Pressure Difference to Make Blood Flow Thru Artery

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SUMMARY

The pressure difference required to facilitate blood flow through an artery with an inner radius of 2.0 mm and a length of 0.18 m at a speed of 5.6 cm/s is calculated using the equation P1-P2 = velocity * 8 * viscosity * L / r². Given a blood viscosity of 4 x 10-3 Pa·s, the resulting pressure difference is 80.64 Pa. Variations in blood viscosity, which can range from 3 x 10-3 to 4 x 10-3 Pa·s at 37 degrees Celsius, may affect the accuracy of this calculation.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the Hagen-Poiseuille equation
  • Knowledge of blood viscosity and its temperature dependence
  • Basic skills in unit conversion (e.g., mm to meters)
NEXT STEPS
  • Research the Hagen-Poiseuille equation for laminar flow in cylindrical pipes
  • Study the effects of temperature on blood viscosity
  • Explore the impact of artery diameter on blood flow resistance
  • Learn about the physiological implications of blood flow pressure differences
USEFUL FOR

Students in biomedical engineering, medical professionals studying hemodynamics, and anyone interested in the mechanics of blood flow in arteries.

dvolpe
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Homework Statement


What is the pressure difference required to make blood flow through an artery of inner radius 2.0 mm and length 0.18 m at a speed of 5.6 cm/s?

Homework Equations


P1-P2 = Q8nL/pi*r fourth
or P1-P2 = velocity*8*viscosity of blood*L/rsquared
viscosity of blood = 4 x 10e-3
r = 2.0 mm = 2 x 10e-3 m
l = .18 m

The Attempt at a Solution


P1-P2 = .056*8*4x10e-3*.18/(2x10e-3)(2x10e-3)
P1- P2 = .322 x 10e-3/4 x 10e-6 = .08064 x 10e3 = 80.64 Pa

This is wrong when I submit it? HELP asap?

I read that whole blood viscosity at 37 degrees celsius is from 3e-3 to 4e-3; in one book it says 2.1e-3? What do I use as I suspect that is what caused my error?
 
Last edited:
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dvolpe said:

Homework Statement


What is the pressure difference required to make blood flow through an artery of inner radius 2.0 mm and length 0.18 m at a speed of 5.6 cm/s?


Homework Equations


P1-P2 = Q8nL/pi*r fourth
or P1-P2 = velocity*8*viscosity of blood*L/rsquared
viscosity of blood = 4 x 10e-3
r = 2.0 mm = 2 x 10e-3 m
l = .18 m

The Attempt at a Solution


P1-P2 = .056*8*4x10e-3*.18/(2x10e-3)(2x10e-3)
P1- P2 = .322 x 10e-3/4 x 10e-6 = .08064 x 10e3 = 80.64 Pa

This is wrong when I submit it? HELP asap?

I read that whole blood viscosity at 37 degrees celsius is from 3e-3 to 4e-3; in one book it says 2.1e-3? What do I use as I suspect that is what caused my error?

Are there any other variables?
 

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