i already got my answer on the fluid mechanics of the pipe from my BME friend, and i know how blood flow and blood pressure work so i don't need your help. i'm a bio major so i get all the bio stuff no prob, but my physics is limited since i only took physics 1 and 2 and they didn't cover fluids in either. i'm good now. thanks though!

Well, your friend is wrong. Given your tone, my better judgement tells me not to help you, but I think I'd like to rise above that to show you how to analyze pressure, volume, flow, and continuity appropriately.

Pressure is NOT constant in the continuity equation. FLOW rate is constant in the continuity equation. That is, the amount (volume) of liquid that passes a given point will be constant.

E.x. If you've got a 5cm area pipe that is seeing the transfer of 3L/s of fluid and you reduce the area to 2cm, the flow rate is still 3L/s. However, given:

A1V1=A2V2 then

V2 = (A1/A2)V2 = (5/2)V2. So, the velocity will increase by a factor of 2.5!

Now, lets assume this pipe is horizontal and that there is no pump, so there is no change in potential energy associated with it. Bernouli's equation is now:

ΔP + 1/2ρΔV^2 = 0

Rearrange and

ΔP = -1/2ρΔV^2

ΔP = -1/2*ρ*(6.25-1)v^2

ΔP = -2.625*ρ*v^2

Pf = Pi - 2.625*ρ*v^2 (note: ρ & v^2 are positive by definition)

In other words, Pressure Initial (Pi) is greater than Pressure Final (Pf). So, pressure surely isn't constant, but flow is.

Glad I could help correct your misunderstandings, again