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Unformatted text preview: Chapter 13 CHAPTER 13 – Fluids 1. When we use the density of granite, we have m = ρ V = (2.7 × 10 3 kg/m 3 )(1 × 10 8 m 3 ) = 3 × 10 11 kg . 2. When we use the density of air, we have m = ρ V = ρ LWH = (1.29 kg/m 3 )(4.8 m)(3.8 m)(2.8 m) = 66 kg . 3. When we use the density of gold, we have m = ρ V = ρ LWH = (19.3 × 10 3 kg/m 3 )(0.60 m)(0.25 m)(0.15 m) = 4.3 × 10 2 kg (˜ 950 lb!). 4. If we assume a mass of 65 kg with the density of water, we have m = ρ V ; 65 kg = (1.0 × 10 3 kg/m 3 ) V , which gives V = 6.5 × 10 –2 m 3 (˜ 65 L). 5. From the masses we have m water = 98.44 g – 35.00 g = 63.44 g; m fluid = 88.78 g – 35.00 g = 53.78 g. Because the water and the fluid occupy the same volume, we have SG fluid = ρ fluid / ρ water = m fluid / m water = (53.78 g)/(63.44 g) = 0.8477 . 6. The definition of the specific gravity of the mixture is SG mixture = ρ mixture / ρ water . The density of the mixture is ρ mixture = m mixture / V = (SG antifreeze ρ water V antifreeze + SG water ρ water V water )/ V , so we get SG mixture = (SG antifreeze V antifreeze + SG water V water )/ V = [(0.80)(5.0 L) + (1.0)(4.0 L)]/(9.0 L) = 0.89 . 7. ( a ) The normal force on the four legs must equal the weight. The pressure of the reaction to the normal force, which is exerted on the floor, is P = F N / A = mg / A = (60 kg)(9.80 m/s 2 )/4(0.05 × 10 –4 m 2 ) = 3 × 10 7 N/m 2 . ( b ) For the elephant standing on one foot, we have P = F N / A = mg / A = (1500 kg)(9.80 m/s 2 )/(800 × 10 –4 m 2 ) = 2 × 10 5 N/m 2 . Note that this is a factor of ˜ 100 × less than that of the loudspeaker! 8. ( a ) The force of the air on the table top is F = PA = (1.013 × 10 5 N/m 2 )(1.6 m)(2.9 m) = 4.7 × 10 5 N (down) . ( b ) Because the pressure is the same on the underside of the table, the upward force has the same magnitude: 4.7 × 10 5 N . This is why the table does not move! 9. The pressure difference on the lungs is the pressure change from the depth of water: ? P = ρ g ? h ; (80 mmHg)(133 N/m 2 ∙ mmHg) = (1.00 × 10 3 kg/m 3 )(9.80 m/s 2 )? h , which gives ? h = 1.1 m ....
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 Spring '08
 ROSS
 Fluid Dynamics, Fnet, Patm, Bernoulli's principle, kg /m

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