According to Poiseuille's equation, what is the effect on flow rate if the pressure difference is doubled, assuming viscosity and radius constant?

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Multiple Choice

According to Poiseuille's equation, what is the effect on flow rate if the pressure difference is doubled, assuming viscosity and radius constant?

Explanation:
Doubling the pressure difference will double the flow rate, assuming viscosity and radius (and the tube length) stay the same. In Poiseuille’s law for laminar flow through a long, straight tube, the flow rate is Q = (π r^4 ΔP) / (8 μ L). Here, everything except ΔP is held constant, and Q is directly proportional to ΔP. So when ΔP doubles, Q doubles exactly in this ideal scenario. It’s also helpful to note that radius has a huge effect (to the fourth power), while higher viscosity or a longer tube reduce flow, but they don’t change the direct linear relationship with ΔP.

Doubling the pressure difference will double the flow rate, assuming viscosity and radius (and the tube length) stay the same. In Poiseuille’s law for laminar flow through a long, straight tube, the flow rate is Q = (π r^4 ΔP) / (8 μ L). Here, everything except ΔP is held constant, and Q is directly proportional to ΔP. So when ΔP doubles, Q doubles exactly in this ideal scenario. It’s also helpful to note that radius has a huge effect (to the fourth power), while higher viscosity or a longer tube reduce flow, but they don’t change the direct linear relationship with ΔP.

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