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.