How Do You Calculate Blood Flow and Power in the Circulatory System?

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SUMMARY

The discussion focuses on calculating blood flow and power in the circulatory system, specifically through the aorta and capillaries. Key parameters include the viscosity of blood at 2.95×10-3 Pa.s, density at 1050 kg/m3, and the aorta's average radius of 1.20×10-2 m with a volume flow rate of 5.40 L/min. The calculations involve determining the average speed of blood flow and the power required to maintain this flow using principles of fluid dynamics.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the concepts of viscosity and density
  • Knowledge of the equations for volume flow rate and pressure drop
  • Basic physics concepts related to force and power
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  • Learn how to apply the continuity equation in fluid dynamics
  • Study the Bernoulli equation for fluid flow analysis
  • Explore the relationship between pressure, flow rate, and resistance in blood vessels
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Students in physics or biology, medical professionals studying circulatory dynamics, and anyone interested in the mechanics of blood flow and its physiological implications.

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Homework Statement



The blood transports substances required by the body and the waste products of metabolism. The blood contains many different constituents including red blood cells, white blood cells, platelets and protein. However, for calculation purposes, it is sufficient to treat blood as a uniform liquid with viscosity = 2.95×10−3 Pa.s and density = 1050 kg/m^3 at normal body temperature. The aorta is the principal blood vessel through which blood leaves the heart in order to circulate around the body. The average radius of the aorta is R(a) = 1.20×10−2m , the average length is L(a)= 0.210m and the volume flow rate is Q(a)= 5.40 L/min The blood circulates very slowly at V(c) = 3.75×10−4 m/s through many small blood vessels called capillaries. The average radius of a capillary is R(c)= 4.00×10−6 .

a) Calculate the average speed of the blood though the aorta.
b) Calculate the average speed of the blood though the aorta.
c) Calculate the average power supplied in maintaining the blood flow through the artery.

*net force to drive blood through the aorta is (the pressure drop along the aorta)*(the area of the aorta).


Homework Equations



h=2ycos(@)/pgr y= force tension p = density of liquid g=gravity =9.81 r = radius

y= F/l F=force l= length (i think)

P(i)-P(o) = 2y/r = 4y/r = y/r ( 3 different equations)


The Attempt at a Solution



I have no clue which equation to use to find the a,b,c...

i don't even know how to begiin..
 
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Hi abcphysics123! :smile:

(erm :redface: … what's the difference between a and b?! :confused:)
abcphysics123 said:
a) Calculate the average speed of the blood though the aorta.
b) Calculate the average speed of the blood though the aorta.
c) Calculate the average power supplied in maintaining the blood flow through the artery.

I have no clue which equation to use to find the a,b,c...

i don't even know how to begiin..

Be logical! :wink:

What is volume flow rate?

Volume flow rate = volume per second

= area times distance per second

= area times speed :smile:
 

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