Calculation: rate, radius, length, density, viscosity, pressure HELP

[hcho88]

Homework Statement

A patient is to be given a blood transfusion through a tube from a raised bottle to a needle inserted in a vein. The needle has an inner diameter of 0.5mm and is 4.0cm long. If the required blood flow rate is 4.0cm^3/minute, how high should the bottle be placed above the needle? The density of blood is 1.05x10^3 kg/m^3, its viscosity is 4.0x10^-3 Pa*s, and the patient's blood pressure is 2.70x10^3 Pa above the atmospheric pressure.

Homework Equations

Q = ($$\Pi$$Pa^2) / (8$$\eta$$$$\ell$$)
Q = A$$\nu$$
<im not sure if the ones below are relevant>
P + 0.5$$\rho$$v^2 + $$\rho$$gh = constant
h = Patm / ($$\rho$$g)

The Attempt at a Solution

I tried many different ways I could think of, but my answer was too big, something like 10m.
I tried to find v from the Q equations and subbed it into the constant equation to get h and I've also tried using only the Q equations to get the length, but all lead to failures.

The lastest I had a go at was finding h from
P + 0.5$$\rho$$v^2 + $$\rho$$gh = constant
and I got h to be 0.3m which seemed to make sense to me.
But I couldn't prove that this was happening with the given rate.

I also found the rate at the needle point using the Q equation, and found it to be 1x10^-6 m^3/s.
4.0 cm^3/minute = 2.4 m^3/s Is this correct?
If it is, I think 2.4 - (1x10^-6) would give a separate rate, for the tube.

I'm doing a lot of thinking but not getting anywhere.
I've been going in circles for a few hours trying to solve this.
Please help!

 

[AJ Bentley]

Are you sure of that viscosity formula? (should be the 4th power of the radius.)

general method would be to calculate the required pressure across the needle, using the viscosity.
Then use density and height of the supply. (Let height = h) required to get that pressure.