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

In summary, the conversation discusses the flow of an ideal fluid through a pipe with radius R and flow speed v. After the pipe splits into three separate paths, each with a radius of (R/2), the question is posed about the flow speed in each path. The flow rate equation is mentioned, with a suggestion that the flow speed in each path would be 4v. The concept of conservation of volume is also brought up, with the equation A*Vin = ∑ AVout used to explain that the volume of fluid flowing in must equal the volume of fluid flowing out. This leads to the conclusion that the flow speed in each path would be 3/4 of the original flow speed, or 3v.
  • #1
nothing123
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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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  • #2
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
 
  • #3
Thanks.
 

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

What is an ideal fluid?

An ideal fluid is a theoretical concept that describes a fluid with no viscosity or internal friction. This means that an ideal fluid would flow without any resistance and would not dissipate energy as heat.

How does the radius of the pipe affect the flow of the ideal fluid?

The radius of the pipe is directly proportional to the flow rate of the ideal fluid. This means that as the radius increases, the flow rate also increases, and vice versa. This is known as the Poiseuille's law.

What is the relationship between the flow speed and the pressure of the ideal fluid?

The flow speed and pressure of the ideal fluid are inversely proportional to each other. This means that as the flow speed increases, the pressure decreases, and vice versa. This is known as Bernoulli's principle.

Can an ideal fluid flow through a pipe with any shape?

Yes, an ideal fluid can flow through a pipe with any shape as long as the pipe is smooth and there are no obstructions or bends that would create turbulence in the flow.

How is the flow rate of the ideal fluid affected by the length of the pipe?

The length of the pipe does not directly affect the flow rate of the ideal fluid. However, a longer pipe may result in a decrease in flow rate due to the increase in friction between the fluid and the pipe walls.

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