A manometer is an instrument for measuring pressure. It consists of a U-shaped tube filled with liquid (usually mercury because of its high density). The difference, 2
, between the heights of the liquid is a function of the pressure difference between the two sides.
is the unit-step function,
is the height above the rest position,
is a time constant),
is the total height of the manometer, and
is the acceleration due to gravity. Also,
is a damping coefficient, where
is the viscosity,
is the density,
is the radius of the manometer, and
is proportional to the applied gas pressure, where
is a unit conversion factor.
This Demonstration shows the height above the rest position versus time. The observed behavior is typical of a second-order process. The overshoot observed in the step response of the manometer, for small values of the damping coefficient, makes it easy for manometers to overflow.