- #1

- 14

- 0

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 3.97 cm long needle is 0.406 mm and the required flow rate is 3.95 cm3 of blood per minute. How high should the bottle be placed above the needle?

Use 0.004 Pa and 1050 kg/m3 for the viscosity and density of blood respectively. Assume the blood pressure is 18.0 torr (mm Hg) above atmospheric pressure.

First of all, I need to determine what pressure is necessary to sustain a fluid flow rate of 3.95cm3/min (SI=6.583x10-8 m^3/s). I can use Poiseulle's equation to find the pressure difference necessary. Using the the following variables (in SI):

Pressure diff= 8*n*l*Q/Pi*r^4

where n=.004Pa-s, l=.0397m, Q=6.58x10^-8m^3/s, r=.000406m

I get 980 Pa, which tells me that 980Pa of pressure is necessary to sustain the above flow rate.

Now, I need to worry about the blood pressure. If bp is 18torr above atm, bp=18torr*133Pa/Torr + 101300Pa = 103694Pa.

So the total pressure that I need going into the needle is 104674Pa (980+103694).

Now I use P=P0+rho*g*h to figure out how high i need to raise the bottle.

104674 = 101300 + 1050kg/m^3* 9.8 m/s^2 * H

and get H = .328m

Which is wrong.. can anyone tell me where I went wrong? I can't figure it out.

Thanks