Inverted U-tube and inclined manometer use

Inverted U-tube manometer

Used to measure the small pressure difference between two points in a pipeline carrying a low-density liquid such as water. The space above the two liquid columns is filled with a lighter fluid (air or oil), so a small pressure difference gives a large, easily read difference in column heights:

$$p_A-p_B=(\gamma_w-\gamma_m)\,h$$

where $\gamma_m$ is the specific weight of the light fluid (A and B at the same level). It is chosen when the fluids are liquids of low density and the pressure difference is very small.

Single-column inclined manometer

Used to measure very small gauge pressures, mostly of gases (low draught pressures), where ordinary manometer readings would be too small to read accurately. One limb is a large reservoir and the other a narrow tube inclined at angle $\theta$ to the horizontal. The liquid moves a length $L$ along the incline for a vertical rise $L\sin\theta$, so the scale is magnified by $1/\sin\theta$. The reservoir level falls by $L\,a/A$, so

$$p=\gamma\,L\left(\sin\theta+\frac{a}{A}\right)\approx\gamma L\sin\theta$$

where $a/A$ is the ratio of the tube area to the reservoir area. It is therefore preferred where high sensitivity is needed.