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 ofthe 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?
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?
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