Question

A 53-years old lady was found by imaging to have 50% narrowing in her left renal artery. The change in blood flow for that artery is: (poiseuille Law)

A. 1⁄3 reduction in flow
B. 1⁄2 increase in flow
C. 1/16 increase in flow
D.1/16 reduction in flow

Answer 1

D. 1/16 reduction in flow

Step-by-step explanation:

Poiseuille's law says that the flow rate in a tube or pipe is:

`Q=(\pi P r^4)/(8 \eta L)`

where P is the pressure difference, r is the radius, η is the viscosity, and L is the length.

Assuming that P, η, and L are constant, then we can say Q is proportional to r⁴.

Q ∝ r⁴

A 50% narrowing means the new radius is r/2. Thus the new flow is:

Q₀ / r⁴ = Q / (r/2)⁴

Q₀ / r⁴ = 16 Q / r⁴

Q = Q₀ / 16

There is a 1/16 reduction in flow.