For a piezometer tube, the pressure in the pipe or container $P_A$ is: $$P_A={\gamma }_1{h}_1+P_{atm}$$ where ${\gamma }_1$ is the specific weight of the fluid in container A, $h_1$ is the height of fluid A in the manometer, ${\gamma }_2$ is the specific weight of the manometer fluid, and $h_2$ is the height of the manometer fluid.

The pressure difference in a differential U-tube manometer can be derived by expanding on the U-tube manometer design equation: $${\gamma }_1{h}_1+P_A={\gamma }_2{h}_2+{\gamma }_3{h}_3+P_B$$ where $P_B$ is the pressure in container B, ${\gamma }_3$ is the specific weight of the fluid in container B, and $h_3$ is the height of the fluid in container B. All the other variables are the same as in a U-tube manometer.

The equation for an inclined manometer can be derived by expanding the equation for a differential U-tube manometer. $$P_A–P_B={\gamma }_2{l}_{2}sin(\theta )+{\gamma }_3{h}_3–{\gamma }_1{h}_1$$  where $l_2$ is the length of the manometer tube and $\theta$ is the angle of the tube.