Calculate Gear Pump Displacement

Gear Pump Displacement Formula:

\[ Disp_{gear} = 2 \times \pi \times (R_o^2 - R_i^2) \times W \]

Gear Pump Displacement (Disp_gear):

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1. What is Gear Pump Displacement?

Gear pump displacement refers to the volume of fluid displaced per revolution of the pump. It is a critical parameter in determining the flow rate and efficiency of gear pumps used in various hydraulic and fluid transfer applications.

2. How Does the Calculator Work?

The calculator uses the gear pump displacement formula:

\[ Disp_{gear} = 2 \times \pi \times (R_o^2 - R_i^2) \times W \]

Where:

\( R_o \) — Outer radius of the gear (inches)
\( R_i \) — Inner radius of the gear (inches)
\( W \) — Width of the gear (inches)
\( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: The formula calculates the theoretical displacement volume by determining the annular area between the outer and inner radii and multiplying by the gear width and a factor of 2 (for two gears in a typical gear pump).

3. Importance of Gear Pump Displacement Calculation

Details: Accurate displacement calculation is essential for proper pump selection, system design, and performance prediction in hydraulic systems. It helps determine flow rates, system efficiency, and appropriate pump sizing for specific applications.

4. Using the Calculator

Tips: Enter outer radius, inner radius, and gear width in inches. All values must be positive numbers, and the outer radius must be greater than the inner radius for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What units are used in this calculation?
A: The calculator uses inches for all dimensions, resulting in displacement in cubic inches per revolution (in³/rev).

Q2: Can I use metric units with this calculator?
A: Currently, the calculator is designed for imperial units. For metric calculations, convert measurements to inches before input or modify the formula accordingly.

Q3: What is the typical range of gear pump displacements?
A: Gear pump displacements can range from less than 0.1 in³/rev for small precision pumps to over 10 in³/rev for larger industrial applications.

Q4: How does displacement relate to flow rate?
A: Flow rate (in³/min) = Displacement (in³/rev) × RPM. The displacement represents the theoretical volume delivered per revolution.

Q5: Are there limitations to this formula?
A: This formula provides theoretical displacement. Actual flow may be slightly less due to internal leakage, fluid compressibility, and other efficiency factors.