Explanation Draw the free body diagram for the hot air balloon. Figure-(1) Write the expression for the buoyancy force. F B = ρ g V (I) Here, the density of the air is ρ , the acceleration due to gravity is g and the volume of the balloon is V . Write the expression for the density of the balloon. ρ b = p R T (II) Here, the gas constant is R , the atmospheric pressure is p and the temperature of the balloon is T . Write the expression for the specific weight of the balloon. γ b = ρ b g (III) Write the expression for the total weight. W = W a + γ b V (IV) Here, the weight of the passenger, fabrics and basket is W a . Write the expression for the radius ( R ) of the sphere using volume expression. R 3 = 3 4 π V (V) Write the expression for the drag force. D = 1 2 ρ U 2 C D π R 2 (VI) Here, the velocity of the balloon is U and the drag coefficient is C D . Write the expression for the buoyancy force using the condition of equilibrium. F B = W + D (VII) Write the expression for the Reynolds number. Re = U ( 2 R ) ν (VIII) Here, the kinematic viscosity of air is ν . Conclusion: Refer to table B.3 “Physical properties of air at standard atmospheric pressure” to obtain the density of air as 2.286 × 10 − 3 slug / ft 3 and kinematic viscosity of the air as 1.69 × 10 − 4 ft 2 / s at the temperature of 80 ° F . Substitute 2.286 × 10 − 3 slug / ft 3 for ρ , 32.2 ft / s 2 for g and 70000 ft 3 for V in Equation (I). F B = ( 2.286 × 10 − 3 slug / ft 3 ) ( 32.2 ft / s 2 ) ( 70000 ft 3 ) = 5152.64 slug ⋅ ft / s 2 ( 1 lb slug ⋅ ft / s 2 ) = 5152.64 lb Convert the temperature from degree Fahrenheit to degree Rankin. T ( ° R ) = T ( ° F ) + 460 = ( 165 ° F + 460 ) ° R = 625 ° R Substitute 14.7 psi for p , 53.33 ft ⋅ lbf / lb ⋅ ° R for R and 625 ° R for T in Equation (II). ρ b = ( 14.7 psi ) ( 53.33 ft ⋅ lbf / lb ⋅ ° R ) ( 625 ° R ) = ( 14.7 psi ( 1 lbf / in 2 1 psi × 144 in 2 1 ft 2 ) ) ( 53.33 ft ⋅ lbf / lb ⋅ ° R ) ( 625 ° R ) = 2116.8 33331.25 lb / ft 3 ( 1 slug 32.2 lb ) = 1.98 × 10 − 3 slug / ft 3 Substitute 1.98 × 10 − 3 slug / ft 3 for ρ b and 32.2 ft / s 2 for g in Equation (III). γ b = ( 1.98 × 10 − 3 slug / ft 3 ) ( 32.2 ft / s 2 ) = 0

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 9.3, Problem 58P

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Chapter 9.3, Problem 57P

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Chapter 9 Solutions

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

Ch. 9.1 - Prob. 1P Ch. 9.1 - Assume that water flowing past the equilateral...Ch. 9.1 - Repeat Problem 9.1 if the object is a cone (made...Ch. 9.1 - Prob. 4P Ch. 9.1 - Prob. 5P Ch. 9.1 - Prob. 6P Ch. 9.1 - Prob. 8P Ch. 9.1 - Typical values of the Reynolds number for various...Ch. 9.1 - Prob. 11P Ch. 9.1 - Consider the following cases. (a) A small...

Ch. 9.2 - Water flows past a flat plate that is oriented...Ch. 9.2 - A viscous fluid flows past a flat plate such that...Ch. 9.2 - Prob. 15P Ch. 9.2 - Prob. 16P Ch. 9.2 - Prob. 17P Ch. 9.2 - Prob. 18P Ch. 9.2 - Air enters a square duct through a 1-ft opening as...Ch. 9.2 - A smooth, flat plate of length and width b = 4 m...Ch. 9.2 - An atmospheric boundary layer is formed when the...Ch. 9.2 - Prob. 22P Ch. 9.2 - Prob. 23P Ch. 9.2 - Prob. 25P Ch. 9.2 - Prob. 26P Ch. 9.2 - Prob. 27P Ch. 9.2 - Prob. 28P Ch. 9.2 - Prob. 29P Ch. 9.2 - Prob. 30P Ch. 9.2 - A laminar boundary layer velocity profile is...Ch. 9.2 - Prob. 32P Ch. 9.2 - Prob. 33P Ch. 9.3 - Should a canoe paddle be made rough to get a...Ch. 9.3 - Prob. 35P Ch. 9.3 - Prob. 36P Ch. 9.3 - Prob. 37P Ch. 9.3 - Prob. 38P Ch. 9.3 - Prob. 39P Ch. 9.3 - Prob. 40P Ch. 9.3 - Prob. 41P Ch. 9.3 - Prob. 42P Ch. 9.3 - Prob. 43P Ch. 9.3 - Prob. 44P Ch. 9.3 - Prob. 45P Ch. 9.3 - Prob. 46P Ch. 9.3 - Prob. 47P Ch. 9.3 - Prob. 48P Ch. 9.3 - Prob. 49P Ch. 9.3 - Prob. 50P Ch. 9.3 - Prob. 51P Ch. 9.3 - Prob. 52P Ch. 9.3 - Prob. 53P Ch. 9.3 - Prob. 54P Ch. 9.3 - Prob. 55P Ch. 9.3 - Prob. 56P Ch. 9.3 - A 38.1-mm-diameter, 0.0245-N table tennis ball is...Ch. 9.3 - Prob. 58P Ch. 9.3 - Prob. 59P Ch. 9.3 - Prob. 60P Ch. 9.3 - Prob. 61P Ch. 9.3 - Prob. 62P Ch. 9.3 - Prob. 63P Ch. 9.3 - Prob. 64P Ch. 9.3 - Prob. 65P Ch. 9.3 - Prob. 66P Ch. 9.3 - During a flash flood, water rushes over a road as...Ch. 9.3 - Prob. 68P Ch. 9.3 - Prob. 69P Ch. 9.3 - Prob. 70P Ch. 9.3 - Prob. 71P Ch. 9.3 - Prob. 72P Ch. 9.3 - Phil’s Pizza Parlor decides to place a thin,...Ch. 9.3 - Prob. 74P Ch. 9.3 - Prob. 75P Ch. 9.3 - Estimate the energy required for an average person...Ch. 9.3 - a vertical wind tunnel can be used for skydiving...Ch. 9.3 - Compare the rise velocity of an -in.-diameter air...Ch. 9.3 - A 50-lb box shaped like a 1-ft cube falls from the...Ch. 9.3 - A 500-N cube of specific gravity SG = 1.8 falls...Ch. 9.3 - The helium-filled balloon shown in Fig P9.81 is to...Ch. 9.3 - A 0.30-m-diameter cork ball (SG = 0.21) is tied to...Ch. 9.3 - A shortwave radio antenna is constructed from...Ch. 9.3 - Prob. 84P Ch. 9.3 - Prob. 85P Ch. 9.3 - Prob. 86P Ch. 9.3 - Prob. 87P Ch. 9.3 - Prob. 88P Ch. 9.3 - A smooth orange ball weighs lb (at sea level) and...Ch. 9.3 - Prob. 90P Ch. 9.3 - A marine location marker is a smoke-producing...Ch. 9.3 - Prob. 92P Ch. 9.3 - An airplane flies at 150 km/hr. (a) The airplane...Ch. 9.3 - Prob. 94P Ch. 9.3 - Prob. 96P Ch. 9.3 - Prob. 97P Ch. 9.3 - Prob. 98P Ch. 9.3 - Prob. 99P Ch. 9.4 - Prob. 100P Ch. 9.4 - Prob. 101P Ch. 9.4 - Prob. 102P Ch. 9.4 - Prob. 103P Ch. 9.4 - Prob. 104P Ch. 9.4 - Prob. 105P Ch. 9.4 - Prob. 106P Ch. 9.4 - Prob. 107P Ch. 9.4 - Prob. 108P Ch. 9.4 - Prob. 109P Ch. 9.4 - Prob. 111P Ch. 9.4 - Prob. 112P Ch. 9.4 - Prob. 113P Ch. 9.4 - Prob. 114P Ch. 9.4 - Prob. 115P Ch. 9.4 - Prob. 116P Ch. 9.4 - Prob. 117P Ch. 9.4 - Prob. 118P Ch. 9.4 - Prob. 119P Ch. 9.4 - Prob. 120P Ch. 9.4 - Prob. 121P Ch. 9.4 - Prob. 122P Ch. 9.4 - (See The Wide World of Fluids article “Why...Ch. 9.5 - Prob. 1LLP Ch. 9.5 - Prob. 2LLP Ch. 9.5 - We have seen in this chapter that streamlining an...

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