TouchofVersed

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Dec 24, 2008
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Attending Physician
3 MCAT PHysics formulas needed are f=Av, p1 + .5(RHO)v^2 + (RHO)gh = p2 + .5(RHO)v^2 + (RHO)gh and P=F/A


ok, so it seems when dealing with fluids, these 3 formulas contradict one another.

Picture a tube with continuous water flow through it. Water flows from left to right. The left end has a small cross sectional area than the right end. (A1 <A2)

According to the flow rate equation, (v1 must be greater than v2). If v2 is smaller, than according to Bernoulli's equation, the pressure on the right side should be GREATER.

However, P=F/A says the pressure should be LESSER on the right side than the left.

anyone figure this out?


thanks
 

medicant

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Apr 14, 2007
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Pre-Medical
you are confusing two different f's. The first f is the flow rate, while the second is Force...nothing says that the forces need to be equivalent.

that being said, there are seeming contradictions in the flow rate formulae when you start looking at the human body... keep in mind that any standard equation has a basic set of assumption, any of which that may not apply in real life examples. Solution? keep the sets of formulae separate in your head.
 

junkct

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Mar 12, 2008
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Bernoulli's equation doesn't take cross-sectional area into account; it's talking about variations in pressure/velocity assuming the same cross-sectional area (or at least that's how I think of it). If a fluid is trying to flow through the tube at some speed/rate, but you slow it down somehow, there will be a pressure buildup and pressure will be higher. However, if you just let it flow at the speed it wants to, the pressure will be less because it's being relieved by being allowed to flow.
 

medicant

10+ Year Member
Apr 14, 2007
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Pre-Medical
it DOES take cross-sectional area into account...assuming laminar flow, the only way to vary the velocity of the water at constant height is to change the diameter of the pipe...
 
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