Continuity Equation: Is It Independent of Pipe Radius?

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Discussion Overview

The discussion revolves around the continuity equation in fluid dynamics, specifically questioning whether it is independent of the pipe radius. Participants explore the relationship between cross-sectional area, velocity, and pipe radius, considering theoretical implications and dependencies.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions if the continuity equation is independent of the pipe radius, seeking clarification on the relationship.
  • Another participant asserts that the cross-sectional area (A) is dependent on the pipe radius, suggesting that as the radius decreases, the area also decreases.
  • A mathematical expression for the area (A = πR²) is provided, indicating the direct dependence on the radius (R).
  • It is proposed that the velocity (v) must increase as the radius decreases to maintain the same volumetric flow rate (Q) through the pipe.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are competing views regarding the independence of the continuity equation from the pipe radius, with some emphasizing the dependence of area on radius and others questioning the implications.

Contextual Notes

The discussion highlights the need for clarity on definitions and assumptions regarding fluid flow and the continuity equation, which may influence interpretations of independence or dependence on pipe radius.

Gear2d
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For the continuity equation (Q= Av, A is cross sectional area, v is velocity), is it independent of the radius of the pipe? If so, why?
 
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Well, is A independent of the pipe radius?
 
A=[tex]\Pi[/tex]*R^2
 
Gear2d said:
For the continuity equation (Q= Av, A is cross sectional area, v is velocity), is it independent of the radius of the pipe? If so, why?

The cross-sectional area is dependent on the radius.

The velocity must increase as the radius decreases to allow the same volume of fluid to pass through over a given time.
 

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