Propagation of Uncertainties in Compound Quantities Problem The governing equati

Question

Propagation of Uncertainties in Compound Quantities Problem The governing equation for the capillary tube viscometer is the well known Hagen-Poiseuelle equation: Q = pi D4/128 Delta p where Q is the volume flow rate of the fluid in the capillary tube D the diameter of the capillary eta the coefficient of dynamic viscosity of the fluid L the length of the capillary tube Delta p the pressure difference across the two ends of the tube If Q,L,D, and Delta p are measured with an uncertainty of 1%, how accurately is eta known? Further, if the uncertainty in the measurement of D is reduced to 0.1% by using improved instrumentation, what is the improvement achieved in the uncertainty of eta ?

Explanation / Answer

The efficieny is given as a function of (D, Q, L, dp)

Error in D, Q, L, dp = +/- 1%

Error in 'eta' = 4*D + Q + L + dp = (4*1+1+1+1) = +/- 7%

Error in Q, L, dp = +/- 1%, Error in D reduced to +/- 0.1 %

Error in 'eta' = 4*D + Q + L + dp = (4*0.1+1+1+1) = +/- 3.4% (Improved eta)  

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