Consider hydraulic pumps in general, for example gear pump shown in the figure above. Select correct equations for calculating pump theoretical volume flow rate \mathrm{ Q_p } and volume per revolution \mathrm{ V_p } .

Question

Consider hydraulic pumps in general, for example gear pump shown in the figure above. Select correct equations for calculating pump theoretical volume flow rate \mathrm{ Q_p }  and volume per revolution \mathrm{ V_p } .

BlackTom AI · Accepted Answer

First, let's restate the problem in our own terms to set the stage for analysis.
Question: Consider hydraulic pumps (e.g., a gear pump) and identify correct equations for calculating the pump theoretical volume flow rate Qp and the volume per revolution Vp.
Options:

a. ωp = Qp / Vp,rad
b. Vp = 2 · π · Vp,rad

Now evaluate each option step by step.

Option a:
- This equation expresses the fundamental relationship between flow rate, angular speed, and volume per radian: Qp is the product of angular velocity ωp (in rad/s) and the volume per radian Vp,rad. In other words, if you move a certain angle (in radians) of pump rotation, you displace Vp,rad for each radian; multiplying by how fast you rotate (rad/s) gives the volumetric flow rate (m^3/s).
- Dimensional check: [Qp] = m^3/s, [ωp] = rad/s, [Vp,rad] = m^3/rad. Multiplying ωp by Vp,rad yields (rad/s) * (m^3/rad) = m^3/s, which matches Qp. This confirms the equation is dimensionally consistent and physically meaningful.

Option b:
- This equation connects the volume per radian to the volume per revolution. A full revolution corresponds to 2π radians, so the volume displaced in one revolution is Vp,rev = Vp,rad × (2π). If Vp,rev is represented here as Vp, = Vp,rad × 2π, this aligns with the idea that total volume per cycle scales with the angular span of a revolution.
- Conceptual check: Since one complete turn sweeps 2π radians, multiplying the per-radian volume by 2π gives the per-revolution volume. This is a standard and correct relation in rotary pump theory.

Summary of reasoning for both options:
- Option a is correct because it matches the direct differential form Qp = ωp · Vp,rad, ensuring units and physical meaning align (flow rate equals angular speed times volume displaced per radian).
- Option b is correct because the total volume per revolution equals the per-radian volume multiplied by the total radians in one revolution (2π).

Since both statements reflect valid relationships between Qp, Vp,rad, and Vp,rev, they are both correct representations in this context.

BK10A6202 Mechatronics - Blended teaching, Lpr 1.9.2025-12.12.2025 Assignment 3 / Week 39

Consider hydraulic pumps in general, for example gear pump shown in the figure above. Select correct equations for calculating pump theoretical volume flow rate \mathrm{ Q_p } and volume per revolution \mathrm{ V_p } .

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