## Homework Statement

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.

## Homework 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:

Redbelly98
Staff Emeritus
Homework Helper
Looks like you would use Poiseuille's law, as in your other recent thread.

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?

I figured it out. Thanks.