Understanding Fluid Velocity in a Normal Tube

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What determines the velocity of a fluid, in a normal tube?
 
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The pressure pushing it along.
The inertia will depend on the density
The viscosity
Any friction with the walls
At higher flow rates - turbulence.
 
Does maximum velocity occur in the center of flow, decreasing outward to zero velocity at the tube wall? Are velocities of this flow a negatively linear function of radius?