Transcription of Chapter 5 Dimensional Analysis and Similarity
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Chapter 5 Dimensional Analysis and Similarity
Chapter 5 Dimensional Analysis and Similarity For axial flow through a circular tube, the Reynolds number for transition to turbulence is approximately 2300 [see Eq. ( )], based upon the diameter and average velocity. If d = 5 cm and the fluid is kerosene at 20 C, find the volume flow rate in m3/h which causes transition. Solution: For kerosene at 20 C, take = 804 kg/m3 and = kg/m s. The only unknown in the transition Reynolds number is the fluid velocity: trVd(804)V( )Re2300, solve for === 32mThen QVA( )( ) 4 3600 4sAns. === A prototype automobile is designed for cold weather in Denver, CO (-10 C, 83 kPa). Its drag force is to be tested in on a one-seventh-scale model in a wind tunnel at 20 C and 1 atm.
5.6 SAE 10 oil at 20°C flows past an 8-cm-diameter sphere. At flow velocities of 1, 2, and 3 m/s, the measured sphere drag forces are 1.5, 5.3, and 11.2 N, respectively. Estimate the drag force if the same sphere is tested at a velocity of 15 m/s in glycerin at 20°C. Solution: For SAE 10 oil at 20°C, take ρ ≈ 870 kg/m3 and μ ≈ 0.104 kg ...
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