Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

as shown in Fig. 1–51. The pressure at point Bis equal to the atmospheric

pressure, and the pressure at Ccan be taken to be zero since there is only

mercury vapor above point Cand the pressure is very low relative to Patm

and can be neglected to an excellent approximation. Writing a force balance

in the vertical direction gives

(1–26)

where ris the density of mercury,gis the local gravitational acceleration,

and his the height of the mercury column above the free surface. Note that

the length and the cross-sectional area of the tube have no effect on the

height of the fluid column of a barometer (Fig. 1–52).

A frequently used pressure unit is the standard atmosphere, which is

defined as the pressure produced by a column of mercury 760 mm in height

at 0°C (rHg13,595 kg/m^3 ) under standard gravitational acceleration (g

9.807 m/s^2 ). If water instead of mercury were used to measure the standard

atmospheric pressure, a water column of about 10.3 m would be needed.

Pressure is sometimes expressed (especially by weather forecasters) in

terms of the height of the mercury column. The standard atmospheric pres-

sure, for example, is 760 mmHg (29.92 inHg) at 0°C. The unit mmHg is

also called the torrin honor of Torricelli. Therefore, 1 atm 760 torr and 1

torr 133.3 Pa.

The standard atmospheric pressure Patmchanges from 101.325 kPa at sea

level to 89.88, 79.50, 54.05, 26.5, and 5.53 kPa at altitudes of 1000, 2000,

5000, 10,000, and 20,000 meters, respectively. The standard atmospheric

pressure in Denver (elevation 1610 m), for example, is 83.4 kPa.

Remember that the atmospheric pressure at a location is simply the

weight of the air above that location per unit surface area. Therefore, it

changes not only with elevation but also with weather conditions.

The decline of atmospheric pressure with elevation has far-reaching rami-

fications in daily life. For example, cooking takes longer at high altitudes

since water boils at a lower temperature at lower atmospheric pressures.

Nose bleeding is a common experience at high altitudes since the difference

between the blood pressure and the atmospheric pressure is larger in this

case, and the delicate walls of veins in the nose are often unable to with-

stand this extra stress.

For a given temperature, the density of air is lower at high altitudes, and

thus a given volume contains less air and less oxygen. So it is no surprise

that we tire more easily and experience breathing problems at high altitudes.

To compensate for this effect, people living at higher altitudes develop more

efficient lungs. Similarly, a 2.0-L car engine will act like a 1.7-L car engine

at 1500 m altitude (unless it is turbocharged) because of the 15 percent drop

in pressure and thus 15 percent drop in the density of air (Fig. 1–53). A fan

or compressor will displace 15 percent less air at that altitude for the same

volume displacement rate. Therefore, larger cooling fans may need to be

selected for operation at high altitudes to ensure the specified mass flow

rate. The lower pressure and thus lower density also affects lift and drag:

airplanes need a longer runway at high altitudes to develop the required lift,

and they climb to very high altitudes for cruising for reduced drag and thus

better fuel efficiency.

Patmrgh

30 | Thermodynamics

h

W=rgh A

A

h

B

Mercury

C

Patm

FIGURE 1–51

The basic barometer.

A 1 A 2 A 3

FIGURE 1–52

The length or the cross-sectional area
of the tube has no effect on the height
of the fluid column of a barometer,
provided that the tube diameter is
large enough to avoid surface tension
(capillary) effects.