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

1. Jul 23, 2010

### hcho88

1. The problem statement, all variables and given/known data
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.

2. Relevant 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)

3. 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.