Question

During a marathon race, a runner's blood flow increases to 10.0 times her resting rate. Her blood's viscosity has dropped to 85.0% of its normal value, and the blood pressure difference across the circulatory system has increased by 50.0%. By what factor has the average radii of her blood vessels increased?

Answer 1

1.543

Step-by-step explanation:

According to Poiseuille's law, blood flow (Q) is given by:

`Q= (\pi *\Delta P*r^4)/(8*\mu*L)`

Where ΔP is the blood pressure difference, μ is the blood viscosity, r is the radius of the blood vessel, and L is the length of the vessel.

During a marathon, the new radii of her blood vessels (r') are

`10*Q= (\pi *1.5\Delta P*(k*r)^4)/(8*0.85\mu*L)\\5.667*Q= (\pi *\Delta P*(k*r)^4)/(8*\mu*L)\\k^4=5.667\\k=1.543`

The average radii of her blood vessels increased by a factor of 1.543