Final answer:
To maintain the flow rate in a pipe if its length is doubled, the pressure difference must be increased due to increased resistance. This is consistent with Poiseuille's Law, which explains how flow rate depends on pressure difference, viscosity, and dimensions of the pipe.
Step-by-step explanation:
If the length of the pipe is doubled for a fluid flowing through a pipe of fixed radius, the pressure difference between the two ends must be increased to maintain the flow rate. This is due to the fact that the resistance to flow in the pipe is proportional to its length according to Poiseuille's Law. Therefore, when the length of the pipe is increased, the resistance to flow increases as well, necessitating a higher pressure difference to push the same volume of fluid through the pipe.
Considering a realistic fluid and Poiseuille's Law, we can illustrate the sensitivity of flow rate to various factors. For example, different conditions will result in different flow rates such as when the pressure difference is increased, when there is a new fluid with a greater viscosity, changes in the length of the tube, changes in the radius of the tube, or a combination of tube radius, length, and pressure changes.