Explanation Given information: Length of the cast iron pipe is 1200 m and the diameter of the pipe is 5 c m The elevation at point 1 is 400 m The volumetric flow rate Q can be defined as below, Q = V A In above equation, V - Velocity of the flow A -Area The steady flow equation between the reservoir 1 & 2 will be, p 1 ρ g + V 1 2 2 g + z 1 = p 2 ρ g + V 2 2 2 g + z 2 + h f + ∑ h m − h p We know that, p 1 = p 2 and V 1 = V 2 ≈ 0 , therefore the above equation can be rewritten as, h p = z 2 − z 1 + h f + ∑ h m The Reynolds’s number is defined as, R e = ρ V D μ D - Diameter of the pipe V - Velocity of the flow μ - Dynamic viscosity of the fluid Calculation: Assume that the water at 20 ° C will have, ρ = 998 k g / m 3 μ = 0.001 k g / m s For cast iron, the roughness ratio will be, ε d = 0.26 × 10 − 3 0.05 = 0.0052 To find the velocity of the flow, V = Q A = 0.005 m 3 / s π ( 2.5 × 10 − 2 m ) 2 = 2.546 m / s To find the Reynolds’s number, R e = ρ V D μ = ( 998 k g / m 3 ) ( 2.546 m / s ) ( 0.05 m ) 0.001 k g / m s = 127045.4 To find friction factor, 1 f 1 / 2 ≈ − 1.8 log ( 6.9 R e + ( ∈ / d 3.7 ) 1.11 ) ≈ − 1.8 log ( 6.9 127045.4 + ( 0.0052 3.7 ) 1.11 ) ≈ 0.03145 Assume the minor loses as, K 45 ° E l b o w = 0

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 6, Problem 6.105P

To determine

The gage pressure required at point 1 to deliver 0.005 m3/s of water at 20°C into the reservoir.

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Chapter 6, Problem 6.104P

Chapter 6, Problem 6.106P

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Chapter 6 Solutions

Fluid Mechanics

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The gage pressure required at point 1 to deliver 0.005 m 3 / s of water at 20 ° C into the reservoir.

The gage pressure required at point 1 to deliver 0.005 m3/s of water at 20°C into the reservoir.

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Chapter 6 Solutions