which single modification to this venturi meter increases the maximum air flow speed at the entrance that can be measured?

The single modification is to increase the density of the manometer fluid (for example, use mercury instead of water in the manometer).

Why this increases the maximum measurable entrance speed

For a Venturi meter, the entrance speed v1v_1v1​ is related to the pressure difference ΔP=P1−P2\Delta P=P_1-P_2ΔP=P1​−P2​ between the entrance and the throat by Bernoulli’s equation and continuity. The manometer does not directly measure ΔP\Delta PΔP; it measures a height difference hhh, and those are related by

ΔP=ρmangh\Delta P=\rho_{\text{man}}ghΔP=ρman​gh

where ρman\rho_{\text{man}}ρman​ is the density of the manometer fluid.

• If ρman\rho_{\text{man}}ρman​ is larger (e.g., mercury vs. water), then for a given maximum readable height hmax⁡h_{\max}hmax​, the maximum pressure difference the instrument can register is larger because ΔPmax⁡=ρmanghmax⁡\Delta P_{\max}=\rho_{\text{man}}gh_{\max}ΔPmax​=ρman​ghmax​ is larger.

• A larger ΔPmax⁡\Delta P_{\max}ΔPmax​ corresponds, via Bernoulli’s equation, to a larger difference in speeds between entrance and throat, and therefore to a higher maximum entrance air speed that can still be measured before the manometer “maxes out.”

So, without changing the geometry of the Venturi tube itself (same entrance and throat area), switching to a denser manometer fluid increases the range of pressure differences you can measure, which in turn increases the maximum air flow speed at the entrance that the meter can accurately capture.

Why not just change the Venturi geometry?

Many students wonder whether decreasing the throat area, changing the angles, or altering the tube length is the “single modification” that increases the maximum measurable speed.

• Changing the throat to a smaller area does increase the speed in the throat for a given entrance speed, but the meter’s limit in this type of question is set by how large a ΔP\Delta PΔP the manometer can represent, not by the Venturi’s geometry itself.

• As long as the air remains in the same (non-choked) regime and the flow assumptions hold, the bottleneck is the maximum measurable ΔP\Delta PΔP, which is controlled by the manometer fluid density and max height , not primarily by adjusting the cone angles or throat length.

Because the problem usually says you may make only one change to the apparatus, and the Venturi dimensions are otherwise fixed by design, the most effective single change is to use a denser manometer fluid so that much larger ΔP\Delta PΔP (hence higher speeds) can be captured before the manometer reading saturates.

TL;DR:
Use a denser manometer fluid (like mercury) so that the device can register larger pressure differences for the same column height, allowing it to measure higher entrance air speeds before reaching its reading limit.

Information gathered from public forums or data available on the internet and portrayed here.