# Expression for height of water as a function of time given flow rate in and out

1. Oct 2, 2008

### rewrew

1. The problem statement, all variables and given/known data

Consider the filling of a horizontal wedge-shape trough of height H, length, L, and width, B with water. (Imagine a water trough for horses with ends that are matching triangles). The volumetric flow rate of water in is given by Qi and the flow rate out by Qj. Obtain an algebraic expression for the change in height of the water in the trough as a function of time.

2. Relevant equations

no idea, open ended question

3. The attempt at a solution

I tried starting with a mass flow rate balance:

dm/dt = p dA/dt v = (Qi-Qj)p

p=density of liquid
v=velocity
A=area

But then I thought maybe I should try doing something with volume?
(Qi-Qj)t= volume in trough
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 2, 2008

### Rake-MC

$$\frac{dH}{dt} = \frac{dH}{dV} \frac{dV}{dt}$$