The flow rate of water through a cylindrical pipe is given by Q = πr²v, 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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The flow rate of water through a cylindrical pipe is given by Q = πr²v, 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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