The velocity profile in fully developed laminar flow in a circular pipe of inner radius R = 2 cm, in m/s, is given by u(r) = 4(1 - r2/R2). Determine the average and maximum velocities in the pipe and the volume flow rate.
Added by Zachary J.
Step 1
The maximum velocity occurs at the center of the pipe where r = 0. So, substitute r = 0 into the velocity profile equation: u_max = 4(1 - 0) = 4 m/s Show more…
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For fully developed laminar pipe flow in a circular pipe, the velocity profile is given by $u(r)=2\left(1-r^{2} / R^{2}\right)$ in $\mathrm{m} / \mathrm{s}$ where $R$ is the inner radius of the pipe. Assuming that the pipe diameter is $4 \mathrm{cm},$ find the maximum and average velocities in the pipe as well as the volume flow rate.
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