Explanation Given: The outer diameter ( D ) is 400 mm . The inner diameter ( d ) is 300 mm. The discharge through the pipe ( Q ) is 0.05 m 3 /s . Calculation: Calculate the velocity of the pipe using the volumetric flow ( Q ). Q = A × V Q = π 4 ( d ) 2 × V 0.05 m 3 /s = π 4 ( 100 mm ) 2 × V 0.05 m 3 /s = π 4 ( 100 mm × 1 m 1000 m ) 2 × V V = 20 π m/s Write the expression for velocity of flow ( V ) in the pipe. − d p d n − ρ g d z d n = ρ V 2 R (I) Here, d p is pressure difference, ρ is density of water at 5 ° C , g is acceleration due to gravity, and n and z are axes. Refer figure. Consider that the axes n and z are opposite to each other. d n = − d z (II) Consider that the pipe is lying on the horizontal plane. d z = 0 (III) Substitute Equation (II) and (III) in (I). − d p d n − ρ g d z d n = ρ V 2 R − d p ( − d R ) − ρ g ( 0 ) d n = ρ V 2 R d p d R = ρ V 2 R d p = ρ V 2 ( d R R ) (IV) Integrate the Equation (IV) on both sides

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ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Problem (13): A pump is being used to lift water from the bottom tank to the top tank in a galvanized iron pipe at a discharge (Q). The length and diameter of the pipe section from the bottom tank to the pump are (L₁) and (d₁), respectively. The length and diameter of the pipe section from the pump to the top tank are (L2) and (d2), respectively. Given the values of Q [L/s], L₁ [m], d₁ [m], L₂ [m], d₂ [m], calculate total head loss due to friction (i.e., major loss) in the pipe (hmajor-loss) in [cm]. Givens: L₁,d₁ Pump L₂,d2 오 0.533 lit/s L1 = 6920.729 m d1 = 1.065 m L2 = 70.946 m d2 0.072 m Answers: (1) 3.069 cm (2) 3.914 cm ( 3 ) 2.519 cm ( 4 ) 1.855 cm TABLE 8.1 Equivalent Roughness for New Pipes Pipe Riveted steel Concrete Wood stave Cast iron Galvanized iron Equivalent Roughness, & Feet Millimeters 0.003-0.03 0.9-9.0 0.001-0.01 0.3-3.0 0.0006-0.003 0.18-0.9 0.00085 0.26 0.0005 0.15 0.045 0.000005 0.0015 0.0 (smooth) 0.0 (smooth) Commercial steel or wrought iron 0.00015 Drawn…

Chapter 5 Solutions

Fluid Mechanics (2nd Edition)

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