Respuestasca 15 Fisica Elemental
Physics, 6th Edition
Chapter 15. FLUIDS
Density
15.1. What volume does 0.4 kg of alcohol occupy? What is the weight of this volume?
ρ=
m ; V
V=
m 0.4 kg = ; ρ 790 kg/m 2
V = 5.06 x 10-4 m3 W = 3.92 N
W = DV = ρgV = 790 kg/m3)(9.8 m/s2)(5.06 x 10-4 m3);
15-2. An unknown substance has a volume of 20 ft3 and weighs 3370 lb. What are the weight densityand the mass density? D= W 3370 lb = ; D = 168 lb/ft3 V 20 ft 3
ρ=
D 168 lb/ft 3 = ; g 9.8 m/s 2
ρ = 5.27 slugs/ft3
15-3. What volume of water has the same mass of 100 cm3 of lead? What is the weight density of lead? First find mass of lead: m = ρV = (11.3 g/cm3)(100 cm3); m = 1130 g Now water: Vw = m 1130 g = = 1130 cm3 ; Vw = 1130 cm3 ρ w 1 g/cm3 D = ρg
D = (11,300 kg/m3)(9.8m/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. An electronic 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
ρ=
m 0.176 kg = ; V 2 x 10−4 m3
ρ = 880 kg/m3, Benzene
203Chapter 15. Fluids
Physics, 6th Edition
Fluid Pressure
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); 0.145 lb/in.2 P = 80 kPa ; 1 kPa P= 80 kPa ; 101.3 kPa/atm P = 80 kPa
P = 11.6 lb/in.2
P = 0.790 atm
15-6. A pipe contains water under agauge 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? A=
π D 2 π (0.004 m) 2 = = 1.257 x 10-5 m 2 ; 4 4
P=
F ; A
F = PA = (400,000 Pa)(1.257 x 10-5 m2);
P = 5.03 N
15-7. A submarine dives to 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 you constructed a barometer using water as the liquid instead of mercury, what height of water would indicate a pressure of oneatmosphere? P = ρ gh; h= P 101,300 Pa = ; ρ g (1000 kg/m3 )(9.8 m/s 2 ) or 34 ft !
h = 10.3 m
204
Chapter 15. Fluids
Physics, 6th Edition
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?
π D 2 π (0.08 m) 2 A= = = 5.027 x 10-3 m 2 ; 4 4
P= (20 kg)(9.8 m/s 2 ) = 3.90 x 104 kPa; -3 25.027 x 10 m
P=
F mg = A A
P = 39.0 kPa Pabs = 140 kPa
Pabs = 1 atm + Pgauge = 101.3 kPa + 39.0 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?
ρ m ghm = ρ 2 gh2 ;
h2 =
ρ m hm (13.6 g/cm3 )(1 cm) == 13.6 cm ρ2 1 g/cm3
V = 13.6 cm3 or 13.6 mL
V = Ah = (1 cm2)(13.6 cm);
15-11. The gauge pressure in an automobile tire is 28 lb/in.2. If the wheel supports 1000 lb, what area of the tire is in contact with the ground? A= F 1000 lb = ; P 28 lb/in.2 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. 1521. Show that the heights ofthe liquids above their surface of separation are inversely
proportional to their densities:
h1 ρ 2 = h2 ρ1
The gauge pressure must be the same for each column: ρ1gh1 = ρ2gh2 So that:
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Chapter 15. Fluids h1 ρ 2 = h2 ρ1
Physics, 6th Edition
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...
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