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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(r) = − R² 
∂p 
1 − r² 4μ ∂x R²
where ∂p/∂x is a constant
The average velocity of fluid in the pipe is
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− R² ∂p 8μ ∂x -
− R² ∂p 4μ ∂x -
− R² ∂p 2μ ∂x -
− R² ∂p μ ∂x
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Correct Option: A
| u = − | | − | | | 1 − | | |||
| 4μ | dx | R |
dQ =u (2πrdr)
Solving, we get
| Q = − | | − | | ||
| 8μ | dx |
Now Q = Area ´ average velocity
| ∴ uav = | = | ||
| Area | πR2 |
| or uav = | | | ||
| 8μ | dx |
