Problem 4.78 - ft s ⋅ ⎛ ⎝ ⎞ ⎠ 2 4 ⋅ in 2 ⋅ 40...

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Problem 4.78 [Difficulty: 2] R x y x CS Given: Water flow through elbow Find: Force to hold elbow Solution: Basic equation: Momentum flux in x direction for the elbow Assumptions: 1) Steady flow 2) Incompressible flow 3) Atmospheric pressure at exit 4) Uniform flow Hence R x p 1g A 1 + V 1 ρ V 1 A 1 () V 2 ρ V 2 A 2 () = R x p 1g A 1 ρ V 1 2 A 1 V 2 2 A 2 + = From continuity V 2 A 2 V 1 A 1 = so V 2 V 1 A 1 A 2 = V 2 10 ft s 4 1 = V 2 40 ft s = Hence R x 15 lbf in 2 4 × in 2 1.94 slug ft 3 10
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Unformatted text preview: ft s ⋅ ⎛ ⎝ ⎞ ⎠ 2 4 ⋅ in 2 ⋅ 40 ft s ⋅ ⎛ ⎝ ⎞ ⎠ 2 1 ⋅ in 2 ⋅ + ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ × 1 ft ⋅ 12 in ⋅ ⎛ ⎝ ⎞ ⎠ 2 × lbf s 2 ⋅ slug ft ⋅ × − = R x 86.9 − lbf ⋅ = The force is to the left: It is needed to hold the elbow on against the high pressure, plus it generates the large change in x momentum...
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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