What is the Minimum Value of h for Fluid to Enter a Vein?

[Dougggggg]

Pressure in a fluid, need help, test tomorrow!

Homework Statement

There is a needle in a patient's arm and then a tube that leads to a reservoir of fluid ($$\rho$$=1050 kg/m³) located at h height above the arm. The reservior is open to air and the gauge pressure inside the vein is 5980 Pa, what is the minimum value of h that allows the fluid to enter the vein?

Homework Equations

The Attempt at a Solution

I keep getting this answer and it is off completely from the answer to the book.

(p1-p2)/((rho)g)
Latex and me don't work well together but I'm sure you get the point.

h=9.26 m

Book answer is .581 and doesn't have a unit even listed with it.


EDIT:Nevermind, I didn't know that gauge pressure was the pressure with respect to atmospheric pressure. Close thread.

 

[anathema]

Hello,

First of all, great job attempting to solve this problem! It's important to understand that gauge pressure is the pressure measured relative to atmospheric pressure. This means that the pressure inside the vein is 5980 Pa greater than the atmospheric pressure. In order to find the minimum value of h, we need to take into account the pressure at the top of the reservoir, which is also atmospheric pressure.

So, the equation you used is correct, but we need to take into account the pressure at the top of the reservoir as well. This means that our equation becomes:

(p1 - p2)/((rho)g) = h + atmospheric pressure - atmospheric pressure

Since atmospheric pressure is the same on both sides of the equation, we can cancel it out and our equation becomes:

(p1 - p2)/((rho)g) = h

Now, we can plug in the values given in the problem:

(5980 Pa - 0 Pa)/(1050 kg/m^3 * 9.8 m/s^2) = h

Solving for h, we get:

h = 0.581 m

This is the minimum value of h that allows the fluid to enter the vein. It is possible that the book answer is in meters as well, but it's always good to double check the units. Keep up the good work and good luck on your test tomorrow! Let me know if you have any other questions.