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Hydraulic Balancing Calculator

Calculate radiator design flows, Darcy pipe losses, required valve kv and pump head for up to six parallel circuits. Compare entered kv values and watch the flow split.

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Published 28. October 2026 · version 1

#balancing valves #Colebrook #Darcy–Weisbach #hydraulic balancing #kv #manifolds #pump head #radiators

This hydraulic balancing calculator sizes one to six parallel radiator circuits connected to a common supply and return manifold. It is for heating engineers, students and homeowners preparing a technical discussion with an installer. It turns radiator heat loads into design water flows, estimates branch pressure losses, and identifies the critical circuit that sets the minimum pump duty.

Start with each radiator's required heat output at the intended operating temperatures. Enter the design supply-to-return temperature drop, the actual internal pipe diameter, and the combined supply and return pipe length for each loop. Add the fitting loss coefficients and any radiator, lockshield or other component pressure losses at that loop's design flow. Keep the balancing valve out of those other losses. Enter water density, heat capacity and viscosity at a consistent mean operating temperature; the defaults approximate liquid water at 60 °C.

Choose a minimum balancing-valve pressure allowance. The calculator adds it to each branch's other losses and uses the largest requirement as the minimum manifold pressure. It then adds the entered common plant and main-pipe loss, evaluated at the total design flow, to obtain the pump head. In a filled closed heating circuit, building height is not added to this circulation head. Static filling pressure and expansion-vessel sizing are separate tasks.

The valve table gives the required conventional kv in m³/h at a 1 bar water pressure drop, together with US Cv at 1 psi. Enter the kv corresponding to a proposed manufacturer preset to compare predicted flow with the design target. No manufacturer's preset table is reproduced, and a kv value is not itself a preset number. The metric/US switch converts supported physical quantities; both L/h and US gallon/minute flow columns are provided explicitly.

Press ▶ to animate the branch flows. The particles show relative volume flow in a schematic of equal drawn widths; they do not show actual pipe velocities or heat output. Switch between balanced design flows and flows with the entered kv values. The entered-kv comparison holds the manifold differential pressure fixed and solves each branch with Darcy friction recalculated. It does not find the operating point of a fixed-speed pump or predict how room temperatures change.

For people researching hydraulischer Abgleich berechnen, this tool explains the engineering calculation behind a balancing schedule. It does not calculate room heat losses, model shared distribution segments between successive radiator takeoffs, or replace measurements and commissioning. Split a larger installation into separately assessed manifolds and account for common losses separately.

This is not official proof for German subsidies or a certification of VdZ Procedure B. The VdZ individual-measures form dated 1 January 2023 is cited only as documentation context, reviewed on 27 October 2026. Check current funding requirements and the standard in force. Installation work and final commissioning belong to a qualified person.

How it is calculated

Design heat load is an input, established separately. For each radiator, conservation of energy gives

\dot m_i = \frac{Q_i}{c_p\Delta T},\qquad \dot V_i=\frac{\dot m_i}{\rho}.

Flows sum at the manifolds. This follows the target-flow method in Caleffi idronics 8 (2011), pp. 31–32; pp. 42–43 discuss manifold balancing.

For the entered round-trip length and actual bore:

v_i=\frac{4\dot V_i}{\pi D_i^2},\quad Re_i=\frac{\rho v_iD_i}{\mu},\quad \Delta p_{pipe,i}=f_i\frac{L_i}{D_i}\frac{\rho v_i^2}{2}.

Fittings contribute $\Sigma K_i\rho v_i^2/2$ . The Darcy factor is $64/Re$ below 2300. Above 4000, twelve fixed-point iterations solve

\frac1{\sqrt f}=-2\log_{10}\left(\frac{\epsilon/D}{3.7}+\frac{2.51}{Re\sqrt f}\right).

Between 2300 and 4000, linear interpolation joins the two endpoint factors; this is an author-selected approximation for an uncertain regime and triggers a warning. Penn State's Cimbala worked example, pp. 1–2, provides an independent Colebrook/Darcy benchmark.

Let $\Delta p_{other,i}$ include calculated pipes/fittings and the entered emitter/component loss. The minimum manifold differential is $\max_i(\Delta p_{other,i}+\Delta p_{min})$ . Its maximizing branch is the critical circuit, with the first reported if tied. A specified manifold differential can instead be assessed. The remaining pressure is assigned to each balancing valve:

\Delta p_{v,i}=\Delta p_{man}-\Delta p_{other,i},\qquad k_{v,i}=\dot V_{i,h}\sqrt{\frac{(\rho/1000)\,1\,bar}{\Delta p_{v,i}}}.

Here $\dot V_{i,h}$ and kv use m³/h. The density correction and kv/Cv convention follow Spirax Sarco, Control valve sizing for water systems, section 6.3. US Cv is computed by explicit flow and reference-pressure conversions.

Pump duty at total design flow is $\Delta p_{pump}=\Delta p_{man}+\Delta p_{common}$ and $H=\Delta p_{pump}/(\rho g)$ , with $g=9.80665$ m/s². No elevation term is added to a filled closed-loop circuit.

For entered kv values, forty-four bisections solve each branch's pressure balance at the selected fixed manifold pressure. Pipe friction is recalculated; emitter/component loss scales with flow squared. The upper flow bound is the valve-only flow. Pressure closure and thermal/flow conservation are checked. Animation uses these already-computed flows; particle positions alone depend on play time.

Assumptions

Steady, incompressible liquid water. Enter density, specific heat and viscosity at the same mean operating temperature. Rounded defaults approximate water at 60 °C; they are editable inputs, not a fitted water-property correlation. NIST's fluid-properties service is a suitable source for other temperatures.
All active radiator loops see the same manifold pressure. Each loop has one equivalent circular bore, the same entered absolute roughness, and a length that includes supply plus return. Manifold pressure variation is neglected.
The radiator load is the required output at the design conditions. This tool does not correct radiator catalogue ratings or calculate building heat loss.
Other branch losses are entered at branch design flow; common plant losses are entered at total design flow. Avoid counting any component twice. The entered-kv comparison scales other branch losses with flow squared.
The chosen minimum valve drop is a design allowance, not a statutory value, prescribed valve authority or manufacturer's recommendation. Available preset ranges and operating limits must be checked separately.
The schematic is original and not to scale. Equal drawn tube widths make particle speed proportional to branch volume flow, not actual bore velocity. Required kv labels remain design values in both animation modes.

Where it applies

Use for preliminary design and comparison of 1–6 parallel manifold-fed radiator circuits carrying liquid water. The pressure model assumes fully developed flow in circular pipes and relative roughness no greater than 0.05. The input ranges are engineering exploration limits, not guarantees of a suitable installation.

Transition between Re 2300 and 4000 is uncertain and flagged. The warning above a design velocity of 1 m/s is a review prompt, not a universal acceptance limit. Valve Reynolds corrections, cavitation, acoustic limits, compressible or two-phase flow, glycol, one-pipe systems and pressure-independent flow-regulating valves are outside this model. Check the valve maker's limits and measure flows during commissioning.

The minimum pump head is conditional on the entered losses and valve allowance. The entered-kv flows are evaluated at a fixed manifold differential; they are not the operating point of a pump curve. Common loss is specified at total DESIGN flow and is not recomputed for the comparison. A flow ratio must not be interpreted as a radiator heat-output ratio.

This tool is not official proof for subsidies and does not certify VdZ Procedure B. Documentation context is the VdZ BEG individual-measures form dated 2023-01-01, consulted 2026-10-27. It does not implement a funding eligibility rule. Obtain the current official documentation and check against the standard in force. Installation work and final commissioning belong to a qualified person.

References

Caleffi (2011), idronics 8, Hydronic Balancing, pp. 31–32, 42–43; target flows, pressure allocation and manifold balancing. https://www.caleffi.com/sites/default/files/media/external-file/Idronics_8_NA_Hydronic%20balancing.pdf
J. M. Cimbala, Penn State (February 2005), EES Solution for Example Problem — Major and Minor Losses in a Piping System, pp. 1–2. https://www.me.psu.edu/cimbala/me320web_Fall_2012/pdf/EES_Solution_Minor_losses_example_problem.pdf
Spirax Sarco, The Steam and Condensate Loop, Control valve sizing for water systems, section 6.3, examples 6.3.1 and 6.3.3. https://www.spiraxsarco.com/learn-about-steam/control-hardware-electric-pneumatic-actuation/control-valve-sizing-for-water-systems
VdZ, Confirmation of hydraulic balancing, BEG individual measures (2023-01-01); documentation context only, consulted 2026-10-27. https://files.vdzev.de/pdfs/hydraulischer-abgleich-einzelmassnahme/VDZ_Formular_HydrAbgleich_Einzelmassnahme_BEG.pdf
NIST Chemistry WebBook, SRD 69, Thermophysical Properties of Fluid Systems; water-property lookup. https://webbook.nist.gov/chemistry/fluid/

Inputs

Input	Symbol	Unit	Default
Radiator circuits Parallel loops on the same supply and return manifold.	`n_rad`		3
Design water temperature drop Supply minus return temperature at design heat load; a temperature difference.	`delta_T`	K	10
Manifold pressure	`pump_mode`		Calculate minimum required
Minimum valve pressure drop Design allowance for each balancing valve. Use the valve maker's requirement; 10 kPa is an illustrative starting value.	`dp_min`	kPa	10
Specified manifold pressure difference Pressure between the supply and return manifolds, excluding common plant losses.	`dp_set`	kPa	25
Common supply, return and plant loss Combined loss at total DESIGN flow, from a separate calculation or measurement. Do not include it again in branch lengths.	`dp_common`	kPa	5
Water density At mean design water temperature. Defaults approximate water at 60 °C; enter matching properties for your operating temperature.	`rho`	kg/m^3	983.2
Water specific heat capacity At mean design water temperature. Use 4185 J/(kg·K) as a rounded 60 °C value.	`cp`	J/(kg*K)	4185
Water dynamic viscosity Use a matching temperature for density, heat capacity and viscosity. Default: approximately 60 °C.	`mu`	mPa*s	0.466
Internal pipe roughness User estimate for all branches. Default is an illustrative smooth-pipe value, not a pipe catalogue specification.	`eps`	mm	0.007
Animate flow split	`animation_mode`		Balanced design flows
Flow animation time Press ▶. Particle speed is proportional to branch flow; the schematic is not to scale.	`t_anim`	s	3.7
Design heat load Required room or radiator output at the design conditions, not its uncorrected nameplate rating.	`Q1`	kW	1
Total branch pipe length Supply PLUS return length from the manifolds; both lengths are included once.	`L1`	m	8
Pipe internal diameter Actual bore, not nominal or outside diameter; one equivalent diameter per branch.	`D1`	mm	12
Sum of fitting loss coefficients Dimensionless ΣK for both flow and return fittings, referenced to this branch pipe velocity. Exclude the balancing valve.	`Z1`		4
Radiator and other component loss Loss at this branch's DESIGN flow, excluding the calculated pipe/fitting losses and the balancing valve. Scaled with flow squared for the kv comparison.	`pe1`	kPa	1
Entered valve kv at selected preset Conventional kv: water flow in m³/h at 1 bar drop. Enter a value from your maker's data; this is not a preset number or US Cv.	`kv1`	m^3/h	0.21
Design heat load Required room or radiator output at the design conditions, not its uncorrected nameplate rating.	`Q2`	kW	1.5
Total branch pipe length Supply PLUS return length from the manifolds; both lengths are included once.	`L2`	m	18
Pipe internal diameter Actual bore, not nominal or outside diameter; one equivalent diameter per branch.	`D2`	mm	12
Sum of fitting loss coefficients Dimensionless ΣK for both flow and return fittings, referenced to this branch pipe velocity. Exclude the balancing valve.	`Z2`		6
Radiator and other component loss Loss at this branch's DESIGN flow, excluding the calculated pipe/fitting losses and the balancing valve. Scaled with flow squared for the kv comparison.	`pe2`	kPa	1
Entered valve kv at selected preset Conventional kv: water flow in m³/h at 1 bar drop. Enter a value from your maker's data; this is not a preset number or US Cv.	`kv2`	m^3/h	0.34
Design heat load Required room or radiator output at the design conditions, not its uncorrected nameplate rating.	`Q3`	kW	2
Total branch pipe length Supply PLUS return length from the manifolds; both lengths are included once.	`L3`	m	30
Pipe internal diameter Actual bore, not nominal or outside diameter; one equivalent diameter per branch.	`D3`	mm	12
Sum of fitting loss coefficients Dimensionless ΣK for both flow and return fittings, referenced to this branch pipe velocity. Exclude the balancing valve.	`Z3`		8
Radiator and other component loss Loss at this branch's DESIGN flow, excluding the calculated pipe/fitting losses and the balancing valve. Scaled with flow squared for the kv comparison.	`pe3`	kPa	1
Entered valve kv at selected preset Conventional kv: water flow in m³/h at 1 bar drop. Enter a value from your maker's data; this is not a preset number or US Cv.	`kv3`	m^3/h	0.55
Design heat load Required room or radiator output at the design conditions, not its uncorrected nameplate rating.	`Q4`	kW	1
Total branch pipe length Supply PLUS return length from the manifolds; both lengths are included once.	`L4`	m	15
Pipe internal diameter Actual bore, not nominal or outside diameter; one equivalent diameter per branch.	`D4`	mm	12
Sum of fitting loss coefficients Dimensionless ΣK for both flow and return fittings, referenced to this branch pipe velocity. Exclude the balancing valve.	`Z4`		4
Radiator and other component loss Loss at this branch's DESIGN flow, excluding the calculated pipe/fitting losses and the balancing valve. Scaled with flow squared for the kv comparison.	`pe4`	kPa	1
Entered valve kv at selected preset Conventional kv: water flow in m³/h at 1 bar drop. Enter a value from your maker's data; this is not a preset number or US Cv.	`kv4`	m^3/h	0.25
Design heat load Required room or radiator output at the design conditions, not its uncorrected nameplate rating.	`Q5`	kW	1.5
Total branch pipe length Supply PLUS return length from the manifolds; both lengths are included once.	`L5`	m	22
Pipe internal diameter Actual bore, not nominal or outside diameter; one equivalent diameter per branch.	`D5`	mm	12
Sum of fitting loss coefficients Dimensionless ΣK for both flow and return fittings, referenced to this branch pipe velocity. Exclude the balancing valve.	`Z5`		6
Radiator and other component loss Loss at this branch's DESIGN flow, excluding the calculated pipe/fitting losses and the balancing valve. Scaled with flow squared for the kv comparison.	`pe5`	kPa	1
Entered valve kv at selected preset Conventional kv: water flow in m³/h at 1 bar drop. Enter a value from your maker's data; this is not a preset number or US Cv.	`kv5`	m^3/h	0.35
Design heat load Required room or radiator output at the design conditions, not its uncorrected nameplate rating.	`Q6`	kW	2
Total branch pipe length Supply PLUS return length from the manifolds; both lengths are included once.	`L6`	m	35
Pipe internal diameter Actual bore, not nominal or outside diameter; one equivalent diameter per branch.	`D6`	mm	12
Sum of fitting loss coefficients Dimensionless ΣK for both flow and return fittings, referenced to this branch pipe velocity. Exclude the balancing valve.	`Z6`		8
Radiator and other component loss Loss at this branch's DESIGN flow, excluding the calculated pipe/fitting losses and the balancing valve. Scaled with flow squared for the kv comparison.	`pe6`	kPa	1
Entered valve kv at selected preset Conventional kv: water flow in m³/h at 1 bar drop. Enter a value from your maker's data; this is not a preset number or US Cv.	`kv6`	m^3/h	0.5

Results

With the default inputs above, the calc gives:

Result	Value
Total design flow	0.394 m³/h
Total design flow · US	1.733 gal/min
Pump head at total design flow	2.468 m
Pump pressure at total design flow	23.792 kPa
Manifold pressure difference	18.792 kPa
Critical radiator circuit	3

Checked against sources

Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).

Caleffi design flow · 50,000 Btu/h and 20 °F drop

Source: Caleffi idronics 8 (2011), p. 32, worked example: 50,000 Btu/h, 170 °F supply, 20 °F drop, published flow 5.13 US gpm. https://www.caleffi.com/sites/default/files/media/external-file/Idronics_8_NA_Hydronic%20balancing.pdf . Their coarse table/interpolation gives 487.5 Btu/(h·gpm·°F). This test uses approximate water properties at the 160 °F mean (rho 977.5 kg/m³, cp 4190 J/(kg·K)), giving about 5.104 gpm. The 1% tolerance allows the published rounded property grouping; the energy equation is unchanged. Only thermal flow is checked; branch geometry is not from the example.

Inputs: Radiator circuits = 1; Design heat load = 14.654 kW; Design water temperature drop = 11.111 K; Water density = 977.5 kg/m³; Water specific heat capacity = 4,190 J/(kg·K); Water dynamic viscosity = 0.4 mPa·s; Total branch pipe length = 0 m; Pipe internal diameter = 25 mm; Sum of fitting loss coefficients = 0; Radiator and other component loss = 0 kPa; the others as above.

Result	Source	This calc
Design flow in US gallons per minute [1]	5.13 ± 0.052 gal/min	5.104 gal/min

Penn State · Colebrook, major and minor pipe losses

Source: J. M. Cimbala, Penn State, EES Solution for Example Problem — Major and Minor Losses in a Piping System (Feb. 2005), pp. 1–2. https://www.me.psu.edu/cimbala/me320web_Fall_2012/pdf/EES_Solution_Minor_losses_example_problem.pdf . Source: D 0.025 m, L 20 m, sum K 13.35, rho 998, mu 0.001 Pa·s, eps/D 0.004, head 35 m, f 0.02943 and rounded volume flow 0.002117 m³/s. Load is a synthetic thermal mapping solely to impose that published volume flow. Source rounding gives calculated head about 34.985 m, within 0.2%; no friction adjustment is made.

Inputs: Radiator circuits = 1; Design heat load = 26.526 kW; Design water temperature drop = 3 K; Water density = 998 kg/m³; Water dynamic viscosity = 1 mPa·s; Internal pipe roughness = 0.1 mm; Total branch pipe length = 20 m; Pipe internal diameter = 25 mm; Sum of fitting loss coefficients = 13.35; Radiator and other component loss = 0 kPa; the others as above.

Result	Source	This calc
Darcy friction factors [1]	0.02943 ± 3 × 10⁻⁵	0.02943
Circuit head loss excluding balancing valve [1]	35 ± 0.07 m	34.985 m
Design water velocities [1]	4.314 ± 0.004314 m/s	4.313 m/s
Design Reynolds numbers [1]	107,627 ± 108	107,602

Spirax Sarco · pressure drop of a kv 16 valve

Source: Spirax Sarco, Control valve sizing for water systems, Example 6.3.1. https://www.spiraxsarco.com/learn-about-steam/control-hardware-electric-pneumatic-actuation/control-valve-sizing-for-water-systems . At 10 m³/h and kv 16 the published chart reads approximately 40 kPa (0.4 bar). The exact kv equation gives 39.0625 kPa; 3% tolerance reflects the chart reading, not an adjustment to the physics. Q1 34.875 kW at 3 K, rho 1000 and cp 4185 is only a thermal mapping to impose the example's 10 m³/h flow.

Inputs: Radiator circuits = 1; Design heat load = 34.875 kW; Design water temperature drop = 3 K; Water density = 1,000 kg/m³; Water dynamic viscosity = 1 mPa·s; Total branch pipe length = 0 m; Pipe internal diameter = 100 mm; Sum of fitting loss coefficients = 0; Radiator and other component loss = 0 kPa; Entered valve kv at selected preset = 16 m³/h; the others as above.

Result	Source	This calc
Entered-valve losses if forced to design flow [1]	40 ± 1.2 kPa	39.063 kPa

Hydraulic Balancing Calculator