Explanation Given information: The diameter at the inlet of the pump is 10 cm . The diameter of jet at exit of the pump is 5 cm . The friction head loss of the system is 6.5 m . The head at the inlet of the pump is 15 m . Write the expression for the Bernoulli’s equation between the inlet and outlet of the pump. p 1 ρ g + V 1 2 2 g + z 1 + h p = p 2 ρ g + V 2 2 2 g + z 2 + h f ( p 1 − p 2 ρ g ) + ( V 1 2 2 g − V 2 2 2 g ) + ( z 1 − z 2 ) = h f − h p ..... (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 outlet 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 water is ρ , the head loss due to friction is h f , the pump head is h p and the acceleration due to gravity is g . Since the pressure at the inlet and outlet are atmospheric pressure, so the magnitude of pressure at both the sections is same. p 1 = p 2 = p a t m Since the velocity of water at the inlet of pump is zero so, V 1 = 0 Substitute p a t m for p 1 , p a t m for p 2 and 0 m / s for V 1 in Equation (I). ( p atm − p atm ρ g ) + ( ( 0 m / s ) 2 g − V 2 2 2 g ) + ( z 1 − z 2 ) = h f + h p − V 2 2 2 g + ( z 1 − z 2 ) = h f + h p ..... (II) Write the expression for z 2 . z 2 = z − D 2 ..... (III) Here, the height of pump outlet from the datum is z and the diameter of pipe at the pump inlet is D . Write the expression for the flow rate. Q = π × D e 2 4 × V 2 ..... (IV) Here, the diameter at the exit of the pump is D e . Write the expression for the velocity of jet using projectile equation of motion. V = V 2 sin θ − g t ..... (V) Here, the velocity after time t is V and the angle of projectile motion is θ . At maximum height the velocity of the object is zero. V = 0 Substitute 0 for V in Equation (V). 0 = V 2 sin θ − g t V 2 sin θ = g t t = V 2 sin θ g Write the expression for the vertical distance travelled by the jet. y = ( V 2 sin θ ) t − 1 2 g t 2 ..... (VI) Substitute V 2 sin θ g for t in Equation (VI). y = ( V 2 sin θ ) ( V 2 sin θ g ) − 1 2 g ( V 2 sin θ g ) 2 y = 1 2 g ( V 2 sin θ ) 2 ..... (VII) Write the expression for the pump power. P = ρ Q g h p

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 3, Problem 3.183P

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