The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression $u\left( r \right) = \frac{{ - {R^2}}}{{4\mu }}\left( {\frac{{dp}}{{dx}}} \right)\left( {1 - \frac{{{r^2}}}{{{R^2}}}} \right)$ , where $\frac{dp}{dx}$ is a constant. The average velocity if fluid in the pipe is

Question

The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression $u\left( r \right) = \frac{{ - {R^2}}}{{4\mu }}\left( {\frac{{dp}}{{dx}}} \right)\left( {1 - \frac{{{r^2}}}{{{R^2}}}} \right)$ , where $\frac{dp}{dx}$ is a constant. The average velocity if fluid in the pipe is

TuteeHUB · Accepted Answer

$- \frac{{{R^2}}}{{4\mu}}\left( {\frac{{dp}}{{dx}}} \right)$

TuteeHUB · Answer

$-\frac{{{R^2}}}{{8\mu}}\left( {\frac{{dp}}{{dx}}} \right)$

TuteeHUB · Answer

$- \frac{{{R^2}}}{{2\mu}}\left( {\frac{{dp}}{{dx}}} \right)$

TuteeHUB · Answer

$-\frac{{{R^2}}}{\mu}\left( {\frac{{dp}}{{dx}}} \right)$

1.	The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression \(u\left( r \right) = \frac{{ - {R^2}}}{{4\mu }}\left( {\frac{{dp}}{{dx}}} \right)\left( {1 - \frac{{{r^2}}}{{{R^2}}}} \right)\) , where \(\frac{dp}{dx}\) is a constant. The average velocity if fluid in the pipe is
A.	\(-\frac{{{R^2}}}{{8\mu}}\left( {\frac{{dp}}{{dx}}} \right)\)
B.	\(- \frac{{{R^2}}}{{4\mu}}\left( {\frac{{dp}}{{dx}}} \right)\)
C.	\(- \frac{{{R^2}}}{{2\mu}}\left( {\frac{{dp}}{{dx}}} \right)\)
D.	\(-\frac{{{R^2}}}{\mu}\left( {\frac{{dp}}{{dx}}} \right)\)
Answer» B. \(- \frac{{{R^2}}}{{4\mu}}\left( {\frac{{dp}}{{dx}}} \right)\)

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