Explanation Given information: The exit pressure from the nozzle is 101 kPa . The specific gravity of manometer fluid is 1.6 and the deflection is 66 cm . The friction is neglected. The diameter at section (1) is 7 cm and the diameter at section (2) is 4 cm . Write the expression for the Bernoulli’s equation between the inlet and outlet of the nozzle. p 1 ρ g + V 1 2 2 g + z 1 = p 2 ρ g + V 2 2 2 g + z 2 ( p 1 − p 2 ρ w g ) + ( V 1 2 2 g − V 2 2 2 g ) + ( z 1 − z 2 ) = 0 ..... (I) Here, the pressure at inlet to the nozzle is p 1 , the velocity at inlet is V 1 , the height of the inlet from the datum is z 1 , the pressure at outlet is p 2 , the velocity at outlet is V 2 , the height of the outlet from the datum is z 2 , the density of water is ρ w , and the acceleration due to gravity is g . Write the expression for the pressure difference. p 1 − p 2 = ( ρ f − ρ w ) g h ..... (II) Here, the density of the fluid is ρ f , the acceleration due to gravity is g and the difference between the fluid column is h . Write the expression for the density of the fluid. ρ f = S G × ρ w Here, the specific gravity of fluid is S G . Substitute S G × ρ w for ρ f in Equation (II). p 1 − p 2 = ( S G × ρ w − ρ w ) g h = ρ w g h ( S G − 1 ) ..... (III) Write the expression for the flow rate at the section (1). Q = A 1 V 1 ..... (IV) Here, the area at section (1) is A 1 and the velocity at section (1) is V 1 . Write the expression for the area of section (1). A 1 = π 4 D 1 2 Here, the diameter is D 1 . Substitute π 4 D 1 2 for A 1 in Equation (IV). Q = ( π 4 D 1 2 ) V 1 ..... (V) Write the expression for the flow rate at the section (2). Q = A 2 V 2 ..... (VI) Here, the area at section (2) is A 2 and the velocity at section (2) is V 2 . Write the expression for the area of section (2). A 2 = π 4 D 2 2 Here, the diameter is D 2 . Substitute π 4 D 2 2 for A 2 in Equation (VI). Q = ( π 4 D 2 2 ) V 2 ..... (VII) Since the flow rate is same at both the sections, we write the expression for continuity equation. Equate the Equation (V) and Equation (VII). ( π 4 D 1 2 ) V 1 = ( π 4 D 2 2 ) V 2 D 1 2 V 1 = D 2 2 V 2 V 1 = ( D 2 D 1 ) 2 V 2 Substitute ( D 2 D 1 ) 2 V 2 for V 1 and ρ w g h ( S G − 1 ) for p 1 − p 2 in Equation (I)

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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