🔄 Centrifugal Pump Impeller & Slip Factor

Size centrifugal pump impellers: Wiesner & Stodola slip factor, Euler head, metric specific speed Ns, backward-curved vanes, and shaft power demand.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

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⚡ Solves 14

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📅 Released Jun 2026

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🔄 Centrifugal Pump Impeller & Backward-Curved Vanes

Real-time visual kinematics: Eye suction, backward curved vanes, relative slip flow, and discharge

📝 Configuration & Presets

💧 Water Booster Pump ⚡ Boiler Feed Stage (BFP) 🧪 Chemical ISO 2858 🚽 Wastewater Mixed-Flow

🌊 Hydraulic Duty & Liquid

Discharge Flow Q [m³/h]:

Head Target H [m]:

Pump Speed N [rpm]:

Liquid Density ρ [kg/m³]:

📐 Impeller Vanes Geometry

Tip Diameter D₂ [mm]:

Exit Width b₂ [mm]:

Blade Exit Angle β_2b [deg]:

Number of Vanes Z:

Hydraulic Efficiency η_h:

Wiesner & Euler Pump Formulation:
• Wiesner Slip Factor: σ = 1 − √(sin β_2b) / Z^0.70
• Real Euler Head: H_e = (U₂ · [σ · U₂ − V_r2 · cot β_2b]) / g
• Actual Delivered Head: H = η_h · H_e [m]
• Metric Specific Speed: N_s = N · √Q_m³/s / H^0.75.

📊 Performance Results

📊 Output Summary
💾 Fortran Source

Actual Delivered Head (H)

185.91 m

Target: 140.0 m | Shaft Power: 102.8 kW

RADIAL IMPELLER (LOW Ns)

Wiesner Slip Factor (σ) 0.834 Stodola σ = 0.810

Impeller Tip Speed (U₂) 56.5 m/s Radial Vr2 = 5.15 m/s

Metric Specific Speed (N_s) 24.7 RADIAL IMPELLER (LOW Ns)

Real Euler Head (H_e) 218.7 m 7 backward vanes

📈 Head H (m) vs Discharge Flow Q (m³/h)

📊 Wiesner Slip Factor σ vs Number of Vanes Z

=================================================================
 THERMOFLUIDCALC — CENTRIFUGAL PUMP IMPELLER REPORT
=================================================================
Case Title                 : High-Pressure Boiler Feed Pump Stage (BFP)
Operating Point            : Q = 180.0 m3/h, H_target = 140.0 m, N = 4500 rpm, rho = 920 kg/m3
Impeller Geometry          : D2 = 240.0 mm, b2 = 14.0 mm, beta2b = 25.0 deg, Z = 7 vanes
-----------------------------------------------------------------
DELIVERED HEAD (H_actual)  : 185.91 m
Euler Head (Real / Inf)    : 218.72 m / 262.41 m
SHAFT POWER DEMAND         : 102.78 kW (Overall Eff: 81.6%)
Wiesner / Stodola Slip     : 0.834 / 0.810
Tip Speed / Exit Radial    : U2 = 56.55 m/s, Vr2 = 5.15 m/s
Metric Specific Speed (Ns) : 24.7 (RADIAL IMPELLER (LOW Ns))
=================================================================

📘 Calculation Methodology & Pump Impeller Standards

Slip Factor Phenomenon (Wiesner & Stodola)

Because the number of vanes is finite, relative eddy circulation within the blade passages causes fluid to leave at an angle flatter than the physical blade angle $\beta_{2b}$, reducing the actual Euler head.

Specific Speed & Impeller Topology

Specific speed $N_s$ determines the optimal impeller geometry: radial impellers for high head and low flow, mixed-flow for intermediate duties, and axial propellers for high flow low head.

Key Engineering Assumptions

Wiesner empirical slip formulation $\sigma = 1 - \sqrt{\sin \beta_{2b}}/Z^{0.7}$.
ISO 9906 hydraulic acceptance grade modeling.
Widely used in water utilities, boiler feed pumps, and chemical processing.

ThermoFluidCalc Engineering Report