Hydraulic

Flow Potential of a New Branch from Pressures Logged on the Network

Before connecting a new consumer to a pressurized network that already exists, the question is how much the branch will be able to draw. The answer comes from the pressures logged at the tap point, the elevation to the consumer and the losses of the branch itself.

When to use

Use it when a new consumer will be connected to an existing pressurized network (process water, cooling water, service water, fire water) and you need to know, before detailed design, whether the branch delivers the required flow. The inputs are field data: a pressure log at the tap point over a representative operating period (24 h or more), with the maximum at off-peak demand and the minimum at peak. The calculation shows the flow for every possible tap pressure and highlights the design scenario, with a margin for the pressure drop the new consumer itself causes.

The problem

An existing pressurized network already serves several consumers, and a new one will be connected to it. Before detailing the branch, the designer needs to know how much that branch can take from the network. There is no new pump or elevated tank to size: the source is the network itself, and what is known about it is the pressure at the tap point.

Where the data comes from

The main input is a pressure log at the tap point over a period that represents operation: at least 24 hours, covering equipment start-ups and shift changes. Two numbers come out of the log:

the maximum pressure, which happens at off-peak demand;
the minimum pressure, which happens at peak.

The maximum is not the shut-off pressure. The network keeps flowing at off-peak, only less. That difference matters for the source curve, described below.

The branch balance

Between the tap and the consumer, the available pressure splits into four parts: the pressure the consumer requires at its inlet, the elevation, the loss in equipment in series and the losses of the branch itself. The first three do not depend on flow; the last grows with its square. The branch flow is the one that closes this balance, found by bisection to 10⁻¹⁰ m³/h.

The losses use the same engine as the other LOGOS calculators: Darcy-Weisbach with the Colebrook-White friction factor and K coefficients per fitting, with the Darby 3-K method for viscous fluids.

The drop the new consumer causes

The minimum logged pressure is the one before the connection. When the new consumer opens, the total network flow increases and the tap pressure falls further. There are two ways to handle it:

Margin: the user estimates the drop as a percentage of the minimum logged pressure. The scenario table shows the flow at the maximum, at the minimum and at the minimum reduced by 5 % to 30 %, so you can see how much the result depends on the margin.
Source curve: if the network flow is known at peak and off-peak, the supply is represented by a curve fitted on those two points, and the design pressure comes from the intersection of that curve with the branch curve. Existing consumers are assumed at constant flow, which is conservative.

Without the off-peak flow, the curve is fitted as if the maximum were at shut-off. It comes out flatter than the real one and the computed drop is smaller: the result sits on the optimistic side, and the calculator warns about it.

Flow potential is not operating flow

The calculation assumes the branch valve fully open. The result is the ceiling of the flow at each pressure. If the branch passes more than the consumer needs, the valve throttles the difference; if it passes less, the branch does not meet the demand. The velocity check at the maximum pressure shows the worst case for erosion and noise, with the valve open at off-peak demand.

Formulas and fundamentals

Head available for the branch H_avail = P_tap − P_req − Δz − h_eq

P_tap is the pressure at the branch point (m of liquid); P_req the pressure required at the consumer inlet (0 for free discharge); Δz the elevation from the tap to the consumer (positive when the consumer is above); h_eq the loss in equipment in series (strainer, meter, exchanger).

Friction loss (Darcy-Weisbach) h_friction = f · (L/D) · v²/(2g)

f is the Darcy friction factor; L the branch length (m); D the internal diameter (m); v the mean velocity (m/s). The loss grows with v², so the flow comes from an iterative solution.

Friction factor (Colebrook-White) 1/√f = −2·log₁₀( ε/(3.7·D) + 2.51/(Re·√f) )

For Re ≥ 4000, solved explicitly (Serghides estimator refined by Newton steps). Below 2000, f = 64/Re; between 2000 and 4000, Dunlop interpolation.

Minor losses h_minor = ΣK · v²/(2g)

ΣK is the sum of the branch fitting coefficients, including the tee off the header. For fluids above 20 cSt each coefficient rises by the Darby 3-K method.

Design pressure with a margin P_design = P_min · (1 − margin)

The minimum logged pressure will drop when the new consumer comes online. The margin is the user's estimate of that drop; the scenario table shows the flow for several margins.

Source curve on the two logged points P(Q) = P_min − k·[(Q_peak + Q)^n − Q_peak^n], k = (P_max − P_min)/(Q_peak^n − Q_offpeak^n)

When the network flow is known at the times of maximum (Q_offpeak) and minimum (Q_peak) pressure, the network supply becomes a curve and the drop at the tap comes from its intersection with the branch. n = 2 corresponds to rough turbulent flow; n = 1.85 is the exponent used in hydrant flow test extrapolation.

Standards & methods

Darcy-Weisbach equation (friction loss)
Colebrook, C. F. (1939) — friction factor in commercial pipes
Darby, R. — Chemical Engineering Fluid Mechanics, 2nd ed. (3-K method)
Azevedo Netto — Manual de Hidráulica (K coefficients per fitting)
NFPA 291 (hydrant flow test extrapolation, exponent 1.85)

Typical reference values

Quantity	Typical range	Note
Usual velocity in water branches	1.0 to 3.0 m/s	Above 3 m/s loss and noise rise; above 5 m/s erosion and water hammer become a risk.
Minimum pressure log period	24 h	It must cover the off-peak and the peak of the network, including start-ups and shift changes.
Absolute roughness — new carbon steel	0.045 mm	Welded steel: ~0.06 mm; stainless: ~0.025 mm; HDPE: ~0.007 mm.
K of the side-outlet tee (branch)	1.3	Dual-branch tee: 1.8; run-through tee: 0.6.
Pressure conversion (water)	10 m ≈ 0.98 bar	For other fluids, P[bar] = P[m] · 0.0980665 · ρ[t/m³].

Worked example

Pressurized consumer branched off a process water main

Inputs

Maximum logged pressure (off-peak): 62 m
Minimum logged pressure (peak): 45 m
Drop margin at the tap: 10 %
Pressure required at the consumer: 15 m
Elevation tap → consumer: 4 m
Equipment loss: 2 m
Branch 1.1/2" Sch 40 (ID 40.9 mm): 120 m
Fittings (ΣK): 10.0 —

Results

Estimated flow (design): 10.57 m³/h
Velocity (design): 2.23 m/s
Friction factor: 0.0227 —
Flow at maximum pressure: 15.54 m³/h
Velocity at maximum pressure: 3.29 m/s

With the minimum logged pressure reduced by 10 % (40.5 m at the tap), 19.5 m of head is left for the branch, and it passes 10.57 m³/h: it meets a 10 m³/h consumer with little spare. At off-peak demand, with the valve fully open, the same branch would pass 15.54 m³/h at 3.29 m/s, above the usual: the branch valve has to limit the flow. If the network flow is known at peak (80 m³/h) and off-peak (30 m³/h), the source curve gives a 12.1 % drop at the tap and 10.31 m³/h, slightly below the result with the 10 % margin.

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Common mistakes

Using a single gauge reading: without a continuous log you cannot tell whether the pressure was the peak or the off-peak of the network.
Taking the maximum pressure as the shut-off pressure: in a field log it is the off-peak demand, with the network still flowing.
Leaving the required pressure at zero for a pressurized consumer: the calculation assumes free discharge and overestimates the flow.
Forgetting the branch tee: the loss at the header side outlet belongs to the branch.
Reading the flow potential as the operating flow: the calculation assumes the branch valve fully open, and the real flow will be set by the valve or the consumer.
Ignoring the drop the new consumer causes: the minimum logged pressure is the one before the connection.

Frequently asked questions

Why log the pressure for 24 hours instead of reading the gauge once?

Because the pressure in an existing network changes with the demand of the other consumers. The log shows the off-peak (maximum pressure) and the peak (minimum pressure). The peak decides whether the new branch delivers at the worst moment, and the off-peak decides the highest velocity it will see.

Is the maximum pressure the shut-off pressure?

No. In a field log the maximum is the off-peak demand: the network is still flowing, only less. The pressure with zero network flow is higher. That is why, on the source curve, the off-peak flow is an input and not zero.

What is the drop margin for?

When the new consumer opens, the total network flow increases and the tap pressure falls below the minimum logged. The margin is the estimate of that drop. The scenario table shows the flow for margins from 5 % to 30 %, so you can see how much the result depends on it.

When should I use the source curve instead of the margin?

When you know the network flow at both logged moments, from a header meter or a balance of the consumers. With two points the supply becomes a curve and the drop at the tap is computed. If the off-peak flow is unknown and left at zero, the curve is flatter than the real one and underestimates the drop.

Is the result the flow the consumer will receive?

It is the flow potential: the most the branch passes at that pressure with the valve fully open. The operating flow will be set by the branch valve or the consumer itself. If the potential is lower than the target, the branch does not meet it.

How do I handle a consumer that discharges to atmosphere?

Enter a required pressure of zero and add the pipe exit (K = 1) to the fittings, to account for the discharged kinetic energy.

Glossary

Tap point: The point on the existing header where the new branch starts, where the pressures are logged.
Flow potential: The flow the branch passes with the valve fully open at a given tap pressure. It is the ceiling; the operating flow is set by the valve or the consumer.
Off-peak and peak demand: The moments of lowest and highest network consumption in the logged period. At off-peak the tap pressure is highest; at peak, lowest.
Source curve: The relation between the tap pressure and the total flow drawn from the network, fitted on the two logged points.
Available head (H_avail): The part of the tap pressure left to overcome the branch losses, after subtracting the required pressure, the elevation and the equipment loss.

Understand the concept

Free interactive lessons from LOGOS Learning: change the inputs and watch the physics behind this calculator.