What is the equation derived from Poisuille's law for flow?

The correct answer reflects a key concept from Poiseuille's law, which describes the flow of a fluid in a cylindrical pipe. According to Poiseuille's law, the flow rate (Q) of an incompressible, Newtonian fluid through a long, straight tube is influenced by several factors: the pressure difference across the tube, the tube's length, the radius of the tube, and the viscosity of the fluid.

The equation derived from Poiseuille's law can be expressed in terms of pressure difference as follows:

Pressure difference (ΔP) = (8 × flow × length × viscosity) / (π × radius^4)

This formulation highlights that the flow rate is directly proportional to the pressure difference and the radius of the tube raised to the fourth power, while it is inversely proportional to the viscosity of the fluid and the length of the tube. When rearranging the equation to isolate the pressure aspect as presented in the correct option, it emphasizes these relationships, making it clear how critical these factors are in determining fluid flow through vessels.

Therefore, the correct answer encapsulates this relationship accurately, confirming that pressure is dependent on factors such as flow rate, length, viscosity, and radius, providing a comprehensive understanding of fluid dynamics in