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Total Head (TDH) Calculator — Multi‑Section Pipes + Fittings + Elevation + Pressure
Build sections with length, diameter, velocity, material (roughness), fittings, and elevation change. Add suction/discharge pressures. Compute Friction head + Static elevation + Pressure head = TDH. Change --accent above to match your palette.
1) Global settings
3) Results
Multi‑Section Head & Elevation Calculator — How It Works + Step‑by‑Step Example
This guide explains what the calculator does (friction + fittings + elevation + pressure head), how the math works, and how to use it confidently. A complete sample project with every intermediate step is included—perfect for submissions and audits.
What this calculator does
The tool computes Total Dynamic Head (TDH) across any number of pipe segments (sections). Each section can have its own length, diameter, velocity, pipe roughness (material), and fittings. It adds:
Output includes KPIs (friction, elevation, pressure head, TDH) and a submission‑ready HTML report with per‑segment step‑by‑step calculations and assumptions.
Method: Darcy–Weisbach + Swamee–Jain (turbulent) or 64/Re (laminar)
How the math works (clean & auditable)
Per section the calculator evaluates:
- Reynolds number: Re = V·D/ν
- Friction factor: f = 64/Re (laminar, Re<2300) or f = 0.25/[log10((ε/D)/3.7 + 5.74/Re^0.9)]² (Swamee–Jain, turbulent)
- Dynamic term: V²/(2g)
- Straight loss: hf = f·(L/D)·V²/(2g)
- Fittings loss: hm = ΣK·V²/(2g)
- Section subtotal: hsec = hf + hm + Δz
System totals then add pressure head from gauge settings:
Hp = (pdischarge − psuction)/(ρg)
TDH = Σ(hsec) + Hp
How to use the calculator (step‑by‑step)
- Select the fluid (ρ, ν). Quick presets: air (~20 °C) and water. Use “Custom” for other fluids.
- Pick a standard/method flavor—this only changes guidance text and assumptions labels in the report.
- Set allowance (design margin) if you want a conservative design TDH.
- Add sections for each straight run between notable fittings clusters or elevation changes.
- For each section, enter L, D, V, and material (ε). Use dropdowns for common values, or custom inputs.
- Add fittings with known K values (elbows, tees, valves). Quantity multiplies K automatically.
- Set elevation Δz for the section: positive uphill, negative downhill, zero if level.
- Set suction & discharge pressures (gauge kPa). 0 kPa means open to atmosphere.
- Click Calculate. Review KPIs, the sparkline, and per‑section results. Export CSV or a full HTML report with all steps and assumptions.
Sample Project — Full Calculations (Water at ~20 °C)
Goal: Compute TDH for a two‑segment line with mixed fittings, modest elevation change, and a pressurized discharge.
Given
| Section | L (m) | D (m) | V (m/s) | Material (ε, m) | Fittings (K × qty) | Δz (m) |
|---|---|---|---|---|---|---|
| 1 | 40.0 | 0.10 | 2.0 | 1.52e‑4 (Galvanized) | Elbow LR 0.6×2; Gate 0.2×1 → ΣK=1.4 | +2.0 |
| 2 | 25.0 | 0.10 | 2.2 | 4.6e‑5 (Steel) | Elbow SR 0.9×2; Tee straight 0.5×1 → ΣK=2.3 | −1.0 |
Section 1 — Step‑by‑Step
- Area A = πD²/4 = π·0.10²/4 = 0.00785398 m²
- Flow Q = A·V = 0.00785398×2.0 = 0.01570796 m³/s
- Re = V·D/ν = 2.0×0.10/1e‑6 = 200 000 → turbulent
- Swamee–Jain: t = (ε/D)/3.7 + 5.74/Re^0.9 = (0.00152)/3.7 + 5.74/200000^0.9 = 0.00050808
log10(t) = −3.29407 → f = 0.25/[log10(t)]² = 0.02304 - Dynamic term V²/(2g) = 2.0²/(2·9.81) = 0.20387 m
- Straight loss hf = f·(L/D)·V²/(2g) = 0.02304·(40/0.10)·0.20387 = 1.87887 m
- Fittings loss hm = ΣK·V²/(2g) = 1.4·0.20387 = 0.28542 m
- Section loss total hloss = 1.87887 + 0.28542 = 2.16429 m
- Elevation Δz = +2.0 m
- Section subtotal hsec = 2.16429 + 2.0 = 4.16429 m
Section 2 — Step‑by‑Step
- Area A = πD²/4 = π·0.10²/4 = 0.00785398 m²
- Flow Q = A·V = 0.00785398×2.2 = 0.01727876 m³/s
- Re = 2.2×0.10/1e‑6 = 220 000 → turbulent
- Swamee–Jain: t = (ε/D)/3.7 + 5.74/Re^0.9 = (0.00046)/3.7 + 5.74/220000^0.9 = 0.00021360
log10(t) = −3.67040 → f = 0.01856 - Dynamic term V²/(2g) = 2.2²/(2·9.81) = 0.24669 m
- Straight loss hf = 0.01856·(25/0.10)·0.24669 = 1.14446 m
- Fittings loss hm = 2.3·0.24669 = 0.56738 m
- Section loss total hloss = 1.14446 + 0.56738 = 1.71184 m
- Elevation Δz = −1.0 m
- Section subtotal hsec = 1.71184 − 1.0 = 0.71184 m
Totals
| Friction head (straight + fittings) | 3.87613 m |
| Static elevation (ΣΔz) | +1.00000 m |
| Pressure head Hp = (200 kPa − 0)/ (ρg) | 20.42822 m |
| TDH = Friction + Elevation + Pressure | 25.30435 m |
| Equivalent Δp = ρg·TDH | 247 739 Pa ≈ 247.74 kPa |
Sanity check: 200 kPa of discharge pressure alone is ≈20.43 m of head in water, so our TDH should be ~20.43 m plus a few meters of friction + elevation—matching the 25.30 m result.
Jargon buster
Total Dynamic Head: energy the pump must add to overcome friction, elevation, and pressure differences.
Universal equation for head loss due to pipe friction; uses friction factor f.
Sum of minor‑loss coefficients for fittings; multiplies the dynamic term V²/(2g).
V·D/ν; indicates laminar (<2300) vs turbulent flow.
Depends on Re and relative roughness ε/D; Swamee–Jain is a fast explicit form.
Pressure relative to atmosphere (0 kPa = open tank at same elevation).
Static lift/drop between nodes; + uphill, − downhill.
V²/(2g); converts velocity to an equivalent head (m of fluid).
Energy & Hydraulic Grade Lines—visualize how head is spent along the route.
Practical tips & common pitfalls
- Use inside diameter (ID) for D; catalog “nominal” sizes may not equal ID.
- Group fittings per section realistically; avoid double‑counting valves on the same joint.
- Enter Δz by section to capture rising and falling terrain; do not “net out” everything unless the geometry allows.
- Gauge pressures: 0 kPa means vented to atmosphere. If both ends are open tanks at the same elevation, set both to 0 kPa so Hp=0.
- Temperature changes alter ν (viscosity) and ρ; use “Custom fluid” for hot/cold liquids or special fluids.
