Dynamic Analysis of First Order Instruments. P M V Subbarao Professor Mechanical Engineering Department. Capability to Reach Exact Equilibrium ……. First Order Instruments.
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P M V Subbarao
Mechanical Engineering Department
Capability to Reach Exact Equilibrium ……
A first order linear instrument has an output which is given by a non-homogeneous first order linear differential equation
The complex function F(s) must be decomposed into partial fractions in order to use the tables of correspondences. This gives
Conservation of Energy during a time dt
Heat in – heat out = Change in energy
Assume no losses from the stem.
Heat in = Change in energy
T determined by the thermal capacity of the thermometer and the thermal contact between the thermometer and the body whose temperature is being measured.s(t)
Change in energy of thermometer:
If the input is a sine-wave, the output response is quite different;
but again, it will be found that there is a general solution for all situations of this kind.
T determined by the thermal capacity of the thermometer and the thermal contact between the thermometer and the body whose temperature is being measured.s,max- Ttf,max
This may be rearranged to read
Force disturbing the equilibrium
Forces opposing the change:
a. Weight of column of liquid
b. Fluid friction due to viscosity of the liquid :
The fricitional pressure drop
Newton’s Law of Motion liquid are:
The essential parameters
The static sensitivity:
The dimensionless damping ratio:
The Natural Frequency:
Transfer Function of a second order system: liquid are:
y(t) liquid are:
z=0.707 liquid are: