In a Couette flow, two large flat plates lie one on top of another, separated by a thin

Chapter 3, Problem 10

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In a Couette flow, two large flat plates lie one on top of another, separated by a thin layer of fluid. If a shear stress is applied to the top plate, the viscosity of the fluid produces motion in the bottom plate as well. The velocity  in the top plate relative to the bottom plate is given by \(V=\tau h / \mu\), where \(\tau\) is the shear stress applied to the top plate,  is the thickness of the fluid layer, and \(\mu\) is the viscosity of the fluid. Assume that \(\mu=1.49 P a \cdot s \text { and } h=10 \mathrm{~mm}\), both with negligible uncertainty.

a. Suppose that \(\tau=30.0 \pm 0.1 P a\). Estimate , and find the uncertainty in the estimate.

b. If it is desired to estimate V with an uncertainty of \(0.2 \mathrm{~mm} / \mathrm{s}\), what must be the uncertainty in  \(\tau\) ?

Equation Transcription:

   

     

     

 

 

Text Transcription:

V=\tau h / \mu

\tau

\mu

\mu=1.49 P a \cdot s \and  h=10 mm

\tau=30.0 \pm 0.1 P a

0.2 mm/s

\tau