Which law describes the relationship between flow and pressure differential, viscosity, and vessel length?

• A. Bernoulli's law
• B. Poiseuille's law
• C. Snell's law
• D. Doppler's law

Answer: (B)

Poiseuille's law specifically addresses the relationship between the flow rate of a fluid through a cylindrical vessel, the pressure differential across the vessel, the viscosity of the fluid, and the length of the vessel. According to this law, the flow rate (Q) is directly proportional to the pressure difference (ΔP) between the two ends of the vessel and inversely proportional to the viscosity (η) and length (L) of the vessel. The equation can be expressed as:

[ Q = \frac{πr^4 (ΔP)}{8ηL} ]

where r is the radius of the vessel.

This relationship is crucial in understanding how fluids move through pipes and capillaries, especially in the context of blood flow in biological systems or fluid transport in engineering. It emphasizes the importance of both the physical properties of the fluid (such as viscosity) and the geometry of the flow path (like length and radius), making Poiseuille's law fundamental in many applications involving fluid dynamics.

In contrast, Bernoulli's law pertains to the conservation of energy in fluid flow and deals with the relationship between pressure, velocity, and height of the fluid, while Snell's law relates to the refraction of light, and