Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 7, Problem 132P
A one-third scale model of an airplane is to be tested in water. The airplane has a velocity of 900 km Ii in air at -50°C. The water temperature iii the test section is 10°C.
The properties of air at 1 atm and -50°C:
The plopelties of water at 1 atm and 10°C:
In order to achieve similarity between the model and the prototype, the water velocity on the model should be
(a) 97 km/h
(b) 186 km/h
(c) 263 km/h
(d) 379 km/h
(e) 450 km/h
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A one-fourth scale model of an airplane is to be tested in water. The airplane has a velocity of 700 km/h in air at −50°C. The water temperature in the test section is 10°C. In order to achieve similarity between the model and the prototype, the test is done at a water velocity of 393 km/h. The properties of air at 1 atm and −50°C: ? = 1.582 kg/m3, ? = 1.474 × 10−5 kg/m·s. The properties of water at 1 atm and 10°C: ? = 999.7 kg/m3, ? = 1.307 × 10−3 kg/m·s. If the average drag force on the model is measured to be 13,800 N, the drag force on the prototype is (a) 590 N (b) 862 N (c) 1109 N (d ) 4655 N (e) 3450 N
The data below is from a passenger hot air balloon. The balloon is designed to lift 10-people (80 kg each person). The balloon consists of a basket, a burner- propane tank system. It will lift up when the cold air trapped inside warms up by the burner. Density of air inside the balloon is 99°C: 0.9486 kg/m³, density of air outside balloon is 20°C (ambient): 1.2041 kg/m³, Assume the balloon is a sphere shape, volume =(4/3)pi R3
Mass (kg)
Balloon
Basket
Burner
Propane tank
113.4 kg
63.5 kg
22.7 kg
183.7 kg
a) Determine the minimum diameter of the balloon that would have a total lifting force to balance the weight of balloon, basket, burner, propane tank and 10 people?
b) If the balloon is converted to survey the weather, it will be filled with hydrogen gas (H2). Assume the weight of the people (800kg) is now replaced by onboard equipment, what is minimum diameter needed to keep it afloat at 18km above the surface of the earth?
For most gases at standard or near standard conditions, the relationshipamong pressure, density, and temperature is given by the perfect gasequation of state: p = ρRT, where R is the specific gas constant. For airat near standard conditions, R = 287 J/(kg · K) in the International System of Units and R = 1716 ft · lb/(slug · ◦R) in the English Engineering System of Units. Using the above information, consider the following two cases:
a. At a given point on the wing of a Boeing 727, the pressure andtemperature of the air are 1.9 × 104 N/m2 and 203 K, respectively.Calculate the density at this point.b. At a point in the test section of a supersonic wind tunnel, the pressureand density of the air are 1058 lb/ft2 and 1.23 × 10−3 slug/ft3,respectively. Calculate the temperature at this point.
Chapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
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