Thermodynamics Solutions Manual

1–50E

1–50E A pressure gage connected to a tank reads 50 psi at
a location where the barometric reading is 29.1 mm Hg.
Determine the absolute pressure in the tank. Take rHg
848.4 lbm/ft
3
. Answer: 64.3 psia

1–49

1–49 A vacuum gage connected to a tank reads 15 kPa at a
location where the barometric reading is 750 mm Hg. Determine the absolute pressure in the tank. Take rHg 13,590
kg/m
3
. Answer: 85.0 kPa
ANS

1-49The vacuumpressure reading of a tank isgiven. The absolutepressure inthe tank istobe determined. Properties The densityof mercuryisgiven tobe ρ= 13,590 kg/m 3 . Analysis The atmospheric (or barometric) pressure can be expressed as 15kPa Pabs kPa 0 . 100 N/m 1000 kPa 1 m/s kg 1 N 1 m) )(0.750 m/s )(9.807 kg/m (13,590 2 2 2 3 atm =             ⋅ = = h g P ρ Patm=750 mmHg Thenthe absolute pressure inthe tankbecomes kPa 85.0 = − = − = 15 100.0 vac atm abs P P P

1–48

1–48 Consider a 70-kg woman who has a total foot imprint
area of 400 cm2. She wishes to walk on the snow, but the
snow cannot withstand pressures greater than 0.5 kPa. Determine the minimum size of the snowshoes needed (imprint
area per shoe) to enable her to walk on the snow without
sinking.
ANS

1-48 The mass of a woman isgiven. The minimumimprintarea per shoe needed toenableher towalkon the snow withoutsinking istobe determined. Assumptions1 The weight of the person isdistributed uniformlyon the imprintarea of the shoes. 2 One footcarries the entire weightof a person during walking, and the shoe issized for walking conditions (rather than standing). 3 The weightofthe shoes is negligible. Analysis The mass of the woman isgiven tobe 70 kg. For a pressure of 0.5 kPa on the snow, the imprintarea of one shoe mustbe 2 m 1.37 =             ⋅ = = = 2 2 2 N/m 1000 kPa 1 m/s kg 1 N 1 kPa 0.5 ) m/s kg)(9.81 (70 P mg P W A Discussion Thisisa verylarge area for a shoe, and such shoes would be impracticaltouse. Therefore, somesinking of the snow should be allowed tohave shoes of reasonable size.

1–47E

1–47E A 200-pound man has a total foot imprint area of 72
in2. Determine the pressure this man exerts on the ground if
(a) he stands on both feet and (b) he stands on one foot.
ANS

1–46E

1–46E Show that 1 kgf/cm2 14.223 psi.
ANS

1–45

1–45 The absolute pressure in water at a depth of 5 m is
read to be 145 kPa. Determine (a) the local atmospheric pressure, and (b) the absolute pressure at a depth of 5 m in a liquid whose specific gravity is 0.85 at the same location.
ANS
1-45The absolute pressure inwater ata specified depth isgiven. The localatmospheric pressure and the
absolutepressure atthe samedepth ina differentliquid are tobe determined.
Assumptions The liquid and water are incompressible.
Properties The specific gravityof the fluid isgiven tobe SG = 0.85. Wetake the densityof water tobe
1000 kg/m
3
. Thendensity ofthe liquidis obtainedbymultiplying its specific gravity by the density of
water,

1–44

1–44 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 9 m.
ANS
1-44The gage pressure ina liquid ata certaindepth isgiven. The gage pressure in the same liquid at a
differentdepth istobe determined.
Assumptions The variation of the densityof the liquid withdepth isnegligible.
Analysis The gage pressure attwo differentdepths of a liquid can be expressed as