A venturi-meter is used to measure the volume flow rate of an ideal...

The volume flow rate $Q$ through a venturi-meter is given by the formula derived from Bernoulli's principle and the equation of continuity:

$Q = A a \sqrt{\dfrac{2 \Delta P}{\rho (A^2 - a^2)}}$

where $A$ and $a$ are the cross-sectional areas of the broader section and the throat respectively, $\rho$ is the density of the liquid, and $\Delta P$ is the pressure difference between the two sections.

From the formula, it is clear that the volume flow rate is directly proportional to the square root of the pressure difference, i.e., $Q \propto \sqrt{\Delta P}$.

If the pressure difference $\Delta P$ is doubled, the new flow rate $Q'$ will be proportional to $\sqrt{2 \Delta P}$.

Therefore, $Q' = \sqrt{2} Q$, meaning the volume flow rate increases by a factor of $\sqrt{2}$.

Answer: Increases by a factor of $\sqrt{2}$