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.
I an working on a problem in the text "Mechanics and Thermodynamics of Propulsion" 2e. The problem states a perfect gas with molecular weight M=20 and a specific heat ratio of Y=1.2 expands adiabatically in steady flow from a pressure of 6MPa, a temperature of 3000K, and a velocity of 200 m/s...
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Why ds=0 only in a steady rev. process? Can't it be zore for a rev. and not steady process?
And if the process isn't rev. but still circular. since the entropy is still a state function it should still be zero if we come back to the starting point ,right?
if it isn't true then dU...
Hi,
I know that the a constant magnetic field is created by a loop of DC. Steady current does not create any EM waves. At the same time, it is told that an electron orbiting around an atom should emit an EM field. In both cases we have a loop but in one case no radiowaves are emitted, in...
Homework Statement
There is a wall 100 mm thick, find the U-value. Then a plasterboard lining is added of thickness x and a gap between it and the wall of 20 mm
wall thickness b=0.1m, thermal conductivity \kappa_1=0.5 W m^{-1} K^{-1}
plasterboard thickness xm, thermal conductivity \kappa_2=0.1...
Hey all:
I am taking a Thermodynamics course and we are studying work and heat through surfaces (i.e. conduction, convection, and radiation). I was given an assignment and I am having trouble arriving at the correct answer. I have scanned the question and the works I have so far. I hope...
Ladies and gentlemen.
I have been trying for literally days on this problem and its completley done me in.
The problem is as follows.
I have to evaluate a jet engine using the SFEE equation.
So far I have concluded that this equation will be the best to use...
Qr – Wrx = ṁ Δ [ h...
It is known that on a wire carrying steady current there are surface charges (and hence electric field outside the wire, but let's forget about it). This surface charges play an important role to maintain a uniform electric filed along the whole wire. There are only few geometries for which one...
When charges are flowing (current) through a combination of conductors of different resistances in series, then why don't the charges flow faster(more current) in the material with lower resistance and slower(less current) in high resistance material? Why is the current same(steady) in the whole...
I have a question (possibly dumb) if someone could humor me with an explanation .
I understand that steady currents don't create electromagnetic radiation. If that's true how does a high-voltage steady DC current create interference? For that matter why does a high voltage capacitor create...
Ok, I'm lost. I've an exam coming up so could so with a speedy reply.
This whole transition matrix stuff is not explained at all in our lecture notes. Here's an example question:
"Suppose that a country has a fixed number of voters, all of whom vote for
either party D or party R. Every...
This is a simple question. I know the equation I am supposed to use but I can not get my head around one part. The part in brackets! I keep getting wild numbers as my answer
The equation is :-
I = V/R * (1 - e^t*R/L)
can I ask someone to give me a step by step example of how you place...
This paper http://arxiv.org/abs/1003.0658 nails down the interpretation of a binary white dwarf system with an orbital period of only 5.4 minutes, versus 8 hours for the celebrated Hulse-Taylor binary neutron star system. This would probably be the strongest source in the sky of steady...
Homework Statement
Question 3 of http://www.damtp.cam.ac.uk/user/examples/B10b.pdf .
Homework Equations
\nabla \times B = \mu_0 J
The Attempt at a Solution
I know for a cylinder, J (vector) = J (scalar) * k (vector), where unit k is the vector in the z-direction. So \nabla \times...
Homework Statement
The power output of an adiabatic steam turbine is 5 MW and inlet and exit conditions are as under
Given Inlet Pressure 2MPa Temprature 400 DEGREE CELSIUS Velocity 50m/s Elevation 10m
Exit Pressure 15 KPa Temprature 0.9 dry Velocity 180m/s...
I have a set of ODE of the following form
\begin{cases}
\displaystype{\frac{dx(t)}{dt}} = F(x, y, z; \delta e^{i\omega t}, \Delta e^{-i\omega t})\\[4mm]
\displaystype{\frac{dy(t)}{dt}} = G(x, y, z; \delta e^{i\omega t}, \Delta e^{-i\omega t})\\[4mm]
\displaystype{\frac{dz(t)}{dt}} = H(z...
Uncle Sam claims that he invented a black-box device which operates at steady state, and has two inlet streams and one outlet stream as shown in the figure below. Inlet 1 allows air to enter at a pressure of 200 kPa, temperature of -50 oC, and mass flow rate of 30 kg/min. Inlet 2 allows air in...
If an object receives heat from a heat reservoir, is it necessary for the heat receiver to release heat?
Can the heat receiver increase its internal energy without heat flow out of the receiver?
And what happens when the system between heat provider and heat receiver reaches a steady state...
Homework Statement
Using cylindrical coordinates rho,phi, and z, let u([rho,phi) denote steady temperatures in a long hollow cylinder a leq rho leq b, -infinity < z < infinity when the temperatures on the inner surface rho= a are f(phi) and the temperature of the outer surface rho = b is zero...
Homework Statement
A 50mm wafer, 2mm thick is implanted with Boron at 100keV and 1mA. Considering only conductive cooling, given that thermal resistance is 10K/W, to room temperature of 25oC, determine the steady state wafer temperature and also the time constant for heating
Homework...
Problem: Find the steady state temperature of a laterally insulated rod subject to the following conditions. Length of the rod 10, , left end kept at 0 and right end at 100
Solution: i got this equation from a book i don't know if this applied to this problem but i don't know what to do...
Problem 1 : Find the steady state temperature of a laterally insulated rod subject to the following conditions. Length of the rod 20, left end insulated and right end held at 100
I am not sure if i fully understand this problem, is this asking me to list the Boundary value conditions ? like...
Homework Statement
Hello,
I've just done a paper on basic electronics and I'm stuck on the last question. I don't know how to go about doing the question.
Homework Equations
N/A
The Attempt at a Solution
I don't know how to even start with the question. I've tried googling...
If this should be in the cosmological section, then i don't mind to see it moved, but since it appears to be an abandoned theory, I'm posting this in the classic physics section.
I was talking to a religious person, and he was claiming that the big bang theory was... wrong, that it had been...
Homework Statement
Question: 18. Show that every 2 x 2 stochastic matrix has at least one steady-state vector. Any such matrix can be written as
P = |1-a b |
| a 1-b |
where a and b are constants between 0 and 1. (There are two linearly independent steady-state...
Can someone tell me what Steady State (Operating) Torque is and how to calculate it?
I'm guessing that it is the troque at operating speed.
Any help would be appreciated.
Thanks,
Homework Statement
The one dimensional steady-state heat conduction equation in a medium with constant conductivity (k) with a constant volumetric heat generation in three different coordinate systems (fuel rods in a nuclear power plant) is given as:
\frac{d^2 T}{dx^2}=-\frac{\dot{q}}{k}...
Homework Statement
Water flows into a nozzle at 3.00 m/s at a pressure of 1.31*105Pa. What should the ratio of input to output diameter be if the flow is to remain steady? What is the flow speed at the exit?
Homework Equations
P_{{\rm{input}}} + \frac{{\rho v_{{\rm{input}}}^2 }}{2}...
This is an ultra vague question, but I'm hoping to bump into an expert who might know.
Consider the steady flow of water over a polygonal surface (like a step, for instance -- something that can be easily conformally mapped). The wavenumber of the far field (large x) gravity waves can be found...
Hi all!
I am asking about a question about Fourier transform.
I can only roughly remember things about Fourier transform.
I am told that Fourier transform gives the steady state solution, is it?
I can hardly relate these two concepts.
Can someone try to explain?
Many thanks.
air enters an adaibatic nozzle steadily at 300 kPa, 200 degree celcius and 30m/s and leaves at 100 kPa and 180 m/s.
find the exit temperature?
when m using energy balance equation: h1 + [ (v1)^2 / 2 ] = h2 + [(v2)^2 / 2 ]
i get the answer 184 degree celcius.
but when i use the other...
I have to solve a problem regarding "2D steady state heat conduction problem with an internal heat generation source". For boundary value, dirichlet is applied at 3 sides and neumann is at one side.
I can solve this problem when no internal heat source exists and only dirichlet is applied...
Recently the expansion of the Universe has been found to accelerate. When studying Hoyle, Gold and Bondi's Steady State Cosmology, it clearly predicts an acceleration like this. I realize that this theory has been 'put to bed', and abolished, and all the other colorful language people like to...
Homework Statement
In order to prodice a more balanced, sustainable long term mix of flower Skwhere the percentage of the offspring of red flowers are p pink and 1-p redSk= A SoSk= [r p w]Twhere A=[1-p* 1/4* 0p***** 1/2* 1/20***** 1/4* 1/2]determine the stady state eigenvectors(you do not have...
Homework Statement
Prove that for any initial state vector
S0=
[r0
p0
w0]
as long as you begin with legitamite proportions (so that r0+p0+w0=1), after a long run you get the same result as
Sk=
[1/4
1/2
1/4]
Homework Equations
Sk= b1(Lambda1)^k [X1] +...
Hi
I was reading BC Kuo's Automatic Control Systems where I came across a solved problem (page 369 of 7th edition) regarding velocity control. I have a problem understanding how the steady state error has been computed. The original problem and its solution as given in the book are quoted...
I went for a run and measured time and distance. I wanted to estimate how many calories I used.
Suppose a ran a distance x in an amount of t time.
if my mass is m, then my stead state average energy would be
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But what is the rate at which...
[SOLVED] Steady state solution
I was wondering if I did this question correctly, solving for y(t) and putting t = infinity to get a steady state solution. Or is this wrong or is there an alternative way that is much quicker (as solving for y(t) would take a page of working, where the working...
Homework Statement
Obtain the temperature distribution T(x,y) of the triangular cross section, assuming constant thermal conductivity, k.
The triangle is a right-isosceles triangle with the right angle at (0,0). The triangle goes "up" to a, and to the right to a, then diagonally across...
Homework Statement
What is the steady state solution to the equation
4y''+4y'+17y=202cos3t (*) ?
2. The attempt at a solution
The steady state solution is, if I've got it right, only the particular solution. It's got to be on the form
Kcos3x+Msin3x.
I calculate the...
Dear all
i've thinking, how can a circuit have a steady current?
the reason for this seemingly naiive question is:
if I is contant it means the velocity at which the charges move is constant. But if the velocity is contant that means their KE is constant. So in a circuit with a resister...
In the steady state heat conduction through a solid rod the theoretical
derivation tells that
heat in-heat out-heat accumulated =0.
What is a practical steady state heat conduction problem? what is
transient heat conduction
Considering the response of a single degree of freedom system to harmonic excitation with viscous damping , following conclusions can be drawn:
Now,
The response of a single degree of freedom system to harmonic excitation can be split into:
a) Steady Sate response (or vibration) which...
I'm wondering if anyone can just run through how this is done. I have the solution so that's now the problem. I just need someone to provide me with the method of finding the steady solution (I can find the transient no problem).
A slender homogeneous conducting bar of uniform cross section...
Hi, first post so here goes:
I'm having a little trouble with a question on my tutorial, and I am not sure what to do. Here it is:
Steam under steady flow conditions has the following states:
Initial Conditions:
Pressure - 47 Bar
Spec Volume - 0.09957 m^3 / kg
Internal energy - 3420...
When a refrigerator has been turned on for some time, steady state refrigeration occurs. This is the normal refrigerator operative state. But what exactly happens?
These things are really hard to do research on, since Internet searches, regardless of search query detailing, result in a lot...
I have some first order differential equations. I have found the steady state response for each equation. However, now I need to estimate how long it will take to reach steady state.
Can anyone tell me the formula for that or get me started on how i go about doing this. I'm not finding...
Hello everyone, confused. the directions to this problem are the following:
Find the steay-steat vector, and assuming the chain starts at 1, find the probablity that it is in state 2, after 3 transitions.
well i got the problem and i got the S0 to S3, because it said after 3 transitions, is...
I have a problem that goes as followed: http://www.webassign.net/pse/p32-19.gif
Consider the circuit in Figure P32.17, taking = 6 V, L = 4.00 mH, and R = 6.00
(a) What is the inductive time constant of the circuit?
I found this to be .6667 ms
(b) Calculate the current in the circuit 250...