Problem 4.55

Problem 4.55 - Problem 4.55[Difficulty 4 Given Data on...

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Problem 4.55 [Difficulty: 4] Given: Data on draining of a funnel Find: Formula for drain time; time to drain from 12 in to 6 in; plot drain time versus hole diameter Solution: 0 = + CS CV A d V V d t r r ρ Basic equation Assumptions: 1) Uniform flow 2) Incompressible flow 3) Neglect air density Treating the funnel as the CV the basic equation becomes t 0 y y ρ A funnel d ρ V A opening + 0 = For the funnel A funnel π r 2 = π y tan θ () 2 = Hence ρπ tan θ 2 t 0 y y y 2 d ρ V π 4 d 2 + 0 = or tan θ 2 t y 3 3 d d 2g y d 2 4 = Then tan θ 2 y 2 dy dt y d 2 4 = Separating variables y 3 2 dy d 2 4 tan θ 2 dt = Hence y 0 0 y y 3 2 d d 4 tan θ 2 t = 2 5 y 0 5 2 d 4 tan θ 2 t = Solving for t t 8 5 tan θ 2 y 0 5 2 d = and using the given data t 2.55 min =

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To find the time to drain from 12 in to 6 in., we use the time equation with the two depths; this finds the time to drain from 12 in and 6
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Problem 4.55 - Problem 4.55[Difficulty 4 Given Data on...

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