# Pressure in a branch

1. May 17, 2013

### Nevonis

Hello guys

So I'm trying to model flow through a branched pipe. The equations I've used are the standard partial differential equations for a hydraulic transmission line:
∂p/∂t = -β/A * ∂q/∂x​
∂q/∂t = -A/ρ * ∂p/∂x - F/ρ + g*Acos(α(x))​

I've discretized and linearized these so that I can model it with boundary conditions, q_in and p_out, and they look like this

∂pi/∂t = β/(A*l) * (qi-1-qi)​
∂qi/∂t = A/(l*ρ) * (pi - pi+1) - fqi

Think staggered grid; q_in, p_1, q_1, p_2, q_2 ... p_N, q_N, p_out.

My problem is that I can't find out how to model the branch itself. It obviously has one inlet and two outlets, can I model it as easy as

∂pbranch/∂t = β/(A*l) * (qin-qout1-qout2)​

..It just seems to easy.

If you know of any articles or books, or know it yourself, please give me a shout.

2. May 17, 2013

### SteamKing

Staff Emeritus
Without knowing any other details about your model, the pressure drop in each branch should be equal, IMO.

3. May 18, 2013

### Nevonis

The branches are not the problem. The problem is the branch itself, how the dynamic model for the branch will look like. This area: http://static.quality-tuning.com/images/stories/virtuemart/product/stainless-steel-y-pipe-l150-(1).jpg [Broken] (just an example)
The form of the branch won't matter. I'm modeling it in 1D without thinking about gravity or anything else.
I'm writing this in Matlab and simulink, and it's a dynamic model as I wrote which should react to changes in the boundary conditions (being flow in and pressures on the two outlets.)

It's in state space form x_dot = Ax+Bu where u are the boundary conditions.

If you need more spesific info about the model, please ask.

Last edited by a moderator: May 6, 2017
4. May 18, 2013

### SteamKing

Staff Emeritus