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