Tank Mass Balance Calculation for Designing w/ Automatic Float Switch

[mudweez0009]

I'll be using a mass balance calc for a tank design at work. We are designing a tank that has an automatic float switch on it, attached to a valve which will start filling the tank when the water level drops below a certain point. This tank is intended to drain quickly (flow rate not known at this time), but the fill rate will not be as large as the discharge rate. I want to have a representative model of the tank so we can ensure it will function properly.

Anyway, I just want to double check to see if I did this correctly. I think I did, as its relatively simple, but another set of eyes never hurts.

What I have done so far:
I'll skip the intro equation sorting, and get to the generic equation below:
A(dh/dt) = Q_in - Q_out

Where,
A = Tank area
h = tank height
Q = flow rate

My attempt:
I moved "A" and "dt" to the right-hand side, and got:
dh = (Q_in - Q_out)/A * dt

I then integrated to get h(t):
h(t) = [(Qin-Qout)/A] * Δt

I think this would be correct, as the units leave me with "ft"
Q (ft³/s) * 1/A (1/ft²) * Δt (s) = ft.

 

[BvU]

So far, so good ! Carry on !