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helppls
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Homework Statement
Consider a layer of paint on a vertical wall, with uniform thickness T and a yield stress of Tau_0. (Paint is a Bingham Plastic).
a) Derive an expression for the maximum thickness T0 that can be sustained without vertical flow.b) Derive an expression for the velocity profile when thickness is larger than T0.
Homework Equations
When shear stress is less than yield stress, du/dy=0
Tau= mu(dU/dy)+yield stress
The Attempt at a Solution
[/B]
For part A, I got (using momentum balance): T0= Tau_0/pg
Basically, the paint won't run if the shear stress does not exceed the yield stress, correct? So if the thickness is larger than the maximum thickness without vertical flow (T0), it can be assumed that the shear stress exceeds the yield stress. I'm confused at what to do from here? Because paint is a Bingham plastic and when the shear stress exceeds the yield stress:
Tau= mu(dU/dy)+yield stress
^Would I just solve this equation for U or does this question require T0 in the answer?