# Finding pressure in a branch with known flows

1. May 21, 2013

### Nevonis

Hey!

So we have these equations that describe flow through and pressure in a pipe.
∂p/∂t = -β/A * ∂q/∂x​
∂q/∂t = -A/ρ * ∂p/∂x - F/ρ + g*Acos(α(x))​
where A = cross area, β = bulk constant for water, p = pressure, q = flow, ρ = density, g = gravity constant, F = forces due to friction, α = angle between gravity and direction of flow

Discretized, we get this (simplefied, linearized with linear friction)
∂pi/∂t = β/(A*l) * (qi-1-qi)​
∂qi/∂t = A/(l*ρ) * (pi - pi+1) - fqi
Where, f = friction constant.
So, basically, for pressure at a certain point (i), we have that
∂pi/∂t = C * (qin-qout)​

I'm wondering if there are any similar equations that describes the pressure at a branch with known flow in and flow out (through both branches).

2. May 21, 2013

### thecolty

Sorry Nevonis, I am unable to help with your question.

However, I came to the forum looking for clues to a problem I am having in a closed loop system with 3 branches, perhaps you or someone else would have an answer...

I have a chilled water loop that travels up into the ceiling 18', diagonally 60', then back down into another room 18'. The line is then divided into 3 branches that I adjust the pressure of to control my flow (9PSI, 10PSI, and 3PSI). The three lines then travel through the tool being cooled and back in three pipes to the room where the chiller is located, about 100' away.

The three lines then recombine after going through a flow meter. The flow meters indicate that each line is very close to one another in flow (~14 GPH).

My question is:
Can the ~14GPH be assumed to be an inaccurate measurement of what the flows are immediately after the pressure regulators, before entering my equipment?

3. May 22, 2013

### Nevonis

I dont see how you could not. Flow into the loop = flow out of the loop. The pressure just decides what the different flows are in each branch.

4. May 22, 2013

### thecolty

My thinking was at the end of the three lines where they recombine, right after the 3 0-60GPH float flow meters there was a back pressure that was causing the readings to be incorrect.

5. May 22, 2013

### Nevonis

Hmm, I wouldn't know.. Sorry

6. May 22, 2013

### Aero_UoP

What about Bernulli's equation? If your flow is incompressible you can apply it between any arbitrary points if the flow is also irrotational or between points on the same streamline if the flow is rotational.