Assume that µ,h, and ? are measured independently and that the measurements are unbiased and normally distributed. The measured values are µ=1.6Pa ? s, h=15 mm, and ?=25 Pa. The uncertainties (standard deviations) of these measurements are =0.05, =1.0, and =1.0.

Question

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=?h/µ where ? is the shear stress applied to the top plate, h is the thickness of the fluid layer, and µ is the viscosity of the fluid.



a. Use the method of propagation of error (Section 3.3) to estimate V and its uncertainty?V.

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

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



a. Use the method of propagation of error (Section 3.3) to estimate V and its uncertainty .

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

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

Answer 1

(a)

(b) If the estimate of V is normally distributed, then a 95% confidence interval for V is 234.375±1.96(19.63862) or (195.883, 272.867).



(c) The confidence interval is valid. The estimate of V is approximately normal.