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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Dynamic Analysis of First Order Instruments
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
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.
This may be rearranged to read
The forces that are acting on the length L of the manometer liquid are:
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
The essential parameters
The static sensitivity:
The dimensionless damping ratio:
The Natural Frequency:
Transfer Function of a second order system: