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:




for all present and future


{\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:







for all present and future


{\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. Bling Fizikst

    Water flowing out of a rotating vessel

    Let's say at the steady state the vertex of the parabola (paraboloid) is at the origin . Then the eqn of the formed parabola would be $$y=\frac{\omega^2x^2}{2g}$$ Now , initial volume of liquid is ##\pi R^2h## . As the liquid flows out of the orifice , the surface would maintain it's structure...
  2. Wrichik Basu

    Engineering Sinusoidal steady state analysis using Laplace transform

    ##\require{physics}##The given circuit is this: The question is taken from this video. The Professor has solved it using Phasor analysis, the final solution being $$\begin{equation} i_x(t) = 7.59 \sin \qty( 4t + 108.4^\circ )~\mathrm{amps}. \end{equation}$$My aim, however, is to use Laplace...
  3. huangdaiyu

    A Steady state confined flow field: Is it cyclic?

    For a fluid that is confined to a finite region with no sources and sinks, are the only options for the flow field a) static, and b) cyclic? The example I have in mind is Rayleigh convection in a shallow dish heated from below, where convection cells are formed beyond a certain temperature...
  4. L

    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. fluidistic

    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. R

    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. TheHeraclitus

    I Can someone explain Quasi-steady-state cosmology to me?

    I know it says Universe is eternal, how does that work with gravity? If all the stars and galaxies had infinite time to attract each other why are they still apart? I guess this is a naïve question because no one talks about it but I can't figure it out. Thank you for answers!
  8. S

    Steady State Thermal Analysis - Simulation

    I am simulating a hot forging process in LS-Dyna. A tool is contacting a hot workpiece for 2 sec every 10 sec (--0 sec--contact--2 sec--no contact---10 sec--) in a factory. Since this is a continuous process, the tool should, at some point, attain steady temperature. I have tried to recreate it...
  9. nobodyjusttrying

    Create a Phasor Diagram for Steady State Circuits

    So all we have to do is find the current and power distribution in the steady state circuit. Create a phasor diagram. I don't exactly know how to tell it in english, but i think there is a thing I called c. & p. paths.
  10. M

    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. M

    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. M

    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: \[ v*=0, u*=c/b \]...
  13. Richard Parker

    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...
  14. dvscrobe

    Buck Converters in DCM in Steady State

    Let K=2Lfs and Pin=Pout, Have, (Vin-Vo)/k D^2 Vin =Vo ^2/R (I am fine up to this part. I am equating input power to output power) V^2=D^2 + D^2 R/2 Vo Vin - R/k D ^2 Vin =0 (This is where the instructor takes over. Can’t figure out how he got to V^2. Where did that come from? Thought I was...
  15. J

    Could someone help with this steady state capacitors questio

    Homework Statement Question: https://imgur.com/a/EmGDW87 Homework Equations Q =VC V = IR The Attempt at a Solution I don't understand how the capacitor C_2 is in parallel with R, which would dictate that they have the same p.d, but then again the circuit is in stead state and so no current...
  16. D

    Air Compressor Model Analysis

    I have an interest in storing, for later use, energy from excess shaft power developed by a wind turbine. Currently I am assuming that the compressor is running in a steady fashion, continually drawing 300K, 1.0 atm. air into the compression chamber and compressing it to 20 atms. before...
  17. Krushnaraj Pandya

    Energy in capacitor at steady state

    Homework Statement In the circuit shown, C1= 1 microfarad, C2=3 microfarad, in steady state, the energy stored in these capacitors are? Homework Equations Kirchoff's laws, E=0.5CV^2, V=IR The Attempt at a Solution At steady state, no current passes through the capacitors, so current is...
  18. M

    What does steady state mean for a pendulum?

    Hi there. I am working on some exercises where they ask about the steady state of a pendulum. I have had quantum mechanics, where the steady state meant a time independence. But I don't really see what this means for a pendulum. Is it steady when it's velocity is zero so there is no time...
  19. S

    Steady state heat flow: radiation and conduction

    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...
  20. Dor

    Steady state boundary conditions between metal/dielectric?

    There are few thing I'm not sure of and be happy for clarifications. In general: at steady state, what are the electric-field,potential, and current boundary conditions between a conductor and a dielectric medium? more specific: a) When dealing with a perfect conductor there exist a surface...
  21. S

    Steady State output for Wave Input

    1. Problem Statement Find the steady state output yss(t) for the input u(t)=t-π in terms of an infinite sum of sinusoids. We are given the transfer function as: 2. Homework Equations G(i) = ... |G(ik)| = ... Φ(ik) = ... (this is the angle) yss(t) = βk||G(ik)|ei(kt+Φ(ik)) ***check that this...
  22. S

    Steady state responses clarification of problem

    Homework Statement I am trying to understand what the difference in the two questions (linked) are. I understand how to find the steady state response for x. Is the second question just asking for the first and fourth element in the Xss matrix? Homework Equations Xss=[q1 q2 q1dot q2dot] The...
  23. Z

    Magnitude of the transfer function

    Hi all, In one of my problems there is a question with a plot of the transfer function magnitude versus frequency. In the graph I notice that the magnitude of the transfer function is greater than 1. This is confusing as I thought that filters are not able to increase the magnitude of the output...
  24. T

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

    Hello, I got this problem but I don't know How can Find Heat loss (or gain) - Q3 - from the curved surface of the metal rod to the surrounding. This is the problem: A metal rod, of diameter (d) and length (L), runs between two hot walls at temperatures, T1 (Wall 1) and T2 (Wall 2)...
  25. 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?
  26. C

    Is specific heat capacity always ignored in Steady State

    Hi, I want to simulate a forced convection cooling problem. Air at ambient temperature is forced through a fan into a system to cool electronics and I would like to assess the temperature of the outlet air. Actually I'm interested in the delta between the ambient and outlet temperature. This...
  27. AGiantGolden49er

    Isentropic Efficiency and Entropy Production Rate of Turbine

    Homework Statement Water vapor at 6 MPa, 600C enters a turbine operating at steady state and expands to 10 kPa. The mass flow rate is 2 kg/s, and the power developed is 2626 kW. Stray heat transfer and kinetic and potential energy effects are negligible. Determine (a) the isentropic turbine...
  28. H

    DG Connection: Estimating Voltage Rise at Point of Common Coupling (PCC)

    Hi! According to the book "Renewable Energy on Power Systems" by Freris & Infield, the voltage rise due to injection of power in pcc can be estimated from the Thevenin equivalent representing the network "upstream" pcc (Figure 1). The Thevenin voltage can be taken as the nominal voltage in the...
  29. N

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

    Hi everyone. I'm designing a steady state feedback H2 control system. Actually, my major is tribology and I have no experience in designing control system. So it is really big problem for me. Anyway, this is my simple model of tribometer which applies normal load on the surface. (is it...
  30. A

    Simple inductance question: Finding steady state current

    Homework Statement Homework Equations I = E / R_total The Attempt at a Solution I mostly just want to clarify that my thinking is correct. The solution for this problem shows that the current is split evenly between the two paths. Is that because we're assuming that the inductor has no...
  31. Hannibal247

    One-dimensional steady state conduction in Cylindrical coordinates

    Hello, Im having some issues with my task. 1. Homework Statement The heat generation rate of a cylindrical fuel (D=0.2 m and 1 m long) is 160 kW. The thermal conductivity of the fuel is 100 W/mK and its surface temperature is maintained at 283 K. Determine the temperature at the axis...
  32. T

    Steady State Solution of Forced, Damped Harmonic Oscillator

    Homework Statement A damped harmonic oscillator is driven by an external force of the form $$F_{ext}=F_0sin(\omega t)$$ Show that the steady state solution is given by $$x(t)=A(\omega)sin(\omega t-\phi)$$ where $$ A(\omega)=\frac{F_0/m}{[(\omega_0^2-\omega^2)^2+4\gamma^2\omega^2]^{1/2}} $$ and...
  33. K

    Steady state error- Control system

    Hello, I have a question about steady state error. how can we get to the C? I think it has to be Ea(G1+D)G2=C which gives(R-NH)(G1+D)G2 / (1+(G1+D)G2H)=C
  34. B

    Solving a System of ODE for Steady State

    I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following: d0 = 0.003, d1 = 0.008, d2 = 0.05, d3 = 1, ry = 0.008, ay = 1.6/100...
  35. S

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

    Homework Statement {Moderator edit: The unlabeled resistance is given to be 3.2 Ω } finding v1 and v2 at t=0+ and t=0- is needed Homework EquationsThe Attempt at a Solution ok I've found the currents by mesh analysis but how can i get the voltage?What voltage is in the inductor or capacitor...
  36. T

    Steady State Distillation Process

    A steady state distillation process is shown diagrammatically as FIGURE 1. Assuming no heat losses to the atmosphere: (i) Write four balanced equations for this system. (ii) Identify where any constitutive equations may be required for the modelling processes.There are two states that I can...
  37. j3dwards

    Circuit settles to steady state and switch is opened

    Homework Statement The circuit consists of three identical light bulbs and two identical coils, connected to a DC current source. The ohmic resistance of the coils is negligible. The system is left to settle into a steady state and then the switch S is opened. Describe and explain in as much...
  38. RJLiberator

    PDE: Annulus question, Steady State Temperature

    Homework Statement Suppose the inner side of the annulus {(r,Φ): r_0 ≤ r ≤ 1} is insulated and the outer side is held at temperature u(1,0) = f(Φ). a) Find the steady-state temperature b) What is the solution if f(Φ) = 1+2sinΦ ? Homework EquationsThe Attempt at a Solution a) A =...
  39. kartmaze

    Steady State Flow out of a Tank Through a Vertical Pipe

    This is not homework, but something work-related. However, I will post it here since it's homework-relatable. 1. Homework Statement Known variables: Qin , A (and obviously the diameter D of the pipe as well as g = 9.81 m/s2). The pipe outlet and the top of the tank is at atmospheric...
  40. O

    Steady state temp. distribution

    Homework Statement Homework Equations ıt is nonhomog type ,2D heat conduction problem The Attempt at a Solution I don't understant To parts so I couldn't attemp a solution.
  41. K

    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)...
  42. jdawg

    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...
  43. J

    Steady State Heat Equation with Source

    I am trying to solve the steady state heat equation with a heat source. I am starting out in 1 dimension (my book gives the solution in 2, but I'm just trying to get a feel right now) and I have a heat source Q, located at 0. It radiates heat through an infinite medium. So what would the steady...
  44. leafjerky

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

    Homework Statement In a jet engine, a flow of air at 1000 K, 200 kPa, and 40 m/s enters a nozzle, where the air exits at 500 m/s and 90 kPa. What is the exit temperature, inlet area, and exit area, assuming no heat loss? Homework Equations min = mout = m where m = mass air flow dE/dt cv = Qcv...
  45. T

    How do you work out wave envelopes and asymmetries?

    Hi Say I took one or all of the four waves here: How would I go about working out the envelope around their peaks, or finding the exponential time constant from start to steady state? Cheers!
  46. D

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

    Homework Statement A small block (mass 0.25 kg) attached to a spring (force constant 16 N/m) moves in one dimension on a horizontal surface. The oscillator is subject to both viscous damping and a sinusoidal drive. By varying the period of the driving force (while keeping the drive amplitude...
  47. F

    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...
  48. M

    CG location effect for steady state cornering

    I am having trouble understanding this. The question was how to limit breakaway oversteer I know that putting the CG to the rear will increase the rear traction and induce understeer as there is less grip on the front tyres. However, I have also found that to reduce oversteer you want to...
  49. B

    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...