# Pressure and Bernoulli's Eqn

1. Nov 1, 2006

### GemmaN

"An artery of radius 1 mm leaves the heart and travels upward 0.3 m to your shoulder, where it breaks into 3 smaller veins, each of radius 0.5 mm. Blood flows through the artery at a speed of 0.8 m/s as it leaves the heart. The density of blood is 1050 kg/m^3."
I determined that the blood moves at 1.07 m/s in the smaller veins, which is correct.

I am suppose to find the difference in pressure "between a point in the artery just as it leaves the heart and a point in one of the smaller veins just at the point where they split off"
I am pretty sure I am suppose to use bernoulli's Eqn.

P1 + d*g*y1 + 1/2 *d*v1^2 = P2 + d*g*y2 + 1/2 *d*v2^2
P1 + (1050 kg/m^3)(9.8 m/s^2)(0.3m) + (1/2)(1050kg/m^3)(0.8m/s)^2 = P2 + 0 + (1/2)(1050kg/m^3)(1.07m/s)^2

I have everything to use this equation, but the initial pressure. Am I missing a way to figure that out? I can't seem to get any of my pressure equations to work for this, P = F/A, P = P0 + dgh

The answer is suppose to be 3341 pascals

2. Nov 1, 2006

### Noein

The initial pressure is not needed. The difference in pressure is equal to (P2-P1), usually abbreviated as $$\Delta P$$.

3. Nov 2, 2006

### arildno

What CRAZY individual thinks up an exercise where Bernoulli's equation is to be used on blood flow????

Blood is an extremely viscous fluid, and the arteries with so small radii, that any information gained from using Bernoulli's equation is guaranteed to be dead wrong.

At the very least, Hagen-Pousseille flow should be used as a base modelling tool (that's probably inaccurate as well).