Flowmetry: find height of fluid in cylinder

[Name15]

Homework Statement

A cylinder with varying diameters is being filled and emptied at the same time. The time is measured.
I know Flow rate into cylinder. How do I find the height of fluid in the cylinder at a particular time?

The diameter of the hole is 0.005m.
The diameter of the bottom of the cylinder is 4cm.
The diameter of the top of the cylinder is 6cm.

I don't know Qout nor height, h.

Homework Equations

Qout= A. Cd. SQRT(2.g.h)

The Attempt at a Solution

At time=0 sec: change in height of fluid is 0
At time=1 sec: change in height of fluid is (Qin-Qout)/Area of cylinder

 

[BvU]

You have a first-order differential equation to solve:
$d\over dt$ holdup = Q_in - Q_out
where
holdup is a function of h(t)
and
Q_out is a function of h(t)

Your initial condition (if what you write is correct) is $d\over dt$ holdup = 0 at t=0

Substitute the appropriate expressions for holdup(h) and Q_out(h)