Height of Blood Transfusion - ?

[mparsons06]

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 PaCan someone please help me out on where to start?

 

[Redbelly98]

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

 

[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?

 

[mparsons06]

I figured it out. Thanks.