To determine The pressure difference in psi . Explanation Write the expression of Bernoulli’s Equation. P 1 γ + V 1 2 2 g + z 1 = P 2 γ + V 2 2 2 g + z 2 (I) Here, the pressure at point ( 1 , 2 ) is P 1 , the pressure at point ( 4 , 4 ) is P 2 , the velocity at point ( 1 , 2 ) is V 1 , the velocity at point ( 4 , 4 ) is V 2 , the datum head at point ( 1 , 2 ) is z 1 , the datum head at point ( 4 , 4 ) is z 2 , the specific weight density of the water is γ and the acceleration due to gravity is g . Substitute z 1 for z 2 in Equation (I) and Rearrange the equation in term of pressure difference. P 1 γ + V 1 2 2 g + z 1 = P 2 γ + V 2 2 2 g + z 1 P 1 γ − P 2 γ = V 2 2 2 g − V 1 2 2 g + z 1 − z 1 ( P 1 − P 2 γ ) = ( V 2 2 − V 1 2 2 g ) P 1 − P 2 = γ ( V 2 2 − V 1 2 2 g ) (II) Write the expression of x component of the velocity. u = ∂ ϕ ∂ x (III) Here, the velocity potential function is ϕ and the displacement in x direction is x . Substitute − ( 3 x 2 y − y 3 ) for ϕ in Equation (III). u = ∂ ∂ x { − ( 3 x 2 y − y 3 ) } = − 3 y ∂ ∂ x ( x 2 ) + ∂ ∂ x ( y 3 ) = − 3 y × 2 x + 0 = − 6 x y (IV) Write the expression of y component of the velocity. v = ∂ ϕ ∂ y (V) Substitute − ( 3 x 2 y − y 3 ) for ϕ in Equation (V). v = ∂ ∂ y { − ( 3 x 2 y − y 3 ) } = − 3 x 2 ∂ ∂ y ( y ) + ∂ ∂ y ( y 3 ) = − 3 x 2 + 3 y 2 (VI) Write the expression of velocity at point ( 1 , 2 ) . V 1 = u 1 2 + v 1 2 (VII) Write the expression of velocity at point ( 4 , 4 ) . V 2 = u 2 2 + v 2 2 (VIII) Conclusion: For coordinate ( 1 , 2 )

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Chapter 6.4, Problem 30P

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