Explanation Write the relation between the volumetric flow rates. Q 1 = Q 2 + Q 3 A 1 V 1 = A 2 V 2 + A 3 V 3 π 4 D 2 V 1 = π 4 D 2 V 2 + π 4 D 2 V 3 V 1 = V 2 + V 3 (I) Write the Bernoulli’s equation between tank A and B . p A γ + V A 2 2 g + z A = p B γ + V B 2 2 g + z B + f 1 l 1 V 1 2 2 g D + f 2 l 2 V 2 2 2 g D (II) Here, the pressure is p , the velocity is V , the datum head is z , the length of the pipe is l and the friction factor is f . Write the Bernoulli’s equation between tank A and C . p A γ + V A 2 2 g + z A = p C γ + V C 2 2 g + z C + f 1 l 1 V 1 2 2 g D + f 3 l 3 V 3 2 2 g D (III) Write the expression for the friction factor. 1 f = − 2.0 log ( ε / D 3.7 + 2.51 Re f ) (IV) Here the Reynolds number is Re, the equivalent roughness is ε . Write the expression for the Reynolds number. Re = V D υ (V) Here, the kinematic viscosity is υ . Write the expression for the flow rate. Q = A V (VI) Conclusion: Substitute, p A for p B , 0 for V A , V B and z B , 0.1 m for D , 80 m for l 1 , 40 m for l 2 and 9.81 m / s 2 for g in Equation (II). p B γ + 0 2 × 9.81 + 15 = p B γ + 0 2 × 9.81 + 0 + f 1 × 80 × V 1 2 2 × 9.81 × 0.1 + f 2 × 40 × V 2 2 2 × 9.81 × 0.1 15 = f 1 × 80 × V 1 2 2 × 9.81 × 0.1 + f 2 × 40 × V 2 2 2 × 9.81 × 0.1 15 × 2 × 9.81 × 0.1 = f 1 × 80 × V 1 2 + f 2 × 40 × V 2 2 29.43 = f 1 × 80 × V 1 2 + f 2 × 40 × V 2 2 0.368 = f 1 V 1 2 + f 2 V 2 2 2 (VII) Substitute, p A for p C , 0 for V A , V C and z C , 0.1 m for D , 80 m for l 1 , 75 m for l 3 and 9.81 m / s 2 for g in Equation (III) p A γ + 0 2 2 g + 15 = p A γ + 0 2 2 g + 0 + f 1 l 1 V 1 2 2 g D + f 3 l 3 V 3 2 2 g D 15 = f 1 × 80 × V 1 2 2 × 9.81 × 0.1 + f 3 × 75 × V 3 2 2 × 9.81 × 0.1 15 × 2 × 9.81 × 0.1 = f 1 × 80 × V 1 2 + f 3 × 40 × V 3 2 29.43 = f 1 × 80 × V 1 2 + f 3 × 75 × V 3 2 0

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ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

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Chapter 8.5, Problem 118P

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The volumetric flow rates.

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Chapter 8.5, Problem 117P

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