eulers method help question

[djspuddy]

here is a pic ive drawn up to do with my problem http://www.mathhelpforum.com/math-help/ ... method.jpg

It is a tank fed by 2 streams with volumetric flow rates A& B - the tank drains naturally through C, The outlet flow rate C is known to be proportional to the liquid level in the tank.
question 1 = if C is shut and the tank is empty , calculate time taken for the tank to fill.

question 3 = calculate the steady state liquid level in the tank for the given conditions

question 4 = Assume that the system is at steady state with the inlets given, demonstrate how the system would respond dynamically to attain steady state if inlet A is was stopped. Show hand calculations for 5 iterations of the Euler method using step size of 20.

im just really stuck on question 4 - question 1 -3 i think im ok on.

 

[galactus]

It would appear you have the incorrect time for the tank to fill.

It is a 24000 liter capacity tank. If it is being filled with A and B together at 150 L/min, that would take 160 minutes to fill.

Also, try using the same units for everything. Maybe Liters instead of cubic meters. The outlfow is given in \(\displaystyle \frac{m^{2}}{s}\). Square meters per second?. That is area, not volume. Unless this means the cross sectional area of the drain hole in square meters. .0005 square meters is 5 cm^2. Or maybe it is .0005 m^3/sec outflow rate. That would be .5 L/sec outlfow rate.

\(\displaystyle \frac{dh}{dt}=\frac{a}{A}\sqrt{2gh}=k\sqrt{h}\)

The height of liquid in the tank at time t is then given by \(\displaystyle h(t)=\left(\sqrt{h_{0}}-k\cdot \frac{t}{2}\right)^{2}\)

\(\displaystyle h_{0}\) is the height of the tank.

The time to empty (with no inflow) is given by \(\displaystyle t_{e}=\frac{2\sqrt{h_{0}}}{k}\)

where \(\displaystyle k=\frac{a}{A}\sqrt{2g}\)

'A' is the cross sectional area of the tank and 'a' is the cross sectional area of the drain hole, 'g' is the gravity constant. Which is \(\displaystyle 9.81 \;\ \frac{m}{s^{2}}\)