Continuity Equation: Is It Independent of Pipe Radius?

AI Thread Summary
The continuity equation, expressed as Q = Av, indicates that the flow rate (Q) is a product of cross-sectional area (A) and velocity (v). The cross-sectional area is directly dependent on the pipe radius, calculated as A = πR². As the radius of the pipe decreases, the velocity of the fluid must increase to maintain the same flow rate. Therefore, the continuity equation is not independent of pipe radius; changes in radius directly affect both area and velocity. Understanding this relationship is crucial for fluid dynamics in pipe systems.
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=\Pi*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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