Initial data
- Pipe inlet: 0.5
- Pipe outlet: 1.0
- 90° elbow: 0.5-1.0
- Tee: 1-2
- Ball valve fully open: 0.05-0.2
- Gate valve fully open: 0.15-0.30
- Globe valve fully open: 3-10
- Check valve: 1.5-3
Dependence of pressure loss on pipe diameter
- Internal pipe diameter, mm =
- Water velocity, m/s =
- Reynolds number Re =
- Pressure loss along pipe, kPa =
- Local pressure loss, kPa =
- Total pressure loss, kPa =
- Total pressure loss, bar =
- Head loss, m water column =
- Specific pressure loss along pipe, Pa/m =
About Pipeline Hydraulic Calculation
This pipeline hydraulic calculator performs a hydraulic calculation of a pressurized water pipeline. It estimates pressure loss and hydraulic resistance and helps with selecting pipe diameters in pressurized piping systems. Based on the specified flow rate, pipe geometry, length, water temperature, roughness and sum of local resistance coefficients, it determines flow velocity, Reynolds number, pressure loss along the pipe, local pressure loss, total pressure loss and head loss.
The calculation is based on the Darcy-Weisbach equation. The Darcy friction factor is selected according to the flow regime, while turbulent flow also accounts for the relative roughness of the internal pipe surface.
Guidelines and recommendations
Flow rate conversion and internal diameter
Water flow rate Q is converted to m3/s before the hydraulic calculation. A value in m3/h is divided by 3600, a value in L/s by 1000, a value in L/min by 60000, and a value in m3/min by 60.
Internal diameter d is calculated from the outside diameter D and wall thickness s. D and s are entered in mm, and the resulting internal diameter is converted to metres.
d = (D - 2·s) / 1000
The internal diameter, not the outside diameter, is used to determine the flow area, water velocity, Reynolds number and hydraulic pressure losses.
Water properties as a function of temperature
Water density ρ is calculated from the average water temperature t. The following approximation gives the density in kg/m3:
ρ = -0.003·t2 - 0.1511·t + 1003.1
Kinematic viscosity ν also depends on temperature. It is first determined in mm2/s:
ν = 1.78 / (1 + 0.0337·t + 0.000221·t2)
For the Reynolds number calculation, this value is converted to m2/s. Water temperature therefore affects not only density but also the flow regime and Darcy friction factor.
Flow velocity and Reynolds number
Water velocity v is calculated from the volumetric flow rate Q and the internal cross-sectional area of the circular pipe.
v = 4·Q / (π·d2)
At a constant flow rate, reducing the internal diameter rapidly increases the velocity because the cross-sectional area is proportional to the square of the diameter.
Reynolds number Re characterizes the flow regime and is calculated from internal diameter, velocity and kinematic viscosity.
Re = v·d / ν
For Re ≤ 2300, the calculation assumes laminar flow. For 2300 < Re < 4000, the flow is in the transitional region and the result is accompanied by a warning about increased uncertainty. For Re ≥ 4000, the turbulent-flow calculation is used.
Darcy friction factor
For laminar flow at Re ≤ 2300, the Darcy friction factor λ is determined directly from the Reynolds number:
λ = 64 / Re
For the transitional region at 2300 < Re < 4000, the Blasius approximation is used. Because transitional flow is inherently unstable, this value should be treated as an estimate.
λ = 0.3164 / Re0.25
For turbulent flow at Re ≥ 4000, the explicit Haaland equation is used. It accounts for both the Reynolds number and the relative roughness ε/d.
λ = [-1.8·log10((ε/(3.7·d))1.11 + 6.9/Re)]-2
This approach accounts for the difference between smooth new pipes and pipes with a rougher internal surface.
Internal surface roughness
Absolute roughness ε is specified in mm and converted to metres before calculation. The calculator uses the following reference values:
- PE, PP, PVC, PEX and multilayer plastic pipes: 0.0015 mm
- copper and brass: 0.0015 mm
- stainless steel: 0.015 mm
- ductile iron with cement mortar lining: 0.03 mm
- steel: 0.05 mm
- galvanized steel: 0.15 mm
- corrugated stainless steel pipe: 0.2 mm
- steel after several years of service: 0.2 mm
- galvanized steel after several years of service: 0.2 mm
- steel or cast iron with significant deposits: 1.0 mm
These values are engineering reference values. Actual roughness depends on the material, manufacturing process, condition of the internal surface, service life, corrosion and deposits.
Pressure loss along the pipe
Pressure loss along the pipe Δpf is calculated with the Darcy-Weisbach equation. The equation uses the Darcy friction factor λ, the ratio of pipe length L to internal diameter d, water density ρ and the square of the velocity.
Δpf = λ·(L/d)·ρ·v2/2
The result is obtained in Pa. Specific pressure loss along the pipe is calculated by dividing this value by the pipe length.
R = Δpf / L
R is expressed in Pa/m and makes it possible to compare the hydraulic resistance of pipes with different diameters independently of the total length of the section.
Local resistance losses
Local pressure loss Δplocal accounts for bends, tees, valves, check valves and other fittings. Each component has a dimensionless local resistance coefficient ζ, and the calculation uses their sum Σζ.
Σζ = ζ1 + ζ2 + ... + ζn
Δplocal = Σζ·ρ·v2/2
Local pressure losses are proportional to the square of the velocity. Therefore, at a high flow rate or small pipe diameter, even a moderate sum of ζ coefficients can noticeably increase the total flow resistance.
Total pressure loss and head loss
Total pressure loss Δp is the sum of pressure loss along the pipe and local pressure loss.
Δp = Δpf + Δplocal
The primary result is calculated in Pa and then converted to kPa and bar.
ΔpkPa = Δp / 1000
Δpbar = Δp / 100000
Head loss H expresses the total pressure loss as an equivalent water column height. Instead of using a fixed conversion factor, the calculation uses the water density determined for the specified temperature.
H = Δp / (ρ·9.81)
Velocity range and graph
The reference flow velocity range is 0.25-1.5 m/s. It is used as a practical guideline and is highlighted on the graph with a light green zone. Values outside this range do not automatically mean that the operating condition is unacceptable because the permitted velocity depends on the system purpose, pipe material, noise requirements and design constraints.
The pressure loss versus pipe diameter graph is calculated with the flow rate, pipe length, water temperature, roughness and sum of local resistance coefficients kept constant. The graph covers pipe diameters corresponding to flow velocities of approximately 0.1 to 10 m/s. The blue point shows the current calculated internal diameter and its corresponding total pressure loss.
Related European standards
EN 806, "Specifications for installations inside buildings conveying water for human consumption" applies to internal drinking-water installations. EN 806-3 covers simplified pipe sizing methods.
EN 805, "Water supply - Requirements for systems and components outside buildings" applies to external water supply systems and contains requirements for design, components, installation, testing and commissioning.
EN 12828, "Heating systems in buildings - Design for water-based heating systems" applies to the design of water-based heating systems. Pipeline hydraulic losses are relevant when balancing circuits and determining circulation requirements.
The calculator performs a general hydraulic calculation using the Darcy-Weisbach equation. When designing a specific piping system, the calculated values should be checked against the requirements of the applicable European standard and the technical documentation supplied by pipe and fitting manufacturers.
FAQs
Why does a small reduction in pipe diameter cause a large increase in pressure loss?
At a constant flow rate, water velocity is inversely proportional to the square of the internal diameter. Pressure loss contains the v2 term and also depends on the L/d ratio. As a result, reducing the pipe diameter can increase hydraulic resistance several times.
How much does pipe roughness affect the hydraulic calculation?
In laminar flow, the friction factor is determined mainly by the Reynolds number, so roughness has practically no effect on λ. In turbulent flow, the influence of ε/d becomes significant, especially for old metal pipes, corrosion and internal deposits.
Why are pressure loss along the pipe and local pressure loss shown separately?
Pressure loss along the pipe occurs continuously because of friction between the flowing water and the pipe wall. Local pressure loss is associated with individual fittings and is calculated from the sum of ζ coefficients. Showing them separately makes it easier to understand whether the pipe itself or the fittings and valves contribute more to the total hydraulic resistance.
What does it mean when the Reynolds number is between 2300 and 4000?
This is the transitional region between stable laminar and turbulent flow. Flow behaviour is less predictable in this range, so the friction factor has greater uncertainty. For this reason, the calculator marks this flow regime separately.
Why is 0.25-1.5 m/s used as the recommended flow velocity range?
This range is used as a general practical guideline for water piping systems, not as a single regulatory limit for every application. Higher velocity increases noise and hydraulic pressure losses, while very low velocity may be undesirable in some systems. The final acceptable range should be selected according to the system purpose and the requirements of the applicable standard.