The question and answer
Transfer 10 m³/h of water between two large, open tanks. The receiving liquid surface is 5 m higher. The line includes two inside diameters, a reducer, fittings and a heat exchanger.
Calculated duty: 12.654 m of water head, equivalent to 123.871 kPa at this flow. This is the system requirement before any design allowance. Select a pump using its curve at 10 m³/h and check suction conditions separately.
Download the JSON file, open the calculator, then use its Open system file control. No account is needed.
1. Define the boundaries and inputs
| Input | Value |
|---|---|
| Flow | 10 m³/h = 0.00277778 m³/s |
| Density; dynamic viscosity | 998.2 kg/m³; 1.002 mPa·s (cP), rounded water values near 20°C |
| Pipe roughness | 0.045 mm in both sections, an assumed condition |
| Inlet / outlet boundary | Reservoir surface / reservoir surface |
| Required outlet gauge pressure | 0 kPa; both tanks are open to the same atmosphere |
| Kinetic energy coefficients | 1 at both boundaries and in both sections |
| Section | Length / inside diameter | Elevation change | Loss assumptions |
|---|---|---|---|
| Supply line | 30 m / 52.5 mm | 0 m | Entrance K = 0.5; four elbows K = 0.9 each, all referenced to 52.5 mm |
| Equipment line | 20 m / 40.9 mm | +5 m | Reducer K = 0.2 at section entrance, based on 40.9 mm; restriction K = 2 at 35 mm bore; exit K = 1 at 40.9 mm; exchanger ΔP = 25 kPa |
The K values and exchanger pressure drop are explicit teaching assumptions at this flow, not universal fitting data. Use custom K entries to reproduce them. Enter the reducer once under the second section's transition, not again as a fitting. The 35 mm restriction bore is deliberately different from its pipe bore.
2. Calculate velocity and friction
Re = ρvD/μ
ΔPpipe = fD × (L/D) × ρv²/2
ΔPfitting = K × ρvfitting²/2
| Section | Velocity (m/s) | Reynolds number | Darcy f |
|---|---|---|---|
| Supply line | 1.28318 | 67112 | 0.0226970 |
| Equipment line | 2.11427 | 86146 | 0.0228238 |
Both sections are turbulent. The calculator solves Colebrook for the Darcy friction factor. At the 35 mm restriction, velocity is 2.88716 m/s and the K = 2 pressure loss is 8.32071 kPa. Using the 40.9 mm pipe velocity there would understate the loss.
3. Add losses and elevation
| Contribution | Pressure requirement (kPa) |
|---|---|
| Supply pipe | 10.658 |
| Supply entrance + elbows | 3.369 |
| Equipment pipe | 24.900 |
| 35 mm restriction + reservoir exit | 10.552 |
| Reducer | 0.446 |
| Heat exchanger | 25.000 |
| Total irreversible losses | 74.926 |
| 5 m elevation, ρgΔz | 48.945 |
| Net boundary velocity change | 0.000 |
| Total system requirement | 123.871 |
The section table shows local velocity-change terms as water enters and changes pipe size. The outlet boundary removes the remaining kinetic term. They sum to zero between reservoir surfaces. The explicit exit K = 1 represents irreversible dissipation and still belongs in the loss total.
For these open-tank boundaries, interpret the calculator's system ΔP and equivalent head as the pump energy addition needed. Its “required inlet gauge pressure” is an equivalent pressure requirement, not the actual atmospheric pressure above the open supply tank.
4. Use the result correctly
Keep the 5 m static rise separate from friction: larger pipe can reduce losses but cannot eliminate the elevation requirement. The exchanger loss may change with flow; do not reuse 25 kPa blindly at another duty. Check pump efficiency, operating range, NPSH, piping pressure rating and the full system curve before selecting equipment.
Next: compare pipe sizes, then check NPSH available.
Method reference: US EPA EPANET documentation covers pipe-network hydraulics and head-loss methods. The numerical example here uses Frictionless Calc's multi-section engine, not EPANET.