Answer to Question #320030 in Mechanics | Relativity for Ankamah

Question

A thin 20-cm x 20-cm flat plate is pulled at 1 m/s horizontally through a 3.6-mm-thick oil layer sandwiched between two plates, one stationary and the other moving at a constant velocity of 0.3 m/s, as shown below. The dynamic viscosity of the oil is 0.027 Pa.s. Assuming the velocity in each oil layer varies linearly (a) plot the velocity profile and find the location where the oil velocity is zero (b) determine the force that needs to be applied on the plate to maintain this motion.

Answer 1

$F_2=\mu A\frac{v-v_1}{dz_2}=3.1~N,$

$F_1=\mu A\frac{dv_1}{dz_1}=7.3~N,$

$F=F_1+F_2=10.4~N.$