Final answer:
The rate of fluid flow in a catheter increases with the fourth power of the increased radius of the catheter lumen (A) and higher pressure applied to the fluid line (B), according to Poiseuille's law. Therefore, the correct answer is D) A and B.
Step-by-step explanation:
The rate of fluid flow in a catheter increases with both the fourth power of the increased radius of the catheter lumen and with higher pressure applied to the fluid line. This is in line with Poiseuille's law, which states that fluid flow through a tube (such as a catheter) is directly proportional to the pressure difference across the tube and to the fourth power of the radius of the tube, while being inversely proportional to the length of the tube and the viscosity of the fluid. Thus, the correct answer to the question is D) A and B.
Increasing the length of the catheter would actually decrease the flow rate. Considering Poiseuille's law, we know that increasing radius will dramatically increase flow, because flow rate is proportional to the fourth power of radius (r4). This means, for instance, doubling the radius would increase the flow by 16 times (24). Additionally, higher pressure will also increase flow, as the flow is directly proportional to the pressure difference. However, increasing the length of the tube will increase the resistance and thus decrease the flow rate, which is why option C is not correct.