Explanation Show the sharp edge splitter plate and the flowing stream as in Figure (1). Express the equation to calculate the cross-sectional area at section 1. A 1 = W H 1 Here, width is W and height of the flow at section 1 is H 1 . Express the equation for mass flow rate at section 1. m ˙ 1 = ρ A 1 V 1 (I) Here, density of the fluid is ρ and velocity at section 1 is V 1 . Substitute W H 1 for A 1 in Equation (I). m ˙ 1 = ρ ( W H 1 ) V 1 = ρ W H 1 V 1 Express the equation for mass flow rate at section 2. m ˙ 2 = ρ A 2 V 2 = ρ W H 2 V Here, height of the flow at section 2 is H 2 . Express the equation for mass flow rate at section 3. m ˙ 3 = ρ A 3 V 3 = ρ W H 3 V Here, height of the flow at section 3 is H 3 . Apply moment equation along vertical direction to calculate the deflection angle of the splitter plate. ( − m ˙ 1 ) ( V 1 y ) + ( m ˙ 2 ) ( − V 2 y ) + ( m ˙ 3 ) ( V 3 y ) = F y (II) Here, reaction force parallel to the splitter plate is F y and velocity at sections 1, 2 and 3 along vertical direction is V 1 y , V 2 y and V 3 y respectively. As there is no reaction force acting parallel to the splitter plate, F y = 0 Substitute ρ W H 3 V for m ˙ 3 , 0 for F y , ρ W H 1 V for m ˙ 1 , 0 for V 1 y , ρ W H 2 V for m ˙ 2 , V for V 2 y and V sin θ for V 3 y in Equation (II). ( − ρ W H 1 V ) ( 0 ) + ( ρ W H 2 V ) ( − V ) + ( ρ W H 3 V ) ( V sin θ ) = 0 0 − ρ W H 2 V 2 + ρ W H 3 V 2 sin θ = 0 sin θ = H 2 H 3 sin θ = h H 1 − h θ = sin − 1 [ h H 1 − h ] Hence, the required expression for the deflection angle of the jet at section 3 is θ = sin − 1 [ h H 1 − h ] Apply moment equation along horizontal direction to calculate the horizontal force acting on the splitter plate. ( − m ˙ 1 ) ( V 1 x ) + ( m ˙ 3 ) ( V 3 x ) = − F x (III) Here, reaction force perpendicular to the splitter plate is F x and velocity at sections 1 and 3 along horizontal direction is V 1 x and V 3 x respectively. Substitute F for F x , ρ W H 1 V for m ˙ 1 , V for V 1 x , ρ W H 3 V for m ˙ 3 and V cos θ for V 3 x in Equation (III)

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 5.2, Problem 75P

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Determine the deflection angle of the jet at section 3 and the required expression for horizontal force acting on the splitter plate.

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Chapter 5.2, Problem 74P

Chapter 5.2, Problem 76P

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Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

Ch. 5.1 - Prob. 1P Ch. 5.1 - An incompressible fluid flows horizontally in the...Ch. 5.1 - Water flows steadily through the horizontal piping...Ch. 5.1 - Water flows out through a set of thin, closely...Ch. 5.1 - Estimate the rate (in gal/hr) that your car uses...Ch. 5.1 - The pump shown in Fig. P5.6 produces a steady flow...Ch. 5.1 - The fluid axial velocities shown in Fig. P5.7 are...Ch. 5.1 - The human circulatory system consists of a complex...Ch. 5.1 - Air flows steadily between two cross sections in a...Ch. 5.1 - A hydraulic jump (see Video V10.11) is in place...

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