Internal Gear Pump Design Calculations

Internal Gear Pump Displacement Formula:

\[ Disp_{int} = \frac{\pi (D_o^2 - D_i^2) W}{4} \]

Displacement (Disp_int):

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1. What is Internal Gear Pump Displacement?

Internal gear pump displacement refers to the volume of fluid displaced per revolution of the pump. It is a critical parameter in hydraulic system design, determining the pump's flow rate capacity and sizing requirements.

2. How Does the Calculator Work?

The calculator uses the internal gear pump displacement formula:

\[ Disp_{int} = \frac{\pi (D_o^2 - D_i^2) W}{4} \]

Where:

\( Disp_{int} \) — Internal displacement (cubic inches per revolution)
\( D_o \) — Outer diameter of gears (inches)
\( D_i \) — Inner diameter of gears (inches)
\( W \) — Width of gears (inches)
\( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: The formula calculates the volumetric displacement by determining the annular area between the outer and inner gears and multiplying by the gear width.

3. Importance of Displacement Calculation

Details: Accurate displacement calculation is essential for proper hydraulic system design, pump selection, flow rate determination, and ensuring the pump meets the required performance specifications.

4. Using the Calculator

Tips: Enter all dimensions in inches. Ensure the outer diameter is larger than the inner diameter. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between displacement and flow rate?
A: Flow rate (Q) equals displacement (D) multiplied by rotational speed (N): Q = D × N.

Q2: Can this formula be used for external gear pumps?
A: No, external gear pumps use a different displacement formula based on tooth geometry and number of teeth.

Q3: How does temperature affect displacement calculations?
A: While the geometric displacement remains constant, effective displacement may vary with temperature due to material expansion and fluid viscosity changes.

Q4: What are typical displacement values for industrial gear pumps?
A: Displacement values typically range from 0.1 to 10 in³/rev, depending on pump size and application.

Q5: How accurate is this displacement calculation?
A: This provides the theoretical displacement. Actual displacement may be slightly less due to manufacturing tolerances and internal leakage paths.