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When a viscous liquid flows through a tube in a laminar flow, why is its velocity highest at the center?

I understand the concept of shear viscosity and why the liquid in contact with moving plate has highest velocity. That's because of viscosity itself. But, I cannot understand how it explains liquid flow in a tube or whether it explains at all.

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When a viscous liquid flows through a tube in a laminar flow,why is its velocity highest at the center?

Because the boundary condition is that it's zero at the walls? Does that answer your confusion? It shouldn't seem surprising that the point furthest from the walls (the center) is the highest velocity, considering that the fluid exactly at the wall is at exactly zero velocity.

I believe it's the Hagen-Poiseuille equation that handles the specifics. With laminar flow, we're talking about equations that are 100% solvable algebraically. That solution is:

$$ v = - \frac{1}{4 \eta} \frac{\Delta P}{\Delta x} (R^2 - r^2) $$

This equation uses $r$ for distance from the center. When that is zero, you're at the center-line, and that above expression has the highest value. You can go look up the exact steps for how to get this expression from the fluid momentum equation itself, which is more-or-less a statement of the definition of viscosity.

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  • $\begingroup$ understanding the Poiseuille equation is a bit hard for me,but thanks!i do get an overall idea. $\endgroup$ – soumyadeep Oct 22 '13 at 17:47
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    $\begingroup$ @soumyadeep Well you shouldn't try to understand the entire thing. If you can understand the directions of the vector quantities it should be clear enough. The fluid velocity is different everywhere, but it's always in the same direction, which is straight down the pipe. Then the viscous friction follows as the derivative of velocity, so on and so fourth. $\endgroup$ – Alan Rominger Oct 22 '13 at 18:00

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