An ideal fluid flows through a pipe with radius R with flow speed v

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In an ideal fluid flowing through a pipe, the flow rate must remain constant despite changes in pipe geometry. When the pipe splits into three paths with a radius of R/2, the flow speed in each path can be determined using the continuity equation, which states that the product of cross-sectional area and flow speed must be conserved. The equation A1*V1 = A2*V2 applies, leading to the conclusion that the flow speed in each smaller path is four times the original speed, resulting in a flow speed of 4v in each path. The splitting of the pipe into three sections directly affects the distribution of flow speed due to the conservation of mass. Therefore, the flow speed through each of the paths is indeed 4v.
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An ideal fluid flows through a pipe with radius R with flow speed v. If the pipe splits up into three separate paths, each with radius (R/2), what is the flow speed through each of the paths?

Would we just use the flow rate equation giving a flow speed of 4v in each of the paths? Does the fact that it split up into three have anything to do with it?
 
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You have a volume of fluid flowing through an area.

That times Velocity is the volume passing that point.

The volume has to go somewhere, so ...

A*Vin = ∑ AVout

R2*Vin = 3*(R2/4)*Vout
 
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