Explanation Given information: The fluid is water at 20 ° C The energy equation can be written as, p 1 ρ g + V 1 2 2 g + z 1 = p 2 ρ g + V 2 2 2 g + z 2 + h f Since, p 1 = p 2 and V 1 ≈ 0 We can rewrite the above equation as, Δ z = h f + V 2 2 g = V 2 2 g ( 1 + f L D ) The Reynolds’s number is defined as, Re = ρ V D μ In the above equation, μ - Dynamic viscosity ρ - Density Time to drain is equal to, t d r a i n = V o l u m e F l o w r a t e Assume, the water at 20 ° C will have, ρ = 998 k g / m 3 μ = 0.001 k g / m s Calculation: When the tank becomes empty, Assume, f = 0.02 Calculate the velocity of the flow V 2 = 2 g Δ z ( 1 + f L D ) = 2 ( 9.81 m / s 2 ) ( 0.8 m ) ( 1 + ( 0.02 ) 0.8 m 0.04 m ) = 11.211 V = 3.35 m / s Calculate the Reynolds’s number Re = ρ V D μ = ( 998 k g / m 3 ) ( 3.35 m / s ) ( 0.04 m ) 0.001 k g / m s = 133732 Calculate the roughness ratio, Assume, the roughness of drawn tubing as ε = 0.0015 m m ε d = 0.0015 40 = 3.75 × 10 − 5 Calculate the friction factor 1 f 1 2 = − 1.8 log ( 6.9 Re + ( ε / D 3.7 ) 1.11 ) 1 f 1 2 = − 1

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 6, Problem 6.65P

To determine

If the flow becomes laminar when tank becomes empty and the depth and time.

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Chapter 6 Solutions

Fluid Mechanics

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