If the tube radius doubles while flow and other factors remain constant, Flow increases by what factor according to Flow = ΔP × r^4?

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Multiple Choice

If the tube radius doubles while flow and other factors remain constant, Flow increases by what factor according to Flow = ΔP × r^4?

The key idea here is that flow in a tube is proportional to the radius to the fourth power. If the radius doubles, the r^4 term becomes (2r)^4 = 16 r^4. With ΔP and other factors held constant, flow scales with r^4, so it increases by a factor of 16. So doubling the radius yields a 16-fold increase in flow. The other options don’t fit because they reflect smaller power changes or no change, but the r^4 relationship means a fourfold-power boost: 2^4 equals 16.

The key idea here is that flow in a tube is proportional to the radius to the fourth power. If the radius doubles, the r^4 term becomes (2r)^4 = 16 r^4. With ΔP and other factors held constant, flow scales with r^4, so it increases by a factor of 16.

So doubling the radius yields a 16-fold increase in flow. The other options don’t fit because they reflect smaller power changes or no change, but the r^4 relationship means a fourfold-power boost: 2^4 equals 16.

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