Which principle describes the relationship between resistance, pressure, and volume?

Which principle describes the relationship between resistance, pressure, and volume?

• A. Bernoulli principle
• B. Poiseuille's law
• C. Ohm's law
• D. Fick's law

Answer: (B)

In laminar flow through a long straight tube, the amount of liquid that moves per unit time (volume flow) is set by the pressure difference that pushes the fluid and the viscous resistance offered by the liquid and the tube. Poiseuille's law captures this relationship: the volume flow Q is proportional to the pressure difference ΔP and to the fourth power of the radius r, while inversely proportional to the viscosity μ and the tube length L. It can be written as Q = (π ΔP r^4) / (8 μ L), and this leads to ΔP = Q R with the resistance R = (8 μ L) / (π r^4). This shows clearly how pressure drives flow and how resistance, determined by viscosity, length, and especially radius (a r^4 effect), governs that flow. Because radius has such a strong influence, small changes in vessel diameter dramatically alter the flow. Other principles don’t describe this specific link. Bernoulli’s principle deals with energy conservation between pressure and velocity in inviscid flow, not viscous resistance. Ohm’s law is the electrical analogy (voltage, current, resistance). Fick’s law describes diffusion flux.

In laminar flow through a long straight tube, the amount of liquid that moves per unit time (volume flow) is set by the pressure difference that pushes the fluid and the viscous resistance offered by the liquid and the tube. Poiseuille's law captures this relationship: the volume flow Q is proportional to the pressure difference ΔP and to the fourth power of the radius r, while inversely proportional to the viscosity μ and the tube length L. It can be written as Q = (π ΔP r^4) / (8 μ L), and this leads to ΔP = Q R with the resistance R = (8 μ L) / (π r^4). This shows clearly how pressure drives flow and how resistance, determined by viscosity, length, and especially radius (a r^4 effect), governs that flow. Because radius has such a strong influence, small changes in vessel diameter dramatically alter the flow.

Other principles don’t describe this specific link. Bernoulli’s principle deals with energy conservation between pressure and velocity in inviscid flow, not viscous resistance. Ohm’s law is the electrical analogy (voltage, current, resistance). Fick’s law describes diffusion flux.