To determine The pressure in the pipe at B . Explanation Given: The diameter of the pipe A ( d A ) is 80 mm. The diameter of the pipe B ( d B ) is 40 mm. The diameter of the pipe C ( d C ) is 20 mm. The velocity of the water at point A ( V A ) is 2.25 m/s . The absolute pressure of the duct ( P A ) at A is 325 kPa . The absolute pressure of the duct ( P C ) at C is 175 kPa . Calculation: Calculate the area of the piezometer at point A ( A A ) . A A = π 4 D A 2 = π 4 ( 80 mm ) 2 = π 4 ( 80 mm × 1 m 1000 mm ) 2 = 0.00503 m 2 Calculate the area of the piezometer at point B ( A B ) . A B = π 4 d B 2 = π 4 ( 40 mm ) 2 = π ( 40 mm × 1 m 1000 mm ) 2 = 0.001256 m 2 Calculate the area of the piezometer at point C ( A C ) . A C = π 4 d C 2 = π 4 ( 20 mm ) 2 = π 4 ( 20 mm × 1 m 1000 mm ) 2 = 0.0031416 m 2 Write the expression for the continuity equation to obtain the relationship between the velocities. Q A = Q B + Q C A A V A = A B V B + A C V C ( 0.00503 m 2 ) ( 2.25 m/s ) = ( 0.0012566 m 2 ) V B + ( 0.00031416 m 2 ) V C ( 0.0012566 m 2 ) V B + ( 0.00031416 m 2 ) V C = 0.0113175 (I) Apply Bernoulli equation between A and C . p A ρ g + V A 2 2 g + z A = p C ρ g + V C 2 2 g + z C [ 325 kPa 1000 kg m 3 × 9.81 m/s 2 + ( 2.25 m/s ) 2 2 ( 9.81 ) + 0 ] = [ 175 kPa 1000 kg m 3 × 9.81 m/s 2 + V c 2 2 ( 9

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ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 5, Problem 45P

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Chapter 5 Solutions

Fluid Mechanics (2nd Edition)

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