- #1
Nevonis
- 8
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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:
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
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
..It just seems to easy.
If you know of any articles or books, or know it yourself, please give me a shout.
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.