Radius: Flow rate vs velocity

[Necr0sis713]

I need just quick help with some physics fluid stuff.

I noticed increasing the radius by 2 would increase flow rate by 16 (2^4), but the velocity by 4?

Is this typically the case? Its Radius^2 for VELOCITY and radius^4 for FLOW RATE? Or am I missing something here?

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[aldol16]

Well, radius^4 is proportional to the volume flow rate as per Poiseuille's Law. And in terms of velocity, use the fact that volume flow rate through a tube of an incompressible fluid is constant. Therefore, flow rate = v*A = v*pi*r^2. Thus, v is inversely related to r^2. So increasing the radius by a factor of two would decrease the velocity by a factor of four.

 

[Necr0sis713]

I meant decrease, but thanks. Basically velocity is related to radius squared, and flow rate by radius^4

 

[NextStepTutor_2]

I meant decrease, but thanks. Basically velocity is related to radius squared, and flow rate by radius^4

You got it. it's all in the units. I like to tell my students that whenever you are doing any kind of physics on the MCAT, keep track of units. It will save you time in the long run and help you derive equations in unfamiliar situations and help when you can't recall the exact equation you need.

good luck!