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 am trying to implement this equation ##−k∇^2 u = e^{-(x^2+y^2)}##
using NDSolve in Mathematica. The idea is to solve for the temperature of a plate 10 x 10 units, with heat inputs as per the RHS.
Here is my attempt:
NDSolve[{ - Laplacian[u, {x, y}] == Exp[-(x^2 + y^2)], u[x, -5] == 0,
u[x...
(This has continued to bother me. I tried asking, and no response. May I please try again?)
Using Euler angles, we rotate about an axis (often, axis three of a gyroscope frame), then a second (axis one of the gimbal frame), then return to the same axis as the first one (back to axis 3, but of...
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...
If I've steady currents i.e ##\frac{\partial}{\partial t} J=0## , does coulombs law hold in this case to find the electric field?
Since this isn't the case of electrostatics so it might not hold, but if we look at the charge density it is the same for all time, this suggests that the charges...
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...
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...
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...
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.
I am looking for help on the following:
a) Given the system shown in the figure below, derive the steady flow energy equation from first principle.
b) Again using first principles, show how the energy equation would change for the case when the system is unsteady.
I am trying to learn this...
I've got this question here, I know to calculate steady states you set dn/dT and dc/dT to 0 and then solve. However can anyone help me understand what it means by the "two cases" and how you go about this?
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.
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
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:
\[ v*=0, u*=c/b \]...
Hi
I am trying to understand the concept of why a gyroscope that is not spinning drops down but when it is spinning then it precesses. I have looked in "University Physics" by Young + Freedman and Kleppner , Morin and Gregory but i am not getting anywhere. Does anyone know of a relatively simple...
What is the difference between streamlined and steady flow? Is unsteady streamlined flow possible? If yes, could you please explain what are the characteristics of unsteady streamlined flow?
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...
Because of temperature, molecules of fluid have chaos movements.So I do not understand why in steady flow,the molecules of fluid can not move through the wall of flow tube?I think two layers of fluid exchange molecules while they move.How do we understand when saying: fluid can not move through...
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...
Hi,
I was studying JFET and it was written that at Pinch off voltage the drain current becomes constant. And when the gate to source voltage is applied. The more negative the voltage is the current will be decreased and eventually reached to 0. I don't understand below both points.
1) At pinch...
Homework Statement
A bacteria that normally divides every 20 minutes express gene X. The production rate of protein X is 5nM/min. The protein is stable and does not degrade.
What is the concentration of X in the steady state?The same bacteria enter into a stress state at t=0 for 3 hours...
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...
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...
Homework Statement
A cylinder is well-insulated at the base and sides (radially). No heat sources and assume steady state. All other BCs are free (I'm aware the problem is underconstrained). Then we have
$$\nabla^2 f = 0\\
\partial_rf(r=R_0) = \partial_rf(r=R_1) = 0\\
\partial_z f(z=0) = 0\\...
Homework Statement
12kg of a fluid per minute goes through a reversible steady flow process. The properties of fluid at the inlet are p1 = 1.4bar, ρ1 = 25kg/m3, C1= 120m/s and u1= 920kJ/kg and at the exit are p2= 5.6bar, ρ
2= 5 kg/m3, C2= 180m/s and u2
Homework Equations
u1 + P1V1 + (C1)2/2 +...
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...
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...
Homework Statement
A pump is used to move water through a pipe of diameter 150mm, Figure below. The water has a temperature of 20 Celsius and an absolute pressure of 100KPa. The pump moves the water up a vertical distance of 2m and the water exists at atmospheric pressure.
Q1)
Assuming the...
Hello
I have a point that I don't understand.
In open steady flow systems, we use SFEE, where there's a term W in addition to a term PV, which are different things.
When we analyse a cycle like Rankine, we always consider either W or PV, but not both. I also think that W=PdV always.
Why that...
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...
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...
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...
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)...
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?
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...
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...
Homework Statement
Vapors of 100 C is added to an ice cube of 0 C.
How much of the ice cube has melted and what's the final temperature if the masses of the steam and the ice cube are 10.0 g & 50.0 g respectively?
Homework Equations
Lw = 3.33 x 105 J/kg
cw = 4186 J/kg*C
Q = m*c*ΔΤ
Q =...
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...
While deriving Poiseuille's law (the relation between flow rate and pressure gradient for fluid flow in a rigid cylindrical tube under a pressure gradient) , we make an assumption that flow is both laminar and steady.Why we need the flow to be laminar. Is it not enough to consider only steady...
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...
I've always heard that maxwell's equations contains essentially all of eletromagnetic theory. However, there's one thing I'm having trouble doing for myself: deriving the magnestatics equations from the maxwell's equations. Of course: it's clear that if you put ∂[t]E=∂[t]B=0 (partial derivative...
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...
Why must steady currents be non-divergent in magnetostatics?
Based on an article by Kirk T. McDonald (http://www.physics.princeton.edu/~mcdonald/examples/current.pdf), it appears that the answer is that by extrapolating the linear time dependence of the charge density from a constant divergence...
Ice melting in a box has the water coming off it at a temp just above freezing until all the ice is gone.
Are all phase change materials pretty much the same, with their immediate containment container exterior staying pretty much just above their phase change temp until all the PCM inside has...
Hi,
I am currently studying Thermodynamics and stumbled upon this equation and is slightly confused as to how this works. Hopefully someone can help me with the understanding.
According to this text here, if I am not wrong e can be h + ke + pe or u + ke + pe depending on where i am looking...
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...
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