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GPM vs Impeller Calculator

Pump Laws Capacity (Constant Speed)

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

Definition: This calculator predicts the change in pump capacity (\( gpm_y \)) 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 flow rate, aiding in system adjustments, pump selection, and performance optimization.

2. How Does the Calculator Work?

The calculator uses the following formula for pump capacity:

Pump Capacity: \[ \frac{gpm_y}{gpm_x} = \frac{d_y^3}{d_x^3} \] or \[ gpm_y = gpm_x \times \frac{d_y^3}{d_x^3} \]

Where:

  • \( gpm_y \): New flow rate (gallon/min, m³/s)
  • \( gpm_x \): Known flow rate (gallon/min, m³/s)
  • \( d_y \): New impeller diameter (in., m)
  • \( d_x \): Known impeller diameter (in., m)

Unit Conversions:

  • Flow Rates (\( gpm_x \), \( gpm_y \)): gpm, m³/s (1 m³/s = 15850.3 gpm; 1 gpm = 6.30902e-5 m³/s)
  • Impeller Diameters (\( d_x \), \( d_y \)): in., m (1 m = 39.3701 in.)

Steps:

  • Enter the known flow rate (\( gpm_x \)), known impeller diameter (\( d_x \)), and new impeller diameter (\( d_y \)), and select their units.
  • Convert \( gpm_x \) to gpm and \( d_x \), \( d_y \) to in.
  • Calculate the new flow rate using the formula.
  • Convert the result to the selected unit (gpm or m³/s).
  • 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 Capacity Calculation

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

  • Pump System Adjustments: Allows engineers to predict how impeller size changes affect flow rate, enabling precise system tuning.
  • Energy Efficiency: Helps optimize pump performance by adjusting impeller size to meet flow requirements, reducing energy consumption.
  • System Design: Supports the selection of impellers and pumps to achieve desired performance at constant speed.

4. Using the Calculator

Examples:

  • Example 1: For \( gpm_x = 400 \, \text{gpm} \), \( d_x = 9.5 \, \text{in.} \), \( d_y = 10 \, \text{in.} \), new flow rate in gpm:
    • \( gpm_y = 400 \times \left( \frac{10}{9.5} \right)^3 \approx 400 \times \left( 1.05263 \right)^3 \approx 400 \times 1.16556 \approx 466.224 \)
    • Since 466.224 < 10000 and > 0.00001, display with 5 decimal places: \( 466.22400 \)
    • Note: The calculated value (466.224 gpm) is close to the example output of 466 gpm, with minor differences likely due to rounding in the original example.
  • Example 2: For \( gpm_x = 0.02524 \, \text{m³/s} \), \( d_x = 0.2413 \, \text{m} \), \( d_y = 0.254 \, \text{m} \), new flow rate in m³/s:
    • Convert: \( gpm_x = 0.02524 \times 15850.3 \approx 400 \, \text{gpm} \)
    • \( d_x = 0.2413 \times 39.3701 \approx 9.5 \, \text{in.} \)
    • \( d_y = 0.254 \times 39.3701 \approx 10 \, \text{in.} \)
    • \( gpm_y = 400 \times \left( \frac{10}{9.5} \right)^3 \approx 466.224 \, \text{gpm} \)
    • Convert to m³/s: \( 466.224 \times 6.30902e-5 \approx 0.029405 \)
    • Since 0.029405 < 10000 and > 0.00001, display with 5 decimal places: \( 0.02941 \)
  • Example 3: For \( gpm_x = 500 \, \text{gpm} \), \( d_x = 8 \, \text{in.} \), \( d_y = 9 \, \text{in.} \), new flow rate in gpm:
    • \( gpm_y = 500 \times \left( \frac{9}{8} \right)^3 \approx 500 \times \left( 1.125 \right)^3 \approx 500 \times 1.42383 \approx 711.914 \)
    • Since 711.914 < 10000 and > 0.00001, display with 5 decimal places: \( 711.91400 \)

5. Frequently Asked Questions (FAQ)

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

Q: How can I determine the input parameters?
A: Known flow rate (\( gpm_x \)) is the current pump output (e.g., 400 gpm). 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 capacity calculation important in pump system design?
A: It allows engineers to predict and adjust pump performance for varying impeller sizes, ensuring efficient flow delivery, optimizing energy use, and supporting system reliability at constant speed.

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