### Gear Pump Volumetric Efficiency Calculation**Problem Statement:**A gear pump has the following specifications:- Outside diameter: 75 mm- Inside diameter: 55 mm- Width: 30 mmThe actual pump flow rate at 2700 rpm and rated pressure is 0.0025 m³/s. What is the volumetric efficiency?**Solution Steps:**1. **Determine the Theoretical Flow Rate:** To find the theoretical flow rate (\(Q_{th}\)), we use the formula for the volumetric displacement of the gear pump: \[ V = \frac{\pi}{4} \cdot (D_o^2 - D_i^2) \cdot W \] Where: - \( V \) is the volumetric displacement per revolution (in \( m^3 \)) - \( D_o \) is the outside diameter - \( D_i \) is the inside diameter - \( W \) is the width Given values: - \( D_o \) = 75 mm = 0.075 m - \( D_i \) = 55 mm = 0.055 m - \( W \) = 30 mm = 0.03 m Substituting these values into the formula: \[ V = \frac{\pi}{4} \cdot (0.075^2 - 0.055^2) \cdot 0.03 \] \[ V \approx \frac{\pi}{4} \cdot (0.005625 - 0.003025) \cdot 0.03 \] \[ V \approx \frac{\pi}{4} \cdot 0.0026 \cdot 0.03 \] \[ V \approx 6.136 \times 10^{-5} \, \text{m}^3 \]2. **Convert Volumetric Displacement to Flow Rate:** The theoretical flow rate \(Q_{th}\) is the product of the volumetric displacement and the rotational speed (in revolutions per minute or rpm): \[ Q_{th} = V \cdot \text{rpm} \] Converting rpm to revolutions per

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Answered: A gear pump has a 75-mm outside…

A gear pump has a 75-mm outside diameter, a 55-mm inside diameter, and a 30-mm width. If the actual pump flow rate at 2700 rpm and rated pressure is 0.0025 m³/s. What is the volumetric efficiency?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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