Head vs Impeller Calculator

Known Head (\( head_x \)):

Known Impeller Diameter (\( d_x \)):

New Impeller Diameter (\( d_y \)):

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

Definition: This calculator predicts the change in pump head (\( head_y \)) 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 head, aiding in system adjustments, pump selection, and performance optimization.

2. How Does the Calculator Work?

The calculator uses the following formula for pump head:

Pump Head: \[ \frac{head_y}{head_x} = \frac{d_y^2}{d_x^2} \] or \[ head_y = head_x \times \frac{d_y^2}{d_x^2} \]

Where:

\( head_y \): New head (ft, m)
\( head_x \): Known head (ft, m)
\( d_y \): New impeller diameter (in., m)
\( d_x \): Known impeller diameter (in., m)

Unit Conversions:

Heads (\( head_x \), \( head_y \)): ft, m (1 m = 3.28084 ft; 1 ft = 0.3048 m)
Impeller Diameters (\( d_x \), \( d_y \)): in., m (1 m = 39.3701 in.)

Steps:

Enter the known head (\( head_x \)), known impeller diameter (\( d_x \)), and new impeller diameter (\( d_y \)), and select their units.
Convert \( head_x \) to ft and \( d_x \), \( d_y \) to in.
Calculate the new head using the formula.
Convert the result to the selected unit (ft or m).
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 Head Calculation

Calculating the change in pump head due to impeller diameter changes is crucial for:

Pump System Adjustments: Allows engineers to predict how impeller size changes affect head, enabling precise system tuning.
System Safety: Ensures the pump head remains within system limits, preventing overpressure or insufficient performance.
System Design: Supports the selection of impellers and pumps to achieve desired performance at constant speed.

4. Using the Calculator

Examples:

Example 1: For \( head_x = 42 \, \text{ft} \), \( d_x = 9.5 \, \text{in.} \), \( d_y = 10 \, \text{in.} \), new head in ft:
- \( head_y = 42 \times \left( \frac{10}{9.5} \right)^2 \approx 42 \times \left( 1.05263 \right)^2 \approx 42 \times 1.10803 \approx 46.537 \)
- Since 46.537 < 10000 and > 0.00001, display with 5 decimal places: \( 46.53700 \)
- Note: The calculated value (46.537 ft) is close to the example output of 46.5 ft, with minor differences likely due to rounding in the original example.
Example 2: For \( head_x = 12.8016 \, \text{m} \), \( d_x = 0.2413 \, \text{m} \), \( d_y = 0.254 \, \text{m} \), new head in m:
- Convert: \( head_x = 12.8016 \times 3.28084 \approx 42 \, \text{ft} \)
- \( d_x = 0.2413 \times 39.3701 \approx 9.5 \, \text{in.} \)
- \( d_y = 0.254 \times 39.3701 \approx 10 \, \text{in.} \)
- \( head_y = 42 \times \left( \frac{10}{9.5} \right)^2 \approx 46.537 \, \text{ft} \)
- Convert to m: \( 46.537 \times 0.3048 \approx 14.184 \)
- Since 14.184 < 10000 and > 0.00001, display with 5 decimal places: \( 14.18400 \)
Example 3: For \( head_x = 50 \, \text{ft} \), \( d_x = 8 \, \text{in.} \), \( d_y = 9 \, \text{in.} \), new head in ft:
- \( head_y = 50 \times \left( \frac{9}{8} \right)^2 \approx 50 \times \left( 1.125 \right)^2 \approx 50 \times 1.265625 \approx 63.281 \)
- Since 63.281 < 10000 and > 0.00001, display with 5 decimal places: \( 63.28100 \)

5. Frequently Asked Questions (FAQ)

Q: What does the pump laws head (constant speed) calculation represent?
A: The pump laws head calculation predicts the new head (\( head_y \)) of a centrifugal pump when its impeller diameter changes, assuming constant speed, based on the quadratic relationship between head and impeller diameter.

Q: How can I determine the input parameters?
A: Known head (\( head_x \)) is the current pump head (e.g., 42 ft). 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 head calculation important in pump system design?
A: It allows engineers to predict and adjust pump performance for varying impeller sizes, ensuring appropriate head delivery, optimizing system safety, and supporting reliable operation at constant speed.