When the radius of a flow tube decreases, the flow rate does what?

When the radius of a flow tube decreases, the flow rate does what?

• A. Increases
• B. Stays the Same
• C. Varies with Pressure
• D. Decreases

Answer: (D)

Flow rate through a tube is highly sensitive to the radius because of Poiseuille’s law. For a long, straight, laminar tube with steady flow, the rate Q of fluid moving through the tube is proportional to the fourth power of the radius: Q ∝ r^4, assuming the pressure difference driving the flow and the fluid’s viscosity and tube length stay fixed. This means that when the radius shrinks, the flow rate drops dramatically. For example, halving the radius reduces flow by 2^4 = 16 times. The underlying reason is that smaller radius greatly increases resistance to flow (resistance scales as 1/r^4), so with the same driving pressure, the flow decreases. In physiological terms, this mirrors how vasoconstriction (radius decrease) reduces blood flow to tissues. If the pressure gradient were allowed to rise to offset the change, flow could be maintained, but under the common assumption of a fixed driving pressure, the flow decreases.

Flow rate through a tube is highly sensitive to the radius because of Poiseuille’s law. For a long, straight, laminar tube with steady flow, the rate Q of fluid moving through the tube is proportional to the fourth power of the radius: Q ∝ r^4, assuming the pressure difference driving the flow and the fluid’s viscosity and tube length stay fixed. This means that when the radius shrinks, the flow rate drops dramatically. For example, halving the radius reduces flow by 2^4 = 16 times. The underlying reason is that smaller radius greatly increases resistance to flow (resistance scales as 1/r^4), so with the same driving pressure, the flow decreases. In physiological terms, this mirrors how vasoconstriction (radius decrease) reduces blood flow to tissues. If the pressure gradient were allowed to rise to offset the change, flow could be maintained, but under the common assumption of a fixed driving pressure, the flow decreases.