Problem 4E

Refer to Exercise 10 in Section 3.2. Assume that τ = 30.0 ± 0.1 Pa, h = 10.0 ± 0.2 mm, and μ= 1.49 Pa · s with negligible uncertainty.

a. Estimate V and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in V: reducing the uncertainty in τ to 0.01 Pa or reducing the uncertainty in h to 0.1 mm?

EXERCISE 10: 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 V in the top plate relative to the bottom plate is given by V = τh/μ, where τ 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. Assume that μ = 1.49 Pa • s and h = 10 mm, both with negligible uncertainty.

a. Suppose that τ = 30.0 ± 0.1 Pa. Estimate V, and find the uncertainty in the estimate.

b. If it is desired to estimate V with an uncertainty of 0.2 mm/s, what must be the uncertainty in τ?

Solution

Step 1 of 5

Here we have to find the uncertainty of the velocity

Given velocity V=

The stress applied to the plate is

From this =30,

The thickness of the fluid layer is

From this h=10,

The viscosity of the fluid is