Yogita S.

asked • 12/14/19# Fluid Dynamics 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.

## 1 Expert Answer

Tom N. answered • 12/16/19

Strong proficiency in elementary and advanced mathematics

Use the equation dQ/dt = π(P_{1} -P_{2}) r^{4}/ 8nl where P_{1 }is the pressure from the bottle and equals P_{0} + hρg where ρ is density and his height. P_{2 } is the pressure at the other end of the bottle and equals P_{0} + P. Hence P_{1} -P_{2} is equal to hρg - P where P is 2400Pa. So dQ/dt = π(h•1.06x10^{3}•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.

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Yogita S.

Also why can you assume that the velocity term cancels out in bernoulli's equation? Shouldn't velocity increase since there is a height difference? Or does that term in bernoulli's equation only depend on the cross sectional area.12/14/19