Calculate position of plate between two fluids

[bill222]

Homework Statement

Problem is as shown in the picture.

The answer is meant to be a 4.59mm.

Homework Equations

Tau=mu(du/dy)

The Attempt at a Solution

Force (tau) acting on plate from both fluids is equal, as is velocity (du).

mu1 (du/dy1) = mu2 (du/dy2)

mu1/dy1 = mu2/dy2
(mu2/mu1) *y1 = y2

y1 + y2 + plate thickness = width
y1 + y2 + 0.7937 = 12.7 mm

By substituting in mu2/mu1 *y1 = y2 I obtain the answer y1 = 3.31 mm.Any help is much appreciated

 

[Chestermiller]

Who says that the force (or shear stress) exerted by each fluid on the plate has to be the same? It seems to me this problem is under-specified.