If you have water flowing through an 8 inch diameter storm sewer at a rate of 12 cubic feet per min. Howe would you calculate the linear velocity in feet per second of the flow?

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Ok... if the pipe is totally filled with water as it exits then you can say that you have a 'disk' of water with area (a) = (pi)r^2

r = radius of the pipe = (8/2)" = 4" = 1/3 ft (need to keep everything in the same units)

a = 0.35 ft^2

a volume of 12 (ft^3)/min means you have a cylinder of water that has an area as described above but has a length of:

Volume(v) = area x length
==> v = aL
==> L = v/a = [12 ft^3]/[0.35 ft^2] = 34.28 ft

So...

... in one minute you have a length of water of 34.28 ft that is traversed.

That's a rate of 34.28 ft/min... or in more familiar units:

34.28 ft/min = 0.57 ft/s [This is about 0.39 mph for your reference]