Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2009
Medium
The velocity profile of a fully developed laminar flow in a straight circular pipe is given by u(r) = -(R²/4μ)(dp/dx)(1-r²/R²), where dp/dx is a constant. The average velocity of fluid in the pipe is
- -R²/(8μ)(dp/dx)
- B-R²/(4μ)(dp/dx)
- C-R²/(2μ)(dp/dx)
- D-R²/μ(dp/dx)
Explanation
For the parabolic Poiseuille profile, the maximum velocity (at r=0) is -(R²/4μ)(dp/dx), and the average velocity over the circular cross-section is exactly half the maximum: Vavg=Vmax/2=-(R²/8μ)(dp/dx).
Source: GATE ME 2009 (2009)
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