1. Apr 13, 2010

### mparsons06

1. The problem statement, all variables and given/known data

A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein. The inside diameter of the 4.07 cm long needle is 0.388 mm and the required flow rate is 3.90 cm3 of blood per minute. How high should the bottle be placed above the needle? Obtain ρ and η from the Tables in the book. Assume the blood pressure is 18.5 torr above atmospheric pressure.

2. Relevant equations

ρ of blood: 1.05 x 103 kg/m3
η of blood: 4.0 x 10-3 Pa*s

I converted all the numbers to the necessary units:

Inside diameter = 0.388 mm = 0.000388 m
Length of needle = 4.07 cm = 0.0407 m
Flow rate = 3.90 cm3/min = 6.5 x 10-8 m3/s
Blood pressure = 18.5 torr above atmospheric pressure = 2466 Pa + 101300 = 103766 Pa

Last edited: Apr 13, 2010
2. Apr 13, 2010

### Redbelly98

Staff Emeritus
Looks like you would use Poiseuille's law, as in your other recent thread.

3. Apr 13, 2010

### mparsons06

Okay. So to find pressure difference:

P = 8 * η * L * Q / pi * r4
P = 8 * (0.004 Pa*s) * (0.0407 m) * (6.5 x 10-8 m3/s) / pi * (0.000194 m)4
P = 19023 Pa

If that is correct, how do I find height from this?

4. Apr 14, 2010

### mparsons06

I figured it out. Thanks.