Tank question (1 Viewer)

[Thylacine]

Can anyone help me with this.
The flow rate of water out of a hole in a tank is known to be proportional to the squareroot of the height of water above the hole.
That is,

dV/dt = sq root(h)

Suppose the tank has constant cross-sectional area A, show that the height of the water in the tank is given by

h = ((-kt + C)/2)²

If the tank is 9m high, and it takes 5hrs for it to drain from full to half full, how much longer will we have to wait until it is completely empty?

 

[bottleofyarn]

With rate of change questions, you usually have to use the given rate (dV/dt) and multiply it with another rate you derive to find another rate in terms of t. In this case, you probably have to find dh/dt and integrate (the -kt+C hints at this). Remember that you can treat dy/dx as a fraction.