Parabolic velocity profile problem?
I not keeping my hopes up for help on this but it's worth a shot.
In the laminar flow of a fluid through a pipe of circular cross section the velocity profile is exactly a true parabola. the volume of the paraboloid represents the rate of discharge. Prove that for this case the ratio of the mean velocity to the maximum velocity is 0.5. Huh???
Comments
-------top of pipe --------------------
\
. \
. | <-- This is the max, velocity=x
. / <-- This is the mean, the average, velocity = (x+0)/2=0.5x
/ <-- this is the min. The fluid here doesn’t move in theory*, velocity=0
-------bottom of pipe ---------------
*doesn't move right on the pipe wall
Here is a better image (fig 3):
http://www.google.com/imgres?imgurl=http://www.med...
Check out the definition of Mean average
http://en.wikipedia.org/wiki/Arithmetic_mean