Explanation Given information: The differential pressure between two section in the pipe filled with water at 20 ° C when the valve A is closed the differential pressure is 75 kPa and when the valve is open the differential pressure is 160 kPa . The flow rate of water is 500 m 3 / h Write the expression for the Bernoulli’s equation between two sections. p 1 ρ + V 1 2 2 + z 1 g = p 2 ρ + V 2 2 2 + z 2 g + h f g ( p 1 ρ − p 2 ρ ) + ( V 1 2 2 − V 2 2 2 ) + ( z 1 g − z 2 g ) = h f g h f g = ( p 1 ρ − p 2 ρ ) + 1 2 { ( V 1 − V 2 ) ( V 1 + V 2 ) } + ( z 1 − z 2 ) g .... (I) Here, the pressure at section (1) is p 1 , the velocity at section (1) is V 1 , the height of the section (1) from the datum is z 1 , the pressure at section (2) is p 2 , the velocity at section (2) is V 2 , the height of the section (2) from the datum is z 2 , the density of oil is ρ , the head loss due to friction is h f , and the acceleration due to gravity is g . Since the area of the pipe is constant; so the velocity difference at both the section is zero. V 1 − V 2 = 0 Substitute 0 for V 1 − V 2 in Equation (I). h f g = ( p 1 ρ − p 2 ρ ) + 1 2 { 0 × ( V 1 + V 2 ) } + ( z 1 − z 2 ) g h f = ( p 1 ρ g − p 2 ρ g ) + ( z 1 − z 2 ) .... (II) Since the valve is closed initially, so there are no friction losses. h f = 0 Substitute 0 for h f in Equation (II)

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ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 3, Problem 3.172P

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The friction head loss in the pipe.

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