3-IC What is the difference between gage pressere and absolute pressure?
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Question
Transcribed Image Text:scalar form as
Pressure is a fundamental property, and it is hard to imag-
ine a significant fluid flow prohlem that does net involve
pressure. Therefore, you will see this property in all chapters
in the rest of this book. The consideration of hydrostatic
forces acting on plane or curved surfaces, however, is mostly
limited to this chapter.
ap
- plg + a)
--pd
-pa.
and
dy
where a, a, and a, are accelerations in the x, y, and z
directions, respoctively. During linearly accelerting motion
in the xz-plane, the pressure distribution is expressed as
P= P,- par- pA +a,iz
REFERENCES AND SUGGESTED READING
1. F. P. Beer, E. R, Johnston, Jr., E. R. Eisenberg, and G. H.
Staab. Vector Mechanies for Engineers, Statics, 7th ed.
New York: McGraw-Hill, 2004.
2. C. T. Crowe, J. A. Roberson, and D. F. Elger. Engineering
Fluid Mechanics, 7th ed. New York: Wiley, 2001.
3. R. W. Fox and A. T. McDonald. Inevduction to Fluid
Mechanics, Sth ed. New York: Wikey, 1999,
4. D. C. Giancoli. Physics, 3rd ed. Upper Saddle River, NJ:
Prentice Hall, 1991.
5. M. C. Potter and D. C. Wiggert. Mechanies of Fluids, 2nd
ed. Upper Saddle River, NJ: Prentice Hall, 1997.
6. F. M. White. FTuid Mechanics, 5th ed. New York:
McGraw-Hill, 2003.
PROBLEMS
Pressure, Manometer, and Barometer
3-IC What is the difference between gage pressure and
absolute pressure?
3-20 Explain why some people experience nose bleeding
and some others experience shortness of breath at high ele-
* Problems designated by a "C" are concept questions, and
students are encouraged to answer them all. Problems designated
by an "E" are in English units, and the Si users can ignore them.
Problems with the icon are solved usirg EES, and complete
so utions together with parametric studies are included on the
erclosed DVD. Problems with the a icon are comorehensive in
rature and are intended to be solved with a computer, preferably
using the EES softaare that accompanies this text.
vations.
3-3C Someone claims that the abselute pressure in a liquid
of constant density doubles when the depth is doubled. Do
you agree? Explain.
104
104
FLUID MECHANICS
3-4C A tiny steel cube is suspended in water by a string. If
the lengths of the sides of the cube are very smalI, how
would you compare the magnitudes of the pressures on the
ton, hottom, und side surfaces of the cube?
3-5C Express Pascal's law, and give a real-world example
of it.
3-12 The absolute pressure in water at a depth of 5 m is
read to be 145 kPa. Determine (a) the local atmospheric pres-
sure, and (b) the absolute pressure at a depth ef 5 m in a lig
mid whose specific gravity is 0.85 at the same location
3-13E Show that I kgfiem - 14.223 psi.
3-14E A 200-lb man has a total foot imprint area of 72 in.
3-6C Consider two identical fans, one at sea level and the
other on top of a high meuntain, running at identical speeds.
How would you compare (a) the volume tlow rates and (b)
the mass flow rates of these twa fans?
Determine the pressure this man exerts on the ground if (o)
he stands on both feet and (b) he stands on one fot.
3-15 Consider a 70-kg woman who has a total foot impeint
area of 400 em'. She wishes te walk on the snow, but the
snow cannot withstand pressures greater than 0.5 kPa. Deter-
mine the minimum size of the snowshoes needed (imprint
area per shoe) to enable ber to walk on the snow without
sinking.
3-7 A vacuum gage connected to a chamber reads 24 kPa
at a location where the atmospheric pressure is 92 kPa.
Determine the absoluse pressure in the chamber.
3-8E A manometer is used to measure the air pressure in a
tank. The fluid used has a specific gravity of 1.25, and the
differential height between the two arms of the manometer is
28 in. If the local atmospheric pressure is 12.7 psia, deter-
3-16 A vacuam gage connected to a tank reads 30 kPa at a
location where the barometrie reading is 755 mmHg. Determine
the absolune pressure in the tank. Take P = 13,590 kg/m
Answer: 70.6 Pa
mine the absolute pressure in the tank for the cases of the
manemeter arm with the (a) higher and (5) kwer fluicd level
being attached to the tank.
3-1TE A pressure gage connected to a tank reads 50 psi at a
location where the barometric reading is 29.1 inHg. Detemine
the absolute pressure in the tank. Take p- 848.4 Iben/t.
Answer. 64.29 psia
3-9 The water in a tank is pressurized by air, and the pres-
sure is measured by a multifluid manometer as shown in Fig.
P3-9. Determine the gage pressure af air in the tank if i,
= 0.2 m, hg = 0,3 m, and h, = 0.46 m. Take the densities of
water, oil, and mercury to be 1000 kg/m', 850 kg/m', and
13,600 kg/m', respectively.
3-18 A pressure gage connected to a tank reads 500 kPa at
a location where the atmospheric pressure is 94 kPa. Deter-
mine the absolute pressare in the tank.
-19 The barometer of a meuntain hiker rends 930 mbars
at the beginning of a hiking trip and 780 mbars at the end.
Neglecting the effect of altitude on local gravitational accel-
eration, determine the vertical distance climbed. Assume an
average air density of 1.20 kg/m'. Answer 1274 m
- Oil
AIR
3-20 The basic barometer can be used to measure the
height of a building. If the barcmetric readings at the top and
at the hottom of a building are 730 and 755 mmHg, respec-
tively. determine the height of the building. Assume an aver
age air density of 1.18 kg/m'.
WATER
Mercury
FIGURE P3-9
3-10 Determine the atmospheric pressure at a location
where the barometric reading is 750 mml lg. Take the density
mercury to be 13,600 kg/m.
P 755 mmHg
FIGURE P3-20
3-11 The gage pressure in a liquid at a depth of 3 m is read
to be 28 kPa. Determine the gage pressure in the same liquid
at a depth of 12 m.
3-21 ES Solve Prob. 3-20 using EES (er other) software.
Print out the entire solution, including the
105
CHAPTER 3
namerical results with proper units, and take the density of
mercury to be 13,600 kg/m'.
the pressure gage is 80 kPa, determine the distance between
the two fluid levels of the manometer if the fluid is (a) mer-
cury (p = 13,600 kg/m') or th) water (p= 1000 kg/m').
3-27 O Recansider Prob. 3-26. Using EES (or other)
software, investigate the effect of the manometer
fluid density in the range of 800 to 13,000 kg/m an the dif-
ferential fluid height of the manometer. Plot the differential
fluid height against the density, and discuss the results.
3-28 A manometer containing oil e = 850 kg/m') is
3-22 Delermine the pressure exerted on a diver at 30 m
below the free surface of the sea. Assume a barometric pres-
sure of 101 kPa and a specific gravity of 1.03 for seawater.
Answer 404.0 kPs
3-23E Determine the pressure exerted on the surface of a
submarine cruising 300 ft helow the free surface of the sea.
Assume that the barometric pressure is 14.7 psia and the
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