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Problem 2.49

Problem 2.49 - Problem 2.49[Difficulty 3 Given Flow data on...

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Problem 2.49 [Difficulty: 3] Given: Flow data on apparatus Find: Sketch of piston speed vs time; the time needed for the piston to reach 99% of its new terminal speed. Solution: Given data: D piston 73 mm = D tube 75 mm = L 100 mm = SG Al 2.64 = V 0 10.2 m s = Reference data: ρ water 1000 kg m 3 = (maximum density of water) (From Problem 2.48) From Fig. A.2, the dynamic viscosity of SAE 10W-30 oil at 25 o C is: μ 0.13 N s m 2 = The free body diagram of the piston after the cord is cut is: Piston weight: W piston SG Al ρ water g π D piston 2 4 L = Viscous force: F viscous V ( ) τ rz A = or F viscous V ( ) μ V 1 2 D tube D piston ( ) π D piston L ( ) = Applying Newton's second law: m piston dV dt W piston F viscous V ( ) = Therefore dV dt g a V = where a 8 μ SG Al ρ water D piston D tube D piston ( ) = If V g a V = then dX dt a dV dt = The differential equation becomes

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