Answer to Question #169585 in Mechanical Engineering for nikko

Question #169585

A 10.000-in-diameter plunger slides in a 10.006-in-diameter cylinder, the annular space being filled with oil having a kinematic viscosity of 0.004 ft2/s and specific gravity of 0.85. If the plunger moves at 0.6ft/s, find the force, in lbf, when 9 ft is engaged in the cylinder


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Expert's answer
2021-03-10T05:53:06-0500

Plunger diameter=10.000inPlunger \space diameter=10.000 in

Cylinder diameter=10.006inCylinder \space diameter=10.006 in

Kinematic viscosity=0.004ft2/sKinematic \space viscosity =0.004ft^2/s

G=0.85G=0.85

Plunger moves 0.6ft/s

ρ=μ(dudx),δ=0.85×62.432.2=1.647plunges/ft3\rho=\mu(\frac{du}{dx}), \delta=\frac{0.85 \times62.4}{32.2}=1.647 plunges/ft^3

μ=1.647×0.004=0.006588lb.s/ft2\mu=1.647 \times0.004=0.006588 lb.s/ft^2

du=10.00610.0002/12=0.000250ftdu=\frac{10.006-10.000}{2}/12=0.000250 ft

Z=0.006588(0.6/0.00025)=15.81lb/ft2Z=0.006588(0.6/0.00025)=15.81 lb/ft^2

Ff=ZA=15.81×(9×π(1012)=372.5lbF_f=ZA=15.81\times(9 \times \pi(\frac{10}{12})=372.5 lb

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