Horsepower vs Impeller Calculator

Known Brake Horsepower (\( bhp_x \)):

Known Impeller Diameter (\( d_x \)):

New Impeller Diameter (\( d_y \)):

1. What is a Pump Laws Horsepower (Constant Speed) Calculator?

Definition: This calculator predicts the change in brake horsepower (\( bhp_y \)) required by a centrifugal pump when the impeller diameter changes from a known diameter (\( d_x \)) to a new diameter (\( d_y \)), with constant pump speed, based on the pump laws.

Purpose: It is used in pump system design to estimate how changes in impeller diameter affect power requirements, aiding in motor selection, energy efficiency, and system performance optimization.

2. How Does the Calculator Work?

The calculator uses the following formula for brake horsepower:

Brake Horsepower: \[ \frac{bhp_y}{bhp_x} = \frac{d_y^5}{d_x^5} \] or \[ bhp_y = bhp_x \times \frac{d_y^5}{d_x^5} \]

Where:

\( bhp_y \): New brake horsepower (hp, kW)
\( bhp_x \): Known brake horsepower (hp, kW)
\( d_y \): New impeller diameter (in., m)
\( d_x \): Known impeller diameter (in., m)

Unit Conversions:

Brake Horsepower (\( bhp_x \), \( bhp_y \)): hp, kW (1 kW = 1.34102 hp; 1 hp = 0.7457 kW)
Impeller Diameters (\( d_x \), \( d_y \)): in., m (1 m = 39.3701 in.)

Steps:

Enter the known brake horsepower (\( bhp_x \)), known impeller diameter (\( d_x \)), and new impeller diameter (\( d_y \)), and select their units.
Convert \( bhp_x \) to hp and \( d_x \), \( d_y \) to in.
Calculate the new brake horsepower using the formula.
Convert the result to the selected unit (hp or kW).
Display the result with 5 decimal places, or in scientific notation if the value is greater than 10,000 or less than 0.00001.

3. Importance of Pump Laws Horsepower Calculation

Calculating the change in brake horsepower due to impeller diameter changes is crucial for:

Pump System Design: Ensures the motor can provide sufficient power for the pump with different impeller sizes, preventing overload or underperformance.
Energy Efficiency: Optimizes motor selection and impeller sizing to match power needs, reducing energy consumption.
System Reliability: Supports consistent pump performance by ensuring adequate power for varying impeller sizes at constant speed.

4. Using the Calculator

Examples:

Example 1: For \( bhp_x = 8.15 \, \text{hp} \), \( d_x = 9.5 \, \text{in.} \), \( d_y = 10 \, \text{in.} \), new brake horsepower in hp:
- \( bhp_y = 8.15 \times \left( \frac{10}{9.5} \right)^5 \approx 8.15 \times \left( 1.05263 \right)^5 \approx 8.15 \times 1.29196 \approx 10.529 \)
- Since 10.529 < 10000 and > 0.00001, display with 5 decimal places: \( 10.52900 \)
- Note: The calculated value (10.529 hp) is close to the example output of 10.53 hp, with minor differences likely due to rounding in the original example.
Example 2: For \( bhp_x = 6.075 \, \text{kW} \), \( d_x = 0.2413 \, \text{m} \), \( d_y = 0.254 \, \text{m} \), new brake horsepower in kW:
- Convert: \( bhp_x = 6.075 \times 1.34102 \approx 8.15 \, \text{hp} \)
- \( d_x = 0.2413 \times 39.3701 \approx 9.5 \, \text{in.} \)
- \( d_y = 0.254 \times 39.3701 \approx 10 \, \text{in.} \)
- \( bhp_y = 8.15 \times \left( \frac{10}{9.5} \right)^5 \approx 10.529 \, \text{hp} \)
- Convert to kW: \( 10.529 \times 0.7457 \approx 7.851 \)
- Since 7.851 < 10000 and > 0.00001, display with 5 decimal places: \( 7.85100 \)
Example 3: For \( bhp_x = 10 \, \text{hp} \), \( d_x = 8 \, \text{in.} \), \( d_y = 9 \, \text{in.} \), new brake horsepower in hp:
- \( bhp_y = 10 \times \left( \frac{9}{8} \right)^5 \approx 10 \times \left( 1.125 \right)^5 \approx 10 \times 1.80203 \approx 18.020 \)
- Since 18.020 < 10000 and > 0.00001, display with 5 decimal places: \( 18.02000 \)

5. Frequently Asked Questions (FAQ)

Q: What does the pump laws horsepower (constant speed) calculation represent?
A: The pump laws horsepower calculation predicts the new brake horsepower (\( bhp_y \)) required by a centrifugal pump when its impeller diameter changes, assuming constant speed, based on the fifth-power relationship between horsepower and impeller diameter.

Q: How can I determine the input parameters?
A: Known brake horsepower (\( bhp_x \)) is the current pump power requirement (e.g., 8.15 hp). Known impeller diameter (\( d_x \)) is the current impeller size (e.g., 9.5 in.). New impeller diameter (\( d_y \)) is the adjusted impeller size (e.g., 10 in.).

Q: Why is the pump laws horsepower calculation important in pump system design?
A: It allows engineers to predict and adjust power requirements for varying impeller sizes, ensuring efficient motor sizing, preventing overload, and supporting reliable system operation at constant speed.