Question

In: Anatomy and Physiology

If the radius of a blood vessel decreases by 30% (1/3), how does it effect blood...

If the radius of a blood vessel decreases by 30% (1/3), how does it effect blood flow?

Expert Solution

According to Hagen–Poiseuille equation

blood flow rate through the vessel depends on the difference in the pressure and the blood flow resistance

flow rate = change in the pressure between the two end of vessel / blood flow resistance

blood flow resistance =8 *N*L/( pi * R⁴)

Where N is the viscosity and L is length of the vessel and R is the radius of the vessel

From this,

the flow rate is directly proportional to Radius4

let us assume the initial radius be R

when the radius is decreased by 30% , the new radius will be

R - 30% R = R-1/3R = 2/3 R

FLOW RATE IS PROPORTIONAL TO R⁴

SO, THE NEW FLOW RATE WILL BE PROPORTIONAL TO (2/3R)⁴

THAT IS NEW FLOW RATE = (2/3)⁴ * OLD FLOW RATE

= 16/81* OF FLOW RATE =0.2* FLOW RATE

that is the flow rate is decreased by 80%

CONCLUSION

WHEN THE RADIUS IS DECREASED BY 30%, THE NEW FLOW RATE BECOME 0.2TIMES OF THE OLD FLOW RATE. THAT IS THE FLOW RATE IS DECREASED BY 80%

Sydney Mullin answered 1 year ago

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