# What is Steady state: Definition and 176 Discussions

In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:

p

t

=
0

for all present and future

t
.

{\displaystyle {\frac {\partial p}{\partial t}}=0\quad {\text{for all present and future }}t.}
In discrete time, it means that the first difference of each property is zero and remains so:

p

t

p

t

1

=
0

for all present and future

t
.

{\displaystyle p_{t}-p_{t-1}=0\quad {\text{for all present and future }}t.}
The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering. If a system is in a steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various states will be repeated will remain constant. See for example Linear difference equation#Conversion to homogeneous form for the derivation of the steady state.
In many systems, a steady state is not achieved until some time after the system is started or initiated. This initial situation is often identified as a transient state, start-up or warm-up period. For example, while the flow of fluid through a tube or electricity through a network could be in a steady state because there is a constant flow of fluid or electricity, a tank or capacitor being drained or filled with fluid is a system in transient state, because its volume of fluid changes with time.
Often, a steady state is approached asymptotically. An unstable system is one that diverges from the steady state. See for example Linear difference equation#Stability.
In chemistry, a steady state is a more general situation than dynamic equilibrium. While a dynamic equilibrium occurs when two or more reversible processes occur at the same rate, and such a system can be said to be in a steady state, a system that is in a steady state may not necessarily be in a state of dynamic equilibrium, because some of the processes involved are not reversible.

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1. ### Water flowing out of a rotating vessel

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2. ### Engineering Sinusoidal steady state analysis using Laplace transform

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3. ### A Steady state confined flow field: Is it cyclic?

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4. ### Solving Equation to Analyze Steady State Current

I set up the equation ##V-iR-L\frac{di}{dt}=0##, with ##i(0)## and by solving it I got ##i(t)=\frac{V}{R}(1-e^{-\frac{R}{L}t})##. Then, since the steady state current is ##i_s=\frac{V}{R}## I imposed the condition ##i(t_1)=\frac{9}{10}\frac{V}{R}\Leftrightarrow...
5. ### Steady state heat equation in a rectangle with a punkt heat source

I have checked several textbooks about the heat equation in a rectangle and I have found none that deals with my exact problem. I have though to use separation of variables first (to no avail), then Green's function (to no avail), then simplifying the problem for example by defining a new...
6. ### Driven oscillator amplitude steady state X(t) = ##Asin(\omega t + \delta)##

I found ## \frac{\gamma}{2} = 7##, ##\gamma = 14## ##\omega_0^2 = \omega_d^2 + \frac{\gamma^2}{4} = 25## ##\omega_0 = \omega = 25##, thus ##\delta = \frac{\pi}{2}## ##A = \frac{\frac{F_0}{m}}{\sqrt((\omega_0^2 - \omega^2)+ \gamma^2\omega^2)} = 0.04## Thus, ##X(t) = 0.04sin(25t + \frac{\pi}{3} -...
7. ### I Can someone explain Quasi-steady-state cosmology to me?

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8. ### Steady State Thermal Analysis - Simulation

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9. ### Create a Phasor Diagram for Steady State Circuits

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10. ### MHB What is the maximum yield for a steady state solution?

I've got a question here which I'm really unsure what the wording is asking me to do, I've calculated (5), so worked out the steady states. However question 6 has really thrown me off with it's wording, any help would be appreciated.
11. ### MHB Steady State Question Understanding

I've got 2 questions here. I was able to work out question 5 and calculate the steady states. However for question 6 I've got no idea with the wording of the equation and where you would start, so any sort of help would be really helpful, cheers
12. ### MHB Find Steady States for Equations: u, v and Get Help with Steady State Question

Got a steady state question and was wondering if anyone would be able to check if I'm on the right track? Find the steady states of these two equations: My working out as far: $0=u*(1-u*)(a+u*)-u*v*$ $0=v*(bu*-c)$ I looked at the 2nd equation first giving: $v*=0, u*=c/b$...

14. ### I Difference between stationary and steady state

I was recently working on a problem of Griffiths and in the solution's manual it used an argument to solve a diffential equation that caught my attention. It said that it would look first to the steady state solution of the ODE. I tought "All right, I get that" but when I got to translate the...
15. ### Buck Converters in DCM in Steady State

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16. ### Could someone help with this steady state capacitors questio

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17. ### Air Compressor Model Analysis

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18. ### Energy in capacitor at steady state

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19. ### What does steady state mean for a pendulum?

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Homework Statement One end of a solid cylindrical copper rod 0.200 m long and 0.0250 m in radius is inserted into a large block of solid hydrogen at its melting temperature, 13.84 K. The other end is blackened and exposed to thermal radiation from surrounding walls at 500.0 K. (Some telescopes...
21. ### Steady state boundary conditions between metal/dielectric?

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22. ### Steady State output for Wave Input

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23. ### Steady state responses clarification of problem

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24. ### Magnitude of the transfer function

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25. T

### Heat gain (or Loss) in steady state from Metal Rod

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26. A

### I Difference between transient and steady state solution

In driven SHM, we ignore an entire section of the solution to the differential equation claiming that it disappears once the system reaches a steady state. Can someone elaborate on this?
27. C

### Is specific heat capacity always ignored in Steady State

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28. ### Isentropic Efficiency and Entropy Production Rate of Turbine

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30. ### MATLAB I with matlab designing a steady state feedback H2 control system

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31. ### Simple inductance question: Finding steady state current

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32. ### One-dimensional steady state conduction in Cylindrical coordinates

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33. ### Steady State Solution of Forced, Damped Harmonic Oscillator

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34. ### Steady state error- Control system

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35. ### Solving a System of ODE for Steady State

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36. ### What is the voltage in the inductor or capacitor for a short/open circuit?

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37. ### Steady State Distillation Process

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38. ### Circuit settles to steady state and switch is opened

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39. ### PDE: Annulus question, Steady State Temperature

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40. ### Steady State Flow out of a Tank Through a Vertical Pipe

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41. ### Steady state temp. distribution

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42. ### Steady state excess carrier - Semiconductor

Please check the following questions. Steady state of semiconductor w.r.t excess carrier. 1. If we shine photons on semiconductor and then turn the light off, semiconductor is not under the steady state condition. (it is under transient state since excess carrier concentration is decreasing)...
43. ### Engineering DC Steady State Circuit Analysis: Solving for iL, i, and Vc in a Simple Circuit

Homework Statement DC steady state circuit analysis: Consider the circuit shown below. The switch shown in the problem opens at time t = 0 seconds. If the circuit is in DC steady state at , find values for iL(0-), iL(0+), i(0-), i+, Vc(0-), Vc(0+). There is no RL or RC analysis to be performed...
44. ### Steady State Heat Equation with Source

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45. ### Thermodynamics - Steady State Nozzle, find area of inlet/exit

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46. ### How do you work out wave envelopes and asymmetries?

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47. ### What Is the Maximum Speed of a Mass in a Driven Damped Oscillator?

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48. ### Finding the Steady State Solution for a RLC circuit

Homework Statement An ideal AC voltage source generating an emf V (t) = V0 cosωt is connected in series with a resistance R, an inductance L, and a capacitance C. a) Find the steady-state solution for the charge, q(ω,t), which is of the form q0(ω)cos(ωt− δ(ω)). b) Find the steady-state...
49. ### CG location effect for steady state cornering

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50. ### Two differential equations -- Need to find steady state values

Homework Statement I have found the two equations describing the system. They are. ċ(t) = 1/θ [ f`(k(t)) -(n + δ + β)]c(t) k̇(t) =f(k(t) - (n +d)k(t) - c(t) Plugging in the numbers: ċ(t) = 2 [ 0,25k^(-0,25) -(0,10)]c(t) k̇(t) =k^0,25 - (0,6)k(t) - c(t) Since ċ(t) and k̇(t) =0 in steady...