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Why we are able to suck more drink through a larger diameter straw than a smaller diameter straw if $p_1 v_1 = p_2 v_2 = Q$ as per Bernoulli's Principle. The pressure difference I create in mouth while sucking will be almost same, but I get more liquid in my mouth with a larger diameter than a smaller one.

Is there any correlation between diameter of the pipe & flow rate, even when the pressure difference is the same?

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up vote 4 down vote accepted

If we assume the flow is laminar, the flow in the straw is best described by Poiseuille flow. The linked website will tell you, that the pressures drop scales with the flow-rate $Q$ and diameter $d$ as

$$ \Delta p \propto \frac{Q}{d^4} $$

The proportionality further depends on the length of the straw and the viscosity of the fluid. You can directly derive it from the Navier-Stokes equations.

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