Answer to Question #169585 in Mechanical Engineering for nikko

Question

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

Answer 1

$Plunger \space diameter=10.000 in$

$Cylinder \space diameter=10.006 in$

$Kinematic \space viscosity =0.004ft^2/s$

$G=0.85$

Plunger moves 0.6ft/s

$\rho=\mu(\frac{du}{dx}), \delta=\frac{0.85 \times62.4}{32.2}=1.647 plunges/ft^3$

$\mu=1.647 \times0.004=0.006588 lb.s/ft^2$

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

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

$F_f=ZA=15.81\times(9 \times \pi(\frac{10}{12})=372.5 lb$