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## Homework Statement

I'm going to regulate a tank using a PID-controller. I want to simulate this in MATLAB though and met a problem while calculating the mathematical model.

The problem is the following: The three valves are either fully open or fully closed. The diameter in the pipes are all equal. If I use Bernoullis equation on the tank if only one of the valves are open, it's pretty straight forward to calculate the water flow. But how do the waterflow change if one or two more valves are opened? My intuition says the flow changes, but my calculations say they dont. Any help or push in the right direction is greatly appreciated!

http://imgur.com/yYzAB9v

## Homework Equations

Bernoulli:

https://en.wikipedia.org/wiki/Bernoulli's_principle

Darcy-Weisbach

https://en.wikipedia.org/wiki/Darcy–Weisbach_equation

## The Attempt at a Solution

I used bernoulli and calculated the flow through the pipes with only one valve fully opened. When multiple ones are open at the same time I dont know how to fit that in the equation to calculate the sum of waterflow out of the tank depending on the hight of the water in the tank.