Lecture no. 8
EXAMPLE 1.21 Pressure Conversion
Convert 35 psia to inches of mercury.
Solution
Use the ratio of 14.7 psia to 29.92 in. Hg, an identity, to carry out the conversion.
Basis: 35 psia
EXAMPLE 1.22 Pressnre Conversion
The density of the atmosphere decreases with increasing altitude. When the pressure
is 340 mm Hg, how many inches of water is it? How many kilopascal?
Solution
Basis: 340 mm Hg
EXAMPLE 1.23 Pressnre Conversion
The pressure gauge on a tank of CO2 used to fill soda-water bottles reads 51.0 psi. At
the sametime the barometer reads 28.0 in. Hg. What is the absolute pressure in the
tank in psia? See Fig. E1. 23.
Solution
The pressure gauge is reading psig, not psia. From Eq. (1.25) the absolute pressure is
the sumof the gauge pressure and the atmospheric (barometric) pressure expressed in
the same units. Wewill change the atmospheric pressure to psia.
Basis: Barometric pressure = 28.0 in. Hg
(Note: Atmospheric pressure does not equal 1 standard atm.) The absolute pressure in
the tank is
51.0 + 13.76 = 64.8 psia
In some instances the fluids in the legs of the manometer are not the same. Examine
Fig. l.l3. When the columns of fluids are at equilibrium (it may take some timel) the
relation between PI, p, and the heights of the various columns of fluid is
Can you show for the case in which PI = p, = p that the manometer expression
reduces to
Finally, suppose that fluids I and 3 are gases. Can you ignore the gas density p relative
to the manometer fluid density? For what types of fluids?
EXAMPLE 1.24 Pressure Conversion
Air is flowing through a duct under a draft of 4.0 em HzO. The barometerindicates
that the atmospheric pressure is 730 mm Hg. What is the absolute pressure of the gas
in inches of mercury? See Fig. E1.24.
Solution
Wecan ignore the gas density abovethe manometer fluid. In the calculations we have
to employ consistent units, andit appears in this case thatthe most convenient units are
those of inches of mercury.
Basis: 730 mm Hg
Basis: 4.0 em H,O draft (under atmospheric)
Whatis another way to makethe conversion?
Since the reading is 4.0 em H,O draft (under atmospheric), the absolute
reading in uniform units is
28.7 - 0.12 = 28.6 in. Hg absolute
EXAMPLE 1.25 Vacuum Pressure Reading
Small animals such as mice can live at reduced air pressures down to 20 kPa
(although not comfortably). In a test a mercury manometer attached to a tank as
shown in Fig. E1.25 reads 64.5 cm Hg and the barometer reads 100 kPa. Will the
mice survive?
Basis: 64.5 em Hg below atmospheric
We ignore any temperature corrections to convert the mercury density and also ignore
the gas density above the manometer fluid. Then, since the vacuum reading on the
tank is 64.5 cm Hg below atmospheric, the absolute pressure in the tank is
The mice probably will uot survive.
EXAMPLE 1.26 Calculation of Pressure Difference
In measuring the flow of fluids in a pipeline. a differential manometer, as shown in
Fig. E1.26, can be used to determine the pressure difference across an orifice plate.
The flow rate can be calibrated with the observed pressure drop. Calculate the
pressure drop P 1 – P 2 in pascal.
Solution
In this problem we cannot ignore the water density above the manometer fluid. Apply
Eq.(1.26b), as the densities of the fluids above the manometer fluid are the same.
P 1 – P 2 = (p f - p)gd