The flow rate of water through a cylindrical pipe is given

QUESTION:

The flow rate of water through a cylindrical pipe is given by \(Q=\pi r^{2} v\), where \(r\) is the radius of the pipe and \(v\) is the flow velocity.

a. Assume that \(r=3.00 \pm 0.03\) and \(v=4.0\pm0.2\mathrm{\ \ m}/\mathrm{s}\). Estimate \(Q\), and find the uncertainty in the estimate.

b. Assume that \(r=4.00\pm0.04\mathrm{\ m}\) and \(v=2.0\pm0.1\mathrm{\ m}/\mathrm{s}\). 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.

Equation Transcription:

Text Transcription:

Q = pi r^2 v

r

v

r = 3.00 pm 0.03 m

v = 4.0 pm 0.2 m/s

Q

r = 4.00 pm 0.04 m

v = 2.0 pm 0.1 m/s