# How does diameter of manometer affect the sensitivity of the manometer?

I have a physics question on

How the sensitivity of the manometer will change if a narrower tube is used for the manometer.

Logically speaking, it seems normal for the sensitivity of the manometer to increase with a decreasing diameter of the manometer.

However, if we use the formula $$P=\frac{F}{a}$$

Assuming same pressure, if we decrease the diameter of the manometer, the area decreases and the force the gas acts on the liquid in the manometer decreases. In that sense, the sensitivity would decrease right.