Intersect the pump curve with the system curve to find the true duty point
m
m
m³/h
m
m
m³/h
Operating Point (Pump ∩ System)
—m³/h
Operating flow Q*
Operating head H*: — mFlow vs rated: — %Pump coeff a: —System coeff R: —
—
Pump curve: H = H₀ − a·Q² → a = (H₀ − H_r) / Q_r²
System curve: H = H_stat + R·Q² → R = h_f / Q_design²
Operating point: Q* = √[ (H₀ − H_stat) / (a + R) ]
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Duty should sit near the pump's BEP (best-efficiency point).
Far-left of BEP → recirculation; far-right → cavitation / overload.
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Design flow only calibrates the system curve (sets R). The duty point is the
curve intersection and can land beyond design flow if the pump is oversized.
Pump Energy & Specific Energy Cost
Annual energy, running cost, and kWh per m³ — the number that drives OPEX
hf = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87)
V = Q / A = 4Q / (π × D²)
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Q in m³/s | D in m | hf in m
Valid for turbulent flow (Re > 4,000)
Typical velocity range: 0.6 – 3.0 m/s
Flow Velocity & Reynolds Number
Pipe velocity, flow regime, and kinematic viscosity at temperature
m³/h
mm
°C
Flow Analysis
—m/s
Pipe velocity
Re: —Flow regime: —ν at temp: — × 10⁻⁶ m²/s
—
V = Q / A = 4Q / (π × D²)
Re = V × D / ν
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Re < 2,000 → Laminar
2,000–4,000 → Transitional
Re > 4,000 → Turbulent
ν(T) = 1.792×10⁻⁶ / (1 + 0.0337T + 0.000221T²) m²/s
Minor Losses — Fittings & Valves (K-method)
Sum of local head losses through fittings, valves, bends, and transitions
m/s
—m
Fitting / Valve
K value
Qty
Gate Valve — fully open
0.10
Gate Valve — 50% open
2.10
Globe Valve — fully open
10.0
Ball Valve — fully open
0.05
Butterfly Valve — fully open
0.60
Check Valve (swing)
2.50
PRV / Control Valve
8.00
90° Standard Elbow
0.90
90° Long-radius Elbow
0.45
45° Elbow
0.40
Tee — straight through
0.60
Tee — branch flow
1.80
Sharp pipe entry
0.50
Rounded pipe entry
0.04
Pipe exit (to reservoir)
1.00
Sudden expansion
1.00
Sudden contraction
0.50
Strainer / screen
2.00
Minor Loss Results
—m
Total head loss
ΣK = —Pressure loss: — barEquiv. pipe length: — m (at D = 100mm, f = 0.02)
Pressure & Head Converter
Convert between metres of water head, bar, kPa, psi and feet — instantly
Equivalent Pressure / Head
—bar
Pressure
Head: — m water— kPa— psi— ft water
—
1 m water = 0.0980665 bar = 9.80665 kPa = 1.42233 psi = 3.28084 ft
1 bar = 10.1972 m | 1 psi = 0.70307 m | 1 ft = 0.3048 m
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Head ↔ pressure assumes water at ρ = 1000 kg/m³ (≈4 °C).
Advanced Pipe Design
Darcy-Weisbach Friction Loss
Rigorous head loss — all flow regimes, pipe roughness ε via Swamee-Jain
hf = f × (L/D) × V²/(2g) [Darcy-Weisbach]
─────────────────────────────
Re < 2,300 → Laminar: f = 64/Re
Re > 4,000 → Turbulent: Swamee-Jain explicit
f ≈ 0.25 / [log(ε/3.7D + 5.74/Re⁰·⁹)]² (±3% of Colebrook-White)
Thrust Block Sizing
Concrete anchor block at pipe bends, tees, and dead-ends
bar
mm
°
kN/m²
Thrust & Block Size
—kN
Net thrust force
Block bearing area: — m²Square block side: — m—
—
F = P × A × 2sin(θ/2) [resultant, N]
A = π D² / 4 [pipe bore area]
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90° bend: F = P × A × √2 Dead end: F = P × A
Block bearing area = F / σ_soil
Min embedment: 0.6 m (below frost / road loads)
Colebrook-White Friction Factor
Solve the Darcy friction factor f — the input the Darcy-Weisbach calc needs
—
mm
mm
Friction Factor
—
Darcy f (Colebrook)
Relative roughness ε/D: —Swamee-Jain f: —Regime: —Converged in — iterations
—
1/√f = −2·log₁₀( (ε/D)/3.7 + 2.51/(Re·√f) ) (implicit — iterated)
Laminar (Re < 2300): f = 64 / Re
Swamee-Jain (explicit): f = 0.25 / [ log₁₀( ε/D/3.7 + 5.74/Re^0.9 ) ]²
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Feed f into Darcy-Weisbach: h_f = f · (L/D) · V²/2g
Pipe Structural & Selection
Barlow's Formula — Pipe Pressure Rating
Allowable internal pressure based on wall thickness and material strength
Boyle's Law: P₀ × V_vessel = P_max × (V_vessel - V_water)
→ V_vessel = V_water × P_max_abs / (P_max_abs - P₀_abs)
P₀ = SF × P_min_abs − 1.013 [bar_g]
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All pressures converted to absolute (bar_a = bar_g + 1.013)
SF = 0.9 recommended (typical industry practice)
─────────────────────────────
⚠ V_water here is a rough proxy (½ · Q · 2L/a). True swing depends on the
column deceleration & pump inertia — use this only for first-pass sizing,
then confirm the vessel with a transient (water-hammer) simulation.
Pipeline Period & Critical Time
Is a valve closure "rapid" or "slow"? The 2L/a test that decides the surge
m
m/s
s
Critical Time Test
—s
Critical time T_c = 2L/a
Wave travel L/a: — sT / T_c: —Closure type: —
—
Critical (pipe) time: T_c = 2L / a
─────────────────────────────
T < T_c → rapid closure: full Joukowsky surge develops (ΔH = aV/g)
T ≥ T_c → slow closure: surge reduced (use Michaud ΔH = 2LV/gT)
Slow-Closure Surge — Michaud
Surge head for gradual valve closure, vs the Joukowsky upper bound
Q = (1/n) × A × R^(2/3) × S^(1/2) [m³/s]
A = π D² / 4 | R = D/4 (full bore)
─────────────────────────────
Self-cleansing: V ≥ 0.6 m/s for sewers
Erosion limit: V ≤ 3.0 m/s for concrete
Avg day = pop × per-capita / 1000 [m³/d], then ÷ (1 − NRW)
Max day = Avg × MDF | Peak hour = Avg × PHF
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Treatment sized on max-day; network & pumps on peak-hour.
Typical MDF 1.4–1.8 · PHF 2.0–3.0 (smaller for larger populations).
Balancing / Storage Volume
Service-reservoir volume: balancing + emergency + fire reserve
m³/d
% MDD
h @ avg
L/s
h
Required Storage
—m³
Total reservoir volume
Balancing: — m³Emergency: — m³Fire reserve: — m³≈ — h of max-day demand
—
Balancing = % × MDD (diurnal equalization, typ. 20–35%)
Emergency = hours × average hourly demand
Fire reserve = fire flow × duration
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Total = balancing + emergency + fire. Confirm balancing % from a
mass-curve (Rippl) of the actual diurnal demand pattern.
Storage & Water Quality
Reservoir / Tank Sizing
Required storage volume — operational, emergency, and fire reserve
Mass (kg/day) = Dose(mg/L) × Q(m³/day) / 1000
Solution (L/day) = Mass / (strength fraction × density)
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Typical alum dose 10–60 mg/L; jar-test to confirm for your raw water.
Weir / Flume Flow Measurement
Open-channel flow from measured head over a V-notch or rectangular weir
m
m
Measured Flow
—L/s
Discharge Q
— m³/h— m³/sEquation: —
—
V-notch 90°: Q = 1.38 · H^2.5
Rectangular (suppressed): Q = 1.84 · b · H^1.5 (Rehbock)
Cipolletti: Q = 1.86 · b · H^1.5 | Q in m³/s, H & b in m
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Valid for free-flow, fully ventilated nappe; measure H ≥ 3–4× upstream of crest.
Economic Optimization
Economic Pipe Diameter
Minimize total annual cost (capital + energy)
m³/h
—
$/kWh
%
h/yr
%/yr
years
$/m·mm
Economic Pipe Diameter
—mm
Nearest standard DN: —
Velocity at D_econ: — m/sAnnual capital cost: — $/mAnnual energy cost: — $/mCapital Recovery Factor: —
—
Minimize: TC/m = CRF × k × D + 8ρfQ³ × C_e × H / (π²η × D⁵ × 1000)
Setting d(TC)/dD = 0 → D_econ = [40ρfQ³C_eH / (π²η × CRF × k × 1000)]^(1/6)
─────────────────────────────────────────────
CRF = i(1+i)^N / [(1+i)^N − 1] (Capital Recovery Factor)
k = pipe cost coefficient [$/m per mm of diameter]
Q in m³/s · ρ = 1000 kg/m³ · C_e in $/kWh
Source: Optimum Pipeline Design (Walski et al.)
Engineering Disclaimer: These calculators are provided for indicative purposes only, based on standard hydraulic engineering formulas. Results must be verified against project-specific conditions, applicable codes (EN, AWWA, ASME, ISO), and reviewed by a qualified engineer before use in design. Mohamed Abokhatwa accepts no liability for decisions based solely on these tools.