You are attempting to measure the Reynolds number of a flow. Recall that the Rey

Question

You are attempting to measure the Reynolds number of a flow. Recall that the Reynolds number is given by Re = rho V/mu where rho is the density, V the flow velocity, L is a characteristic length scale, and mu is the dynamic viscosity of the fluid. You have taken measurements of each of the necessary quantities, and have determined the following: rho = (2.204 plusminus 0.171) middot 10^-3 slug/ft^3 V = 32.15 + 1.38 ft/s L = 17.042 plusminus 0.0005 in mu= (3.94 plusminus 0.13) 10^-7 lbf middot s/ft^2 Assuming that all of the uncertainties are reported at 95% confidence, determine the uncertainty in the Reynolds number.

Explanation / Answer

Re = VL /

(Re)/Re = (/) + (V/V) + (L/L) + ( /)

(Re)/Re = (0.171/2.204) + (1.38 / 32.15) + (0.0005/17.042) + (0.13 * 10-7/3.94 * 10-7)

(Re)/Re = 0.1535

Re = VL / = 2.204 * 10-3 * 32.15 * 17.042 / 3.94 * 10-7

Re = 3064904

Uncertainty = 3064904 * 0.1535 = 470477

SO UNcertainty in reynolds number = +- 470477

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