{A}  p_{B} = ρ_{2}gh_{2} + ρ_{3}gh_{3}  ρ_{1}gh_{1} 



InclinedTube Manometer 

Another type of manometer is the inclinedtube manometer which is used
to measure small pressure differences between two systems (say for gases).
The advantage of the inclined manometer is that the differential reading scales along the
tube can be made large compared to a vertical manometer for a given
pressure difference, hence improving the accuracy in reading the scale.
The pressure difference between point A and B is given by
p_{A} + ρ_{1}gh_{1}  ρ_{2}gL_{2}sinθ  ρ_{3}gh_{3} = p_{B}
For cases where the columns h_{1} and h_{3 }are gas, the weights can be neglected, simplifying the equation
p_{A}  p_{B} = ρ_{2}gL_{2} sinθ 


