State Poiseuille's law and its relevance to vascular resistance.

• A. Flow = ΔP / R, with R ∝ 8ηL / π r^4; small radius changes have large effects on flow.
• B. Flow equals velocity times area.
• C. Flow is independent of pressure difference.
• D. Resistance inversely proportional to length.

Answer: (B)

Poiseuille's law describes how laminar flow through a long, cylindrical vessel depends on the pressure difference, the fluid's viscosity, the vessel's length, and its radius. The flow Q is given by Q = (π ΔP r^4) / (8 η L), which means flow is driven by the pressure gradient and opposed by resistance that scales with η and L and with r^4 in the denominator. Equivalently, resistance R = ΔP / Q = (8 η L) / (π r^4). This shows why small changes in radius dramatically affect flow: because resistance varies with the fourth power of radius, a tiny narrowing drastically reduces flow for the same ΔP. In the vascular system, this makes radius the dominant determinant of vascular resistance and perfusion.

Flow equals velocity times cross-sectional area is a general way to relate how much fluid passes a point, but it does not express how flow changes with pressure, viscosity, length, or radius. Poiseuille's law specifically links these factors to flow and resistance, clarifying why radius changes have such a big impact on blood flow.