Question

The rate of volume flow of water through a canal is found to be a function of cross -section of canal and velocity of water.show that the rate of volume flow is proportional to the velocity of flow of water

Answer 1

Rateflow=C*area*velocity given

Now, to prove this, look at a sliver of the line, area A, length L. Call that volume deltaV.

Now assume some flow in the canal, so that the speed down the canal is such that the length L passes in t seconds.
The velocity then is L/t. The amount of flow then is Area*L

amountflow= Area*L
amountflow/time=area*L/T
flow rate=area*velocityflow

In the basic equation, the constant C allows for unit conversions.

Answer 2

V=kvA^-2