In the shown pressure catheter–diaphragm sensor, liquid resistance RL arises from viscous friction. Only catheter radius is doubled, with pressure difference fixed. What happens to RL?
For laminar flow in a circular catheter, Poiseuille resistance is RL=8μL/(πr⁴). Holding fluid and length fixed, doubling radius multiplies r⁴ by sixteen, so resistance becomes RL/16. Thus A. Fixed pressure difference changes flow rate accordingly.
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