Which law predicts flow in a long, straight vessel and is directly related to pressure differences and the radius of the vessel?

• A. Poiseuille's law
• B. Bernoulli's principle
• C. Ohm's law
• D. Navier-Stokes equations

Answer: (A)

Flow in a long straight vessel under steady, laminar conditions is described by Poiseuille's law. It shows that the rate of fluid flow depends on the pressure difference across the vessel and on the radius raised to the fourth power, while being opposed by the fluid’s viscosity and the vessel’s length. In practical terms, this means small changes in radius produce large changes in flow because of the r^4 relationship (doubling the radius can increase flow by a factor of 16). The law assumes a Newtonian fluid, a long straight tube, and laminar flow, which makes it a good fit for many vessels under stable conditions. In ultrasound contexts, this helps explain why narrowing of a vessel can drastically reduce flow and alter Doppler readings.

Bernoulli's principle relates pressure and velocity along a streamline and isn't the direct predictor of flow rate from a pressure difference and radius. Ohm's law is an electrical analogy and doesn't provide the specific flow–radius–pressure relationship for a pipe. Navier-Stokes equations are the general fluid-motion framework from which Poiseuille's result is derived under simplifying assumptions, but Poiseuille's law gives the explicit simple relationship described in the question.