Blood transfusion pressure problem where did i go wrong?

[mrbling]

Here is the question and my solution (Which is wrong..) my question is.. where did I go wrong?

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

 

[Bystander]

BP = 18? That is one relaxed patient!

 

[M98Ranger]

for sharing your solution and asking for feedback on where you may have gone wrong. It shows that you are actively trying to learn and improve, which is a great attitude to have in any field.

After reviewing your solution, I believe the error may lie in your calculation of the required pressure difference. While you correctly used Poiseuille's equation, you used the wrong value for the viscosity of blood. The value given for viscosity in the problem is 0.004 Pa-s, which is equivalent to 0.004 kg/m-s. However, in your calculation, you used 0.004 Pa-s instead of 0.004 kg/m-s. This leads to a much higher value for the required pressure difference, which in turn leads to a higher value for the height of the bottle.

To correct this, simply use the correct value for viscosity (0.004 kg/m-s) in your calculation. This should give you a more accurate value for the required pressure difference and the height of the bottle.

I hope this helps and good luck with your future problem-solving!