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
Calculation
Dependence of pressure loss on pipe diameter
About Pipeline Hydraulic Calculation
This calculator performs a hydraulic calculation for a pressurized water pipeline. It determines flow velocity, flow regime, friction factor, and the total pressure losses due to pipe friction and local losses. The calculation is useful for choosing a diameter, estimating the required pump head, and comparing pipe and fitting options.
Reference points and recommendations
1) Converting input data
Flow rate Q is converted to m3/s. If the value is given in m3/h, L/s, or L/min, it is converted to m3/s by dividing by the corresponding factor.
Internal diameter d is obtained from the outside diameter and wall thickness.
d = (Douter − 2·s)/1000
where Douter and s are in mm. The result d is in m.
2) Water properties from the average temperature
Water density ρ is calculated by an approximation as a function of the mean water temperature tavg. Inside the calculator, ρ is obtained in t/m3, which is numerically equal to kg/L.
ρ = (−0.003·tavg2 − 0.1511·tavg + 1003.1)/1000
Kinematic viscosity ν is also taken as an approximation of tavg. The result ν is in m2/s.
ν = 0.0178 / (1 + 0.0337·tavg + 0.000221·tavg2) · 10−4
3) Flow velocity and flow regime
Velocity v is calculated from the flow rate and the cross-sectional area. The formula includes density ρ to keep the internal unit system consistent.
v = 4·Q / (ρ·π·d2)
Reynolds number Re is used to classify the flow regime.
Re = v·d / ν
The regime limits are taken as 2300 and 4000. For Re ≤ 2300 the flow is treated as laminar. For Re ≥ 4000 the flow is treated as turbulent. In the range 2300-4000 the result is more sensitive to assumptions and typically requires careful checking.
4) Friction factor λ and roughness
Absolute roughness ε is taken from the selected material and converted from mm to m. Relative roughness ε/d is then used.
Darcy friction factor λ is selected based on the flow regime and on Re and ε/d.
λ = 75/Re
The formula above is used for laminar flow.
λ = 0.3164 / Re0.25
The formula above is used as an approximation in the developing turbulent region.
λ = 0.11 · (68/Re + ε/d)0.25
The formula above is used as an approximation for turbulent flow with roughness effects.
λ = 0.11 · (ε/d)0.25
The formula above is used for fully rough turbulent flow, where the influence of Re becomes small.
5) Friction losses and local losses
Friction losses along the length are calculated with the Darcy-Weisbach equation using λ, velocity v, length L, and internal diameter d. First the length-related part is computed, then local losses are added.
Local losses are included through the sum of loss coefficients Σζ for all fittings and valves. Σζ is dimensionless, and the added loss is proportional to v2.
Δplocal = Σζ · (ρkg/m³ · v2 / 2)
Here ρkg/m³ is density in kg/m3. Inside the calculator, consistent unit conversions are applied.
6) Final values and units
Total pressure loss Δp is reported in several units. The base result is calculated in Pa, then converted.
ΔpkPa = ΔpPa / 1000
Δpbar = ΔpPa / 100000
H = ΔpPa / 9807
H is the head loss in meters of water column. The factor 9807 Pa/m corresponds to ρ≈1000 kg/m3 and g≈9.807 m/s2.
Hydraulic characteristic S is calculated as the pressure loss divided by the square of the flow rate. This is convenient for comparing routes and plotting relationships.
S = ΔpPa / Qh2
where Qh is the flow rate in m3/h. The units of S are Pa/(m3/h)2.
7) Practical checks for the result
Velocity v in water systems is often kept within 0.25-1.5 m/s. Lower velocities may promote air accumulation and sedimentation. Higher velocities increase noise, erosion, and pressure losses.
Sum of local coefficients Σζ depends on the number of fittings and valves. For a simple line, values around 1-3 are common. For routes with many bends and valves, values around 5-15 are also typical.
Roughness ε has a stronger impact at higher velocities and smaller diameters. For old steel pipes with deposits, higher ε can sharply increase Δp, so existing systems are often checked with a more conservative roughness value.
8) Related standards and documents
EN 806 (Parts 1-5) describes requirements for drinking water installations inside buildings, including general approaches to selecting pipes and fittings and to calculating pressure losses.
EN 805 applies to water supply systems outside buildings and can be used as a reference for design and verification of pipeline systems.
EN 12828 covers water-based heating systems in buildings and helps connect pressure-loss calculations with pump selection and system balancing.
ISO 80000 defines rules for quantities and units, which helps interpret Pa, kPa, bar, and meters of water column correctly.
FAQs
Why do pressure losses increase so quickly when the pipe diameter is reduced
Pressure loss depends on velocity v, and for a fixed flow rate the velocity is inversely proportional to d2. In the Darcy-Weisbach equation, Δp grows approximately with v2, so reducing diameter can cause a sharp rise in losses.
What matters more in the calculation: roughness or Reynolds number
In moderately turbulent flow, both factors affect the result. At very high Re and noticeable roughness, the flow approaches a regime where ε/d dominates and the influence of Re becomes smaller. That is why choosing a realistic roughness is critical for old pipes.
What is Σζ and how can local losses be estimated
Σζ is the sum of loss coefficients ζ for all fittings and valves, and it is dimensionless. Local loss is calculated as Σζ·(ρ·v2/2). For a preliminary estimate, you can add typical ζ values and then refine them using valve and fitting data.
How to choose a “good” flow regime for the calculation
Most engineering water systems operate in the turbulent range, where Re is typically above 4000. If Re falls in the 2300-4000 interval, the result becomes less certain. In that case, designers often adjust diameter or flow, or refine assumptions for viscosity and roughness.
What is the difference between Pa, bar, and meters of water column
Pa is the SI unit of pressure. Bar is a convenient derived unit, where 1 bar = 100000 Pa. Meters of water column express an equivalent head loss and are related to pressure by H = Δp/(ρ·g). In the calculator, the conversion 9807 Pa per 1 m water column is used.