15.1. What volume does 0.4 kg of alcohol occupy? What is the weight of this volume?
[pic]; V = 5.06 x 10-4 m3
W = DV = ρgV = 790 kg/m3)(9.8 m/s2)(5.06 x 10-4 m3); W = 3.92 N
15-2. An unknown substance has a volume of 20 ft3 and weighs 3370 lb. What are the weight density and the mass density?
[pic]; D = 168 lb/ft3 [pic]; ρ = 5.27slugs/ft3
15-3. What volume of water has the same mass of 100 cm3 of lead? What is the weight density of lead?
[pic]First find mass of lead: m = ρV = (11.3 g/cm3)(100 cm3); m = 1130 g
Now water: [pic]; Vw = 1130 cm3 D = ρg
D = (11,300 kg/m3)(9.8 m/s2) = 110,740 N/m3; D = 1.11 x 105 N/m3
15-4. A 200-mL flask (1 L = 1 x 10-3 m3) is filled with an unknown liquid. Anelectronic balance indicates that the added liquid has a mass of 176 g. What is the specific gravity of the liquid? Can you guess the identity of the liquid?
V = 200 mL = 0.200 L = 2 x 10-4 m3; m = 0.176 kg
[pic]; ρ = 880 kg/m3, Benzene
15-5. Find the pressure in kilopascals due to a column of mercury 60 cm high. What is this pressure in lb/in.2 and in atmospheres?
P =ρgh = (13,600 kg/m3)(9.8 m/s2)(0.60 m); P = 80 kPa
[pic] P = 11.6 lb/in.2
[pic]; P = 0.790 atm
15-6. A pipe contains water under a gauge pressure of 400 kPa. If you patch a 4-mm-diameter hole in the pipe with a piece of tape, what force must the tape be able to withstand?
[pic] ; [pic]
F = PA = (400,000 Pa)(1.257 x 10-5 m2); P = 5.03 N
15-7. A submarine divesto a depth of 120 ft and levels off. The interior of the submarine is maintained at atmospheric pressure. What are the pressure and the total force applied to a hatch 2 ft wide and 3 ft long? The weight density of sea water is around 64 lb/ft.3
P = Dh = (64 lb/ft3)(120 ft); P = 7680 lb/ft2; P = 53.3 lb/in.2
F = PA = (7680 lb/ft2)(3 ft)(2 ft); F = 46,100 lb
15-8. If youconstructed a barometer using water as the liquid instead of mercury, what height of water would indicate a pressure of one atmosphere?
h = 10.3 m or 34 ft !
15-9. A 20-kg piston rests on a sample of gas in a cylinder 8 cm in diameter. What is the gauge pressure on the gas? What is the absolute pressure?
[pic] P = 39.0 kPa
Pabs = 1 atm + Pgauge = 101.3 kPa +39.0 kPa; Pabs = 140 kPa
*15-10. An open U-shaped tube such as the one in fig. 15-21 is 1 cm2 in cross-section. What volume of water must be poured into the right tube to cause the mercury in the left tube to rise 1 cm above its original position?
V = Ah = (1 cm2)(13.6 cm); V = 13.6 cm3 or 13.6 mL
15-11. The gauge pressure in an automobile tire is 28 lb/in.2. If thewheel supports 1000 lb, what area of the tire is in contact with the ground?
[pic]; A = 35.7 in.2
15-12. Two liquids that do not react chemically are placed in a bent tube like the one in Fig. 15-21. Show that the heights of the liquids above their surface of separation are inversely proportional to their densities: [pic]
The gauge pressure must be the same for each column:ρ1gh1 = ρ2gh2 So that:
15-13. Assume that the two liquids in the U-shaped tube in Fig. 15-21 are water and oil. Compute the density of the oil if the water stands 19 cm above the interface and the oil stand 24 cm above the interface. Refer to Prob. 15-12.
[pic]; ρoil = 792 kg/m3
15-14. A water-pressure gauge indicates a pressure of 50 lb/in.2 at the foot of a building. What isthe maximum height to which the water will rise in the building?
[pic]; h = 115 ft
The Hydraulic Press
15-15. The areas of the small and large pistons in a hydraulic press are 0.5 and 25 in.2, respectively. What is the ideal mechanical advantage of the press? What force must be exerted to lift a ton? Through what distance must the input force move, if the load is lifted a distance of...