HW4+solutions

HW4+solutions - Solutions HW4 ENG 103 Fall 2011 P5.11...

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ENG 103 Fall 2011 P5.11 During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate the wave speed of an atomic bomb explosion. He assumed that the blast wave radius R was a function of energy released E , air density ρ , and time t . Use dimensional analysis to show how wave radius must vary with time. Solution : The proposed function is R = f ( E, ρ , t ). There are four variables ( n = 4) and three primary dimensions (MLT, or j = 3), thus we expect n-j = 4-3 = 1 pi group. List the dimensions: Assume arbitrary exponents and make the group dimensionless: The single pi group is P5.17 If you disturb a tank of length L and water depth h , the surface will oscillate back and forth at frequency Ω , assumed here to depend also upon water density ρ and the acceleration of gravity g . ( a ) Rewrite this as a dimensionless function. ( b ) If a tank of water sloshes at 2.0 Hz on earth, how fast would it oscillate on Mars ( g 3.7 m/s
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HW4+solutions - Solutions HW4 ENG 103 Fall 2011 P5.11...

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