Two flat plates are oriented parallel above a fixed lower...

Two flat plates are oriented parallel above a fixed lower plate as shown in the figure. The top plate, located a distance b above the fixed plate, is pulled along with speed V. The other thin plate is located a distance cb, where 0<c<1, above the fixed plate. This plate moves with speed V1, which is determined by the viscous shear forces imposed on it by the fluids on its top and bottom. The fluid on the top is twice as viscous as that on the bottom. Plot the ratio V1/V as a function of c for 0<c<1.

Transcript

00:01 Hello, in the question we have given two flat plates are oriented parallel above a fixed lower plate.

00:06 So this is a fixed plate and these are the two parallel plates which are oriented above it.

00:12 So the velocities of these plates are given.

00:15 So and their locations what at what they are located at what distance they are located from the fixed axis from this fixed plate.

00:23 That is what is given in the question and the c varies from zero to one.

00:28 So we have to, what we have to do is we have to plot v1 upon v as a function of c.

00:33 So this is what we have to do.

00:35 So let us find out now.

00:37 So if, if v1 is constant, if, so not if, for constant.

00:46 So let us write like this for constant, for constant v1.

00:54 So that is the middle plate for the constant v1.

00:58 Acceleration is zero.

00:59 So if acceleration is zero, then force will also be zero.

01:05 Then net force acting on this plate will be on plate will be equal to zero.

01:18 So can we write then the force at bottom or force at the top of the plate is equal to the force at the bottom.

01:30 Sorry, so this is bottom.

01:35 So force at the bottom.

01:36 So if we can write this, then what we can do is force at the top.

01:42 Now we know one more formula that force is given by force is given by tau a, where tau is at the torque, but it is sheer stress.

01:53 So this tau is the shear stress.

01:55 So can we write then tau at the top, tau at the top is equal to tau at the bottom.

02:03 So now let us define what is tau.

02:05 So tau is given by mu times t u pi.

02:08 D .y...

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