Question

Three large plates are separated bythin layers of ethylene glycol and water. The top plate moves to the right at 2m/s. At what speed and in what direction must the bottom plate be moved to hold the center plate stationary?

Answer 1

Answer:

speed = 0.17m/s

Explanation:

For water at 20°c,

$m = 1*10^3Ns/m^2$

For ethylene glycol at 20°c,

$m =1.99*10^2N.s/m^2$

Shear stress due to motion of the upper plates:

$r_1 =u(dv/dy)$;

= u(v/b)

$= 1*10^-^3 * (2.00/0.0015)$;

$= 1.33N/m^2$

Therefore, for the middle plate to be stationery, the bottom plate must move to the left at a speed that produces equal oppostite force.

Therefore,

$r_1=r_2= 1.33N/m^2$;

$r_1 = u(dv/dy)$;

$= 1.99*10^3 *(v/0.0025) = 1.33$

To find V we have

$V = (0.0025*1.33) / 1.99*10^-^3$

V= 0.17m/s

N.b: I believe you have the diagram