What is the difference between distributed and localized head loss?
The distributed loss occurs along the straight length through wall friction and depends on length, diameter, velocity, roughness and flow regime. The localized loss occurs at elbows, valves, tees, reducers, strainers, inlets and outlets and is represented by a K coefficient. The total loss is the sum of the two.
For industrial pump operators, pressure loss has direct impact on two points: (1) At suction, it reduces available NPSH — if the loss is too large, the pump cavitates. (2) At discharge, it increases the total head the pump must overcome — if not accounted for, the pump delivers less flow than designed. In FB Bombas application engineering experience, poorly calculated suction pressure loss is among the most frequent causes of cavitation in industrial gear and centrifugal pump installations.
| Type | Origin | Variables | Equation |
|---|---|---|---|
| Distributed | Friction in the straight run | L, D, v, roughness, regime | Hf = f × (L/D) × v²/2g |
| Localized | Elbows, valves, tees, reducers, strainers | K coefficient of each fitting and local v | Hf = K × v²/2g |
What is the distributed head loss formula?
Darcy–Weisbach computes Hf = f × (L/D) × v²/(2g), with Hf and L in meters, D in meters, v in m/s and g = 9.81 m/s². The factor f depends on the Reynolds number and the relative roughness. The equation holds for any fluid when properties and regime are correctly informed.
The friction factor f depends on the flow regime. For laminar flow (Reynolds < 2,100, typical in viscous fluid pumping with FBE pumps), f = 64/Re — and head loss is proportional to viscosity and velocity. For turbulent flow (Reynolds > 4,000, typical in water pumping with FBCN pumps), f depends on pipe relative roughness and is obtained from the Moody diagram or Colebrook-White equation.
In the transition zone (2,100 < Re < 4,000), behavior is unstable and should be avoided in design.
For water and low-viscosity fluids, the established alternative in water supply and fire protection networks is the Hazen-Williams formula: Hf = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87), with Q in m³/s, D in meters and L in meters. The C coefficient expresses the pipe inner smoothness: PVC C = 150, new carbon steel and stainless steel C = 140, cast iron C = 130, galvanized steel C = 120.
The advantage is skipping Reynolds and friction factor; the limitation is that it only applies to water in turbulent flow — for oils and viscous fluids (FBE and FBEI pumps), always use Darcy-Weisbach with the actual fluid viscosity at operating temperature.
The table below provides ready-to-use distributed head loss values for water at 20°C in carbon steel pipe (roughness ε = 0.045 mm), calculated by Darcy-Weisbach with Colebrook-White friction factor — the same calculation engine as the FB Bombas head loss calculator (at /en/head-loss-calculator), which reruns these numbers for any diameter, material, flow and viscosity, including localized losses by K coefficient.
Note how loss grows with the square of velocity: in the 50 mm diameter, doubling flow from 10 to 20 m³/h multiplies the loss by 3.7.
Hf = f × (L / D) × v² / (2g)Darcy–Weisbach equation
| Internal diameter | Flow rate | Velocity | Loss (m / 100 m) |
|---|---|---|---|
| 50 mm | 10 m³/h | 1.41 m/s | 4.7 |
| 50 mm | 20 m³/h | 2.83 m/s | 17.4 |
| 65 mm | 20 m³/h | 1.67 m/s | 4.6 |
| 65 mm | 30 m³/h | 2.51 m/s | 10.0 |
| 80 mm | 30 m³/h | 1.66 m/s | 3.5 |
| 80 mm | 50 m³/h | 2.76 m/s | 9.3 |
| 100 mm | 50 m³/h | 1.77 m/s | 3.0 |
| 100 mm | 80 m³/h | 2.83 m/s | 7.4 |
| 150 mm | 100 m³/h | 1.57 m/s | 1.5 |
| 150 mm | 200 m³/h | 3.14 m/s | 5.5 |
When to use Darcy–Weisbach or Hazen–Williams?
Use Darcy–Weisbach for any fluid and regime, with consistent viscosity, Reynolds and roughness. Hazen–Williams is a practical approximation for water in turbulent flow and must not be transferred to oils or viscous fluids. In both cases, flow and diameter must use the units declared by the formula.
| Method | Domain of use | Required properties | Main limitation |
|---|---|---|---|
| Darcy–Weisbach | Any fluid and regime | Viscosity, density, roughness, Reynolds | Requires computing the friction factor f |
| Hazen–Williams | Water in turbulent flow (water supply, fire) | Only the material C coefficient | Not valid for oils and viscous fluids |
How to calculate localized head loss?
Add the losses of each fitting via Hf = K × v²/(2g), using the velocity in the run where the fitting is installed. If several items share the same diameter, add their K coefficients before applying the formula. In critical suction lines, prefer K coefficients over equivalent length.
Localized loss occurs at each piping fitting: elbows, tees, valves, reducers, expansions, strainers, tank inlet and outlet. The K values in the table below are indicative for industrial design — they vary with exact geometry, opening degree and fitting manufacturer.
Equivalent length method: alternatively, each fitting can be converted to an equivalent length of straight pipe (in diameters). Examples: 90° long radius elbow ≈ 20D, 90° short radius elbow ≈ 30D, gate valve open ≈ 8D, globe valve open ≈ 300D. This method is practical for quick field estimates. For critical NPSH designs (especially in FBE gear pump suction with viscous fluids), FB Bombas recommends calculating by the K coefficient method, which is more accurate.
| Fitting | K coefficient |
|---|---|
| 90° long-radius elbow | 0.3 |
| 90° short-radius elbow | 0.9 |
| 45° elbow | 0.2 |
| Tee, straight-through | 0.3 |
| Tee, branch | 1.5 |
| Gate valve, open | 0.2 |
| Globe valve, open | 6.0–10.0 |
| Check valve | 2.5 |
| Concentric reducer | 0.5 |
| Y-strainer (clean) | 2.0–5.0 |
| Sharp-edged entry | 0.5 |
| Chamfered entry | 0.04 |
How to calculate total head loss step by step?
First compute v = Q/A, using flow and internal diameter in compatible units. Then compute the distributed portion, add the localized portions and take Hf,total = Hf,distributed + Σ Hf,localized. Use the viscosity at the real operating temperature and report the result in meters of the pumped liquid.
The FB Bombas head loss calculator runs exactly these steps with Colebrook-White friction factor and tabulated K coefficients — for any diameter, material, flow and viscosity.
Hf,total = Hf,distribuída + Σ Hf,localizadaSum of the portions
How does suction head loss cause cavitation?
At suction, Hf enters as a direct subtraction: NPSHa = Pa ± Hz − Hf − Pv. Therefore, 1 m of additional loss reduces the available NPSH by 1 m and shrinks the margin over the required value.
Do not treat NPSHa = NPSHr as a no-cavitation condition: NPSH3 — the basis of catalog NPSHr, per the Hydraulic Institute technical FAQ — is measured at the point where head has already dropped 3%, that is, with cavitation under way; that is why designs carry a margin above NPSHr.
Practical example with FBCN 50-200 centrifugal pump: manufacturer NPSHr = 3.2 m. Installation with flooded suction (Hz = +2.0 m), atmospheric pressure (Pa = 10.33 mlc), water at 60°C (Pv = 2.03 mlc), DN65 piping with 5 m straight pipe + 2 × 90° elbows + 1 gate valve. Calculation: velocity v = Q/A = 2.5 m/s (turbulent, Re ≈ 330,000), f = 0.019 (Moody). Distributed loss = 0.019 × (5/0.065) × (2.5²/19.62) = 0.47 m.
Localized loss = (0.3+0.3+0.2) × (2.5²/19.62) = 0.26 m. Total Hf = 0.73 m. NPSHa = 10.33 + 2.0 - 0.73 - 2.03 = 9.57 m. Margin over NPSHr = 9.57 - 3.2 = 6.37 m — safe situation.
But if the same installation had 15 m of pipe + 5 long-radius 90° elbows + dirty strainer (K=8.0) + gate valve + negative suction (−3 m): with f = 0.019 and ΣK = 9.7, Hf would rise to ≈ 4.5 m (1.40 m distributed + 3.09 m localized) and NPSHa would drop to ≈ 0.8 m — below NPSHr. Cavitation.
How does viscosity change head loss?
In laminar flow, the friction factor is f = 64/Re, and the loss grows with viscosity for the same geometry and flow. Therefore, the calculation must use the viscosity at operating temperature and also check startup, when the fluid can be colder. FBE velocity recommendations are FB criteria, not universal limits.
In FBE gear pump applications, the fluid is typically viscous (oils, asphalt, resins, chocolate) and flow tends to the laminar regime (Re < 2,100), where doubling viscosity doubles the head loss in the same line and flow. For that reason, as an internal design criterion, FB Bombas recommends a maximum velocity of 0.5 m/s in FBE pump suction with viscous fluids (versus 1.5 m/s for water in FBCN centrifugal pumps).
Another particularity: many viscous fluids have temperature-dependent viscosity (e.g., asphalt CAP goes from solid at 25°C to pumpable liquid at 180°C). Pressure loss must be calculated for the WORST condition — usually at startup, when the fluid is colder and more viscous. FB Bombas offers heating jackets (CA option) on FBE pumps precisely to keep the fluid heated in the suction zone during startup, reducing local viscosity and consequently pressure loss.
Practical suction sizing rules
Based on FB Bombas field experience, these are the rules that minimize suction pressure loss: (1) Suction pipe diameter always ≥ pump connection diameter — never reduce before the pump; (2) Total suction line length: as short as possible, ideally < 10 diameters; (3) Avoid globe-type valves in suction (K = 6–10) — prefer gate (K = 0.2) or butterfly (K = 0.3); (4) Eccentric reducer (not concentric) in horizontal suction — avoids air pockets; (5) Suction strainer with passage area ≥ 3× pipe area, with differential pressure gauge to monitor clogging; (6) Flooded suction whenever possible — each meter of positive head is one extra meter of NPSHa; (7) For FBE gear pumps with viscous fluids: consider heating suction piping if viscosity at startup exceeds 50,000 SSU.
Need help with the calculation?
The FB Bombas application engineer calculates the pressure loss for your installation and verifies NPSH as part of the pump selection process — at no cost. Send the piping layout (length, diameter, fittings), fluid data (type, viscosity at operating temperature, density) and operating conditions (flow, pressure, temperature) to comercial@fbbombas.com.br or WhatsApp +55 11 97287-4837. Within 3-5 business days after engineering analysis, you receive the model recommendation with NPSH analysis included.