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.

Answer:

Step 1 of 6:

Given that, the flow rate of water through a cylindrical pipe is given by

Where, r is the radius of the pipe and v is the flow velocity.