
Differentiation problem
A cylindrical tank contains water to depth h. The surface area, Aw is constant, while the orifice in the
base has area Ao. As the water leaves the container, the water
level will vary with time, t.
Torricelli’s law assumes that the flow rate through the orifice,
v, can be estimated by equating the kinetic energy of the water
as it exits, 1/2mv^2 and the potential energy mgh, giving the flow
rate as:
v = 2gh .
a) Show by derivation that the governing equation for h is
dh/dt=(Ao/Aw)*sqrt(2gh)
Hint: Consider the relationship between the change in volume
of water in the container and h.
Can anyone help solve this? cheers