Fluid Dynamics Question

Question

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 4.0 cm long needle is 0.40 mm and the required flow rate is 4.0 cm3 of blood per minute. How high should the bottle be placed above the needle? 

Please help!

The n value is 4*10^-3

the density is 1.06*10^3

these values are in SI units

The professor wrote to assume blood pressure is 2400 Pa over atmospheric pressure. However, I do not know how to use this information.

Answer 1

Use the equation dQ/dt = π(P₁ -P₂) r⁴/ 8nl where P₁ is the pressure from the bottle and equals P₀ + hρg where ρ is density and his height. P₂ is the pressure at the other end of the bottle and equals P₀ + P. Hence P₁ -P₂ is equal to hρg - P where P is 2400Pa. So dQ/dt = π(h•1.06x10³•9.8 - 2400)(.2x10^-3)⁴/8•4x10^-3•.04. So 4x10^-6/60 = π( h• 10388 -2400)1.6x10^-15/1.28x10^-3. Then h•10388 -2400 = 5.12x10^-9/60•π•1.6x10^-15 =16976 and h = (16976 + 2400)/10388 wich gives h=1.87m for the height.