In the Poiseuille Flow equation, what does r represent?

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In the Poiseuille Flow equation, what does r represent?

In Poiseuille's equation for laminar flow in a circular pipe, the variable r is the radius of the tube—the distance from the center of the pipe to its wall. The flow rate Q scales with r to the fourth power (Q ∝ r^4), as shown by the full expression Q = (π ΔP r^4) / (8 μ L). This means that even small changes in the pipe radius produce large changes in flow: doubling the radius increases the flow by sixteen times, all else equal. The other factors in the equation are the pressure drop ΔP, the fluid’s dynamic viscosity μ, and the pipe length L. Temperature does not appear in the standard form.

In Poiseuille's equation for laminar flow in a circular pipe, the variable r is the radius of the tube—the distance from the center of the pipe to its wall. The flow rate Q scales with r to the fourth power (Q ∝ r^4), as shown by the full expression Q = (π ΔP r^4) / (8 μ L). This means that even small changes in the pipe radius produce large changes in flow: doubling the radius increases the flow by sixteen times, all else equal. The other factors in the equation are the pressure drop ΔP, the fluid’s dynamic viscosity μ, and the pipe length L. Temperature does not appear in the standard form.

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