How high should the bottle be placed above the needle?

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SUMMARY

The discussion focuses on calculating the height at which a blood transfusion bottle should be placed above a needle to achieve a required flow rate of 3.88 cm³ per minute. The relevant equation used is Q = [πr⁴ΔP] / [8ηL], where the parameters include the needle's diameter of 0.393 mm and a blood pressure of 19.3 torr. The user attempts to derive the height using the equation h = (P2 - Patm + ΔP) / (ρ * g) but arrives at an incorrect answer, indicating a need for further clarification on the calculations.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Poiseuille's law.
  • Familiarity with blood properties, including density and viscosity.
  • Knowledge of pressure units, particularly torr and Pascal.
  • Basic algebra and calculus skills for manipulating equations.
NEXT STEPS
  • Review Poiseuille's law and its application in fluid flow calculations.
  • Study the properties of blood, focusing on viscosity and density values.
  • Learn about pressure conversions between torr and Pascal for accurate calculations.
  • Explore common mistakes in fluid dynamics problems to avoid similar errors.
USEFUL FOR

This discussion is beneficial for medical students, healthcare professionals involved in transfusion procedures, and anyone studying fluid dynamics in a biomedical context.

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Homework Statement



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 3.82 cm long needle is 0.393 mm and the required flow rate is 3.88 cm3 of blood per minute. How high should the bottle be placed above the needle? Obtain r and h from the Tables in the book. Assume the blood pressure is 19.3 torr above atmospheric pressure.

Homework Equations



Q = [pi*r4*\DeltaP] / [8\eta*L]


The Attempt at a Solution



Q = [pi*r4*\DeltaP] / [8\eta*L]

=> \LambdaP = [(3.88*10^-6)/60s) * 8*4*10^-3*3.82*0.01] / pi*(0.1965)^4 = 16877 Pa

h = (P2 - Patm + \DeltaP ) / \rho * g

= 2573 Pa - 101325Pa + 16877Pa / (1.05*10^3 * 9.8) = wrong answer.

Please advise! Thanks!
 
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