Smoking causes blood vessels to constrict. If the average blood vessel radius of a smoker decreases 7.6% and the body increases blood pressure to maintain a constant flow. Calculate the needed percent increase in pressure.

To calculate the needed percent increase in pressure, we can use the relationship between blood flow, blood vessel radius, and blood pressure.

According to Poiseuille's Law, blood flow (Q) is directly proportional to the fourth power of the blood vessel radius (r) and the pressure difference (ΔP), and inversely proportional to the viscosity of blood (η) and the length of the blood vessel (L):

Q ∝ r^4 * ΔP / η * L

Since we want to maintain a constant flow (Q) despite the decrease in blood vessel radius due to smoking, we can rewrite the equation as follows:

r_initial^4 * ΔP_initial / η * L = r_smoker^4 * ΔP_smoker / η * L

We know that the radius decreases by 7.6%, so the new radius (r_smoker) is 92.4% (100% - 7.6%) of the initial radius (r_initial). Substituting this value, the equation becomes:

(r_initial * 0.924)^4 * ΔP_initial / η * L = r_initial^4 * ΔP_smoker / η * L

Simplifying the equation, we can cancel out the common terms:

0.924^4 * ΔP_initial = ΔP_smoker

To calculate the needed percent increase in pressure, we need to find the difference between the initial pressure (ΔP_initial) and the smoker's pressure (ΔP_smoker), and then calculate the percentage increase relative to the initial pressure.

Percent increase in pressure = [(ΔP_smoker - ΔP_initial) / ΔP_initial] * 100

However, since we don't have specific values for the initial pressure or the smoker's pressure, we cannot calculate the exact percent increase without those values.