Problem 4.116

# Problem 4.116 - 14.1 m s = Applying x momentum to the vane...

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Problem *4.116 [Difficulty: 3] Given: Stream of water striking a vane Find: Water speed; horizontal force on vane Solution: Basic equations: Bernoulli; Momentum flux in x direction p ρ V 2 2 + gz + constant = Assumptions: 1) Steady flow 2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow Given or available data D5 0 m m = ρ water 1000 kg m 3 = ρ Hg 13.6 ρ water = θ 30 deg = h 0.75 m = From Bernoulli p 0 p 1 2 ρ water V 2 + = and for the manometer p 0 p ρ Hg g h = Combining 1 2 ρ water V 2 ρ Hg g h = or V 2 ρ Hg g h ρ water
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Unformatted text preview: 14.1 m s = Applying x momentum to the vane R x ρ water V ⋅ V − π 4 ⋅ D 2 ⋅ ⎛ ⎝ ⎞ ⎠ ⋅ ρ water V − cos θ ( ) ⋅ ( ) ⋅ V π 4 ⋅ D 2 ⋅ ⎛ ⎝ ⎞ ⎠ ⋅ + = R x ρ water − V 2 ⋅ π 4 ⋅ D 2 ⋅ 1 cos θ ( ) + ( ) ⋅ = R x 733 − N = Assuming frictionless, incompressible flow with no net pressure force is realistic, except along the vane where friction will reduce flow momentum at the exit....
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