Solved: In a Couette flow, two large flat plates lie one atop another, separated by a

Chapter 5, Problem 21

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In a Couette flow, two large flat plates lie one atop 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 V 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, h is the thickness of the fluid layer, and \(\mu\) is the viscosity of the fluid.

Assume that \(\mu, h \text { and } \tau\) are measured independently and that the measurements are unbiased  and normally distributed. The measured values are  \(\mu=1.6 P a \cdot s, h=15 \mathrm{~mm}, \text { and } \tau=25 P a\). The uncertainties (standard deviations) of these measurements  are \(\sigma \mu=0.05, \sigma_{h}=1.0, \text { and } \sigma \tau=1.0\)

Use the method of propagation of error (Section 3.3) to estimate V and its uncertainty \(\sigma_{v}\)

Assuming the estimate of V to be normally distributed, find a 95% confidence interval for V.

Perform a simulation to determine whether or not the confidence interval found in part (b) is valid.

Equation Transcription:

Text Transcription:

V=\tau h / \mu

\tau

\mu

\mu, h and  \tau

\mu=1.6 P a \cdot s, h=15 \mathrm{~mm}, \text { and } \tau=25 P a

\sigma \mu=0.05, \sigma_{h}=1.0, \text { and } \sigma \tau=1.0

\sigma_{v}