Problem 4.117

# Problem 4.117 - F − p 1 A 2 ⋅ p 2 A 2 ⋅ − V 1 ρ...

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Problem *4.117 [Difficulty: 2] Given: Data on flow and venturi geometry Find: Force on convergent section; water pressure Solution: Basic equations: Bernoulli equation and x momentum p ρ V 2 2 + gz + const = The given data is ρ 999 kg m 3 = D 100 mm = d5 0 m m = p 1 200 kPa = Q 1000 L min = For pressure we first need the velocities A 1 π D 2 4 = A 1 0.00785 m 2 = A 2 π 4 d 2 = A 2 0.00196 m 2 = Then V 1 Q π 4 D 2 = V 1 2.12 m s = V 2 Q A 2 = V 2 8.49 m s = Applying Bernoulli between inlet and throat p 1 ρ V 1 2 2 + p 2 ρ V 2 2 2 + = Solving for p 2 p 2 p 1 ρ 2 V 1 2 V 2 2 + = p 2 200 kPa 1 2 999 kg m 3 2.12 2 8.49 2 () × m 2 s 2 Ns 2 kg m × kN 1000 N × + = p 2 166 kPa
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Unformatted text preview: F − p 1 A 2 ⋅ + p 2 A 2 ⋅ − V 1 ρ − V 1 ⋅ A 1 ⋅ ( ) ⋅ V 2 ρ V 2 ⋅ A 2 ⋅ ( ) ⋅ + = or F p 1 A 1 ⋅ p 2 A 2 ⋅ − ρ V 1 2 A 1 ⋅ V 2 2 A 2 ⋅ − ⎛ ⎝ ⎞ ⎠ ⋅ + = F 200 kN m 2 ⋅ 0.00785 × m 2 ⋅ 166 kN m 2 ⋅ 0.00196 × m 2 ⋅ − 999 kg m 3 ⋅ 2.12 m s ⋅ ⎛ ⎝ ⎞ ⎠ 2 0.00785 ⋅ m 2 ⋅ 8.49 m s ⋅ ⎛ ⎝ ⎞ ⎠ 2 0.00196 ⋅ m 2 ⋅ − ⎡ ⎢ ⎣ ⎤ ⎥ ⎦ × N s 2 ⋅ kg m × ⋅ + = F 1.14 kN =...
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