Answer: The percentage increase in diameter is 19%
Explanation:
<em>Using Poiseuille's law which states that Flow rate , Q = ΔPπr⁴/8ηl</em>
<em>where ΔP is pressure difference, π is a constant, r is the radius which is half of the diameter, η is viscosity of blood, l is length of blood vessel</em>
Let Q₁ be the intitial flow rate, Q₂ the final flow rate,r₁ and r₂ the initial and final radius.
Note: r = d/2, therefore, r₁⁴ = d₁⁴/16 r₂⁴ = d₂⁴/16
Also, Q₂ = 2Q₁, since the flow rate is doubled
Since all factors except diameter is constant, d₂⁴/16 = 2d₁⁴/16
d₂⁴/16 = d₁⁴/8
multiply both sides of the equation by 16
d₂⁴ = 2d₁⁴
taking the fourth root of both sides
d₂ = 1.19*d₁
d₂ - d₁ = 1.19d₁ - d₁
d₂ - d₁ = d₁(1.19 - 1)
d₂ - d₁ = 0.19d₁
d₂ - d₁/d₁ = (0.19d₁/d₁)*100%
(d₂ - d₁/d₁)*100% = 19%
Therefore, the percentage increase in diameter is 19%
