Question

A thin 20 cm 20 cm flat plate is pulled at 1 m/s horizontally through a 3.6 mm thick oil laver sandwiched between two plates, oue stationary and the other moving at a constant velocity of 0.3 m/s, as shown in Figure 1.4. The dynamic viscosity of oil is 0.027 Pas. Assuming the velocity in each oil layer to vary linearly, (a) plot the velocity profile and find the location where the oil velocity is zero and (b) determine the force that needs to be applied on the plate to maintain this motion.
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Answer 1

Answer:

The force that needs to be applied on the plate to maintain this motion, N.F=F1+F2=10.4 N.

Explanation:

From the above question,

They have given :

A thin 20 cm 20 cm flat plate is pulled at 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 mls, as shown in the figure. The dynamic viscosity of oil is 0.027 Pa.s. Assuming the velocity in each oil layer to vary linearly, (a Plot the velocity profile and find the location where the oil velocity is zero .

Dimensions of plate A=20×20cm2A=20×20cm2

Velocity of the plate VP=1m/s

MM V= ms h2 2.6 mm

 V = 0.3 ms Moving wall'

Here we have to find

$F_2=\mu A\frac{v-v_1}{dz_2}=3.1~N,F2=μAdz2v−v1=3.1 N,F_1=\mu A\frac{dv_1}{dz_1}=7.3~N,F1=μAdz1dv1=7.3 N,$

F=F_1+F_2=10.4~N.F=F1+F2=10.4 N.

The force that needs to be applied on the plate to maintain this motion, N.F=F1+F2=10.4 N.

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