The flow rate of water through a cylindrical pipe is given by Q=?r2v , where r is the radius of the pipe and v is the flow velocity.
a. Assume that r=3.00 ± 0.03 m and v=4.0 ± 0.2 m/s. Estimate Q, and find the uncertainty in the estimate.
b. Assume that r=4.00 ± 0.04 m and v=2.0 ± 0.1 m/s. Estimate Q, and find the uncertainty in the estimate.
c. If r and v have not been measured, but it is known that the relative uncertainty in r is 1% and that the relative uncertainty in v is 5%, is it possible to compute the relative uncertainty in Q? If so, compute the relative uncertainty. If not, explain what additional information is needed.
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