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:
2
τ
2
d
d
2
t
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 /s 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 =32.1740 is a unit conversion factor.
U(t)
h
2
τ
L
2g
τ
L
g=9.81
2
m
γ=
2Lμ
ρg
2
R
2g
L
μ
ρ
R
f=
P
g
c
2ρg
g
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.