MEI, differential equations, rate of change of volume

Bump

let the water velocity from the hole = u

let the volume of water remaining above the hole = V

let the cross section area of the cylinder = A

let the cross section area of the hole = a

the volume of water leaving the hole in one second = au = -dV/dt

we are told that u ∝ √y

so u = j√y for some constant j

this means that au = aj√y = -dV/dt

or dV/dt = -aj√y



now dV/dt = dV/dy * dy/dt

so dy/dt = dV/dt / dV/dy = -aj√y /dV/dy

since the tank is cylindrical the volume of water above the hole is Ay

V = Ay

dV/dy = A

so

dy/dt = -aj√y * A = -aAj√y = -k√y since aAj are all constants.

I understand​ everything, except the initial part, how do you get dV/dt =au ?