LOGOS Learning · 8
Flow distribution in pipe branches: two branches share the same pump
In a branched network the flow splits so that both branches leave the node with the same energy: H_node = z_top,A + hf,A = z_top,B + hf,B, with Q_total = Q_A + Q_B. The pump runs where its curve meets the combined system curve.
Water takes the easiest path. Close the valve on branch B and see where the spare flow goes.
Quick test
Three questions about this lesson. Got one wrong? The explanation shows right away.
1. How does flow split between the branches from the node?
2. Closing the valve on branch B, branch A…
3. Both branches start from the same node. So they…
Why this happens
Arrows compare with valve B fully open. Highlighted terms have changed.
Continuity at the node
All the water that reaches the node leaves through the two branches.
Energy at the node
Both branches start at the same node with the same energy, and each spends it on elevation up to the top of its own pipe plus losses. When B closes, Hnode rises and there is more head to push water through A.
Pump, suction and main line
With less total flow, the pump climbs its own curve and delivers more head.
What PIT-01 reads
The PIT is on the main line, before the node: it reads the node energy plus the loss of the stretch up to it. Closing B raises Hnode, and the main-line pressure goes up with it.
Teaching pump with an illustrative curve.
Formulas in plain text
- Continuity at the node
Q_total = Q_A + Q_B- Q_total = flow in the main line (m3/h) · Q_A, Q_B = flow in each branch (m3/h)
- Energy at the node
H_node = z_top,A + hf,A = z_top,B + hf,B- H_node = head at the node (m) · z_top,A, z_top,B = elevation of the top of each branch pipe (m) · hf,A, hf,B = head loss in each branch, valve included (m)
- Pump head
H_pump(Q_total) = hf_suc + hf_main + H_node- H_pump = pump head at the total flow (m) · hf_suc = suction loss (m) · hf_main = main-line loss up to the node (m)
- Main-line transmitter reading
p_PIT = rho * g * (H_node - z_PIT + hf_PIT->node - v^2 / (2 * g))- p_PIT = gauge pressure at the transmitter (Pa) · z_PIT = elevation of the pressure tap (m) · hf_PIT->node = loss from the tap to the node (m) · v = main-line velocity (m/s) · rho = density (kg/m3)
Frequently asked questions
How does flow split between two pipe branches?
Each branch takes the flow at which its elevation plus its losses equals the common node head. The branch with the lower discharge or the smaller resistance gets more flow, and the sum of both must equal the main-line flow.
What happens to the other branch when one valve closes?
Closing one branch reduces total flow, so the pump climbs its curve and delivers more head. The node head rises and the open branch receives more flow than before, even though the total dropped.
Why does the higher branch get less flow?
Part of the node head is spent just lifting water to the top of that branch, so less is left for friction. With equal pipes, the branch with the higher discharge always gets the smaller share.
How are larger pipe networks solved?
With the same two laws, continuity at each node and energy balance along each path, solved iteratively by methods such as Hardy Cross or the global gradient method used in EPANET.