Pump Sizing Calculator Documentation

Note: This documentation is based on standard fluid dynamics principles for centrifugal pumps. The actual implementation in the code may vary.

1. Objective

The Pump Sizing Calculator is a tool to determine the key performance requirements for a centrifugal pump in a given process system. It calculates the Total Dynamic Head (TDH), Net Positive Suction Head Available (NPSHa), and the required power.

2. Design Basis & Methodology

The calculator applies the energy balance equation (an extension of Bernoulli's equation) to the piping system.

Key Formulas:

Total Dynamic Head (TDH): The total equivalent height that the fluid is to be pumped, considering both static and friction losses.
```
TDH = (P_discharge - P_suction)/ρg + (Z_discharge - Z_suction) + H_friction
```
Where P is pressure, Z is elevation, and H_friction is the total head loss due to friction in the suction and discharge piping (calculated using the Darcy-Weisbach equation).
Net Positive Suction Head Available (NPSHa): The absolute pressure at the pump suction above the liquid's vapor pressure. It's a measure of how close the fluid is to flashing or cavitating.
```
NPSHa = P_suction_abs/ρg - P_vapor/ρg - H_friction_suction
```
To prevent cavitation, NPSHa must be greater than the pump's Net Positive Suction Head Required (NPSHr), which is provided by the pump manufacturer.
Power Calculation:
- Hydraulic Power (Water Horsepower): The actual power delivered to the fluid.
```
P_hydraulic = (Q * TDH * ρ * g)
```
- Brake Horsepower: The power that must be supplied to the pump shaft, accounting for pump inefficiency.
```
P_brake = P_hydraulic / η_pump
```

3. Input Parameters

Fluid Properties: Flow Rate (Q), Density (ρ), Viscosity (μ), and Vapor Pressure (P_vapor).
System Geometry: Suction and discharge vessel pressures, liquid levels/elevations, and piping details (length, diameter, fittings) for both suction and discharge lines.
Pump Efficiency (η_pump): The expected efficiency of the pump.

4. Output Results

Total Dynamic Head (TDH): The primary pump performance requirement.
NPSHa: To be compared against the manufacturer's NPSHr.
Hydraulic Power & Brake Horsepower: To size the pump motor.

5. Limitations and Assumptions

Assumes single-phase, steady-state, incompressible flow.
The accuracy of friction loss calculations depends on the accuracy of pipe roughness and fitting loss coefficients (K values).

6. Example Calculation

Goal: Determine the TDH and power for a pump transferring water.

Given:

Fluid (Water): ρ = 1000 kg/m³, Q = 20 m³/hr = 0.00556 m³/s
Suction: Open tank (0 barg), liquid level is 2m above pump centerline (Z_suction = 2m).
Discharge: Pressurized tank (2 barg), liquid level is 15m above pump centerline (Z_discharge = 15m).
Head Losses: H_friction_suction = 0.5m, H_friction_discharge = 4.0m.
Pump Efficiency (η_pump): 75%

Calculation Steps:

Convert Pressures to Head (meters of fluid): P_suction_head = (0 barg * 100000 Pa/bar) / (ρ * g) + P_atm_head = 0 + 10.33m = 10.33m (absolute) P_discharge_head = (2 barg * 100000 Pa/bar) / (ρ * g) + P_atm_head = 20.39m + 10.33m = 30.72m (absolute)
Calculate Total Dynamic Head (TDH): TDH = (P_discharge_head - P_suction_head) + (Z_discharge - Z_suction) + H_friction_total H_friction_total = 0.5m + 4.0m = 4.5m TDH = (30.72 - 10.33) + (15 - 2) + 4.5 = 20.39 + 13 + 4.5 = 37.89 meters
Calculate Hydraulic Power (P_hydraulic): P_hydraulic = Q * TDH * ρ * g P_hydraulic = 0.00556 m³/s * 37.89 m * 1000 kg/m³ * 9.81 m/s² = 2069 Watts = 2.07 kW
Calculate Brake Horsepower (P_brake): P_brake = P_hydraulic / η_pump = 2.07 kW / 0.75 = 2.76 kW

Result: The pump must provide 37.9 m of head. A motor of at least 2.76 kW (e.g., a standard 3 kW motor) is required.

Reference Standards

ANSI/HI 1.1-1.2: Hydraulic Institute Standards for Centrifugal Pumps.
API Standard 610: Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries.