Problem 4.56 - Problem 4.56 [Difficulty: 4] Given: Data on...

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Problem 4.56 [Difficulty: 4] Given: Data on draining of a funnel Find: Diameter that will drain in 1 min.; plot diamter versus depth y 0 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
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