Question

10. Viscous blood is flowing through an artery partially clogged by cholesterol to double the flow rate of blood through this artery. If the original diameter of the artery is D, what should be the new diameter (in terms of D) to accomplish this for the same pressure gradient?

Answer 1

Answer:

D’ =1.19D

Explanation:

Flow rate of pressure in blood artery can be written as

Q= ΔP × π(D/2)4 / 8ηL

where Q be the initial flow rate, ΔP pressure gradient,  L be the length of artery and η is the viscosity and D is the initial diameter

Now to make flow rate double (2Q) Q’, we take the new diameter as D’.

Multiplying the original equation with 2;

2Q = 2×ΔP×π(D/2)4 / 8ηL

2×ΔP×π(D/2)4 / 8ηL = ΔP ×(D’/2)4 / 8ηL

2×(D/2)4=(D’/2)4

Solving the above we get

D’ =1.19D