# Step Response of a Manometer

Step Response of a Manometer

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.

h

The step response of a manometer obeys the following equation:

τ+2τγ+h=fU(t)

2

dh

2

dt

2

dh

dt

where 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.

U(t)

h

τ=

2

L

2g

τ

L

g=9.81

m/s

2

γ=

2Lμ

ρRg

2

2g

L

μ

ρ

R

f=

Pg

c

2ρg

g=32.1740

c

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.