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Problem 4.65 [Difficulty: 2] Given: Data on flow and system geometry Find: Force required to hold plug Solution: Basic equation: The given data is D1 0.25 m⋅= D2 0.2 m⋅= Q 1.5 m3 s ⋅= p1 3500 kPa⋅= ρ 999 kg m3 ⋅= Then A1 π D1 2⋅ 4 = A1 0.0491 m2= V1 Q A1 = V1 30.6 m s = A2 π 4 D1 2 D2 2−⎛⎝ ⎞⎠⋅= A2 0.0177 m2= V2 QA2= V2 84.9 m s = Applying the basic equation F− p1 A2⋅+ p2 A2⋅− 0 V1 ρ− V1⋅ A1⋅( )⋅+ V2 ρ V2⋅ A2⋅( )⋅+= and p2 0= (gage) Hence F p1 A1⋅ ρ V12 A1⋅ V22 A2⋅−⎛⎝ ⎞⎠⋅+= F 3500 kN m2 × 0.0491⋅ m2⋅ 999 kg m3 ⋅ 30.6 m s ⋅⎛⎜⎝ ⎞ ⎠ 2 0.0491⋅ m2⋅ 84.9 m s ⋅⎛⎜⎝ ⎞ ⎠ 2 0.0177⋅ m2⋅− ⎡⎢⎣ ⎤⎥⎦×+= F 90.4 kN⋅=
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