Steady state value

Measurement by quasi - constant current (steady - state value of pulse current) providing a compete tuning out from the effect of not only electric but also magnetic material properties. 

The basic assumption is that the Langmuir equation applies to each layer, with the added postulate that for the first layer the heat of adsorption Q may have some special value, whereas for all succeeding layers, it is equal to Qu, the heat of condensation of the liquid adsorbate. A furfter assumption is that evaporation and condensation can occur only from or on exposed surfaces. As illustrated in Fig. XVII-9, the picture is one of portions of uncovered surface 5o, of surface covered by a single layer 5, by a double-layer 52. and so on.f The condition for equilibrium is taken to be that the amount of each type of surface reaches a steady-state value with respect to the next-deeper one. Thus for 5o... 

This expression is the sum of a transient tenu and a steady-state tenu, where r is the radius of the sphere. At short times after the application of the potential step, the transient tenu dominates over the steady-state tenu, and the electrode is analogous to a plane, as the depletion layer is thin compared with the disc radius, and the current varies widi time according to the Cottrell equation. At long times, the transient cunent will decrease to a negligible value, the depletion layer is comparable to the electrode radius, spherical difhision controls the transport of reactant, and the cunent density reaches a steady-state value. At times intenuediate to the limiting conditions of Cottrell behaviour or diffusion control, both transient and steady-state tenus need to be considered and thus the fiill expression must be used. Flowever, many experiments involving microelectrodes are designed such that one of the simpler cunent expressions is valid. 

Many process simulators come with optimizers that vary any arbitrary set of stream variables and operating conditions and optimize an objective function. Such optimizers start with an initial set of values of those variables, carry out the simulation for the entire flow sheet, determine the steady-state values of all the other variables, compute the value of the objective function, and develop a new guess for the variables for the optimization so as to produce an improvement in the objective function. 

X from both equations can be plotted against T, with the intersections at the steady state values of T and corresponding values of x. 

After the tank is filled, pumping is continued and overflow is permitted at the same flow rate. Find the concentration in the tank when it first becomes fuU, and find how long it takes for the effluent concentration to get within 95% of the steady state value. 

The steady state values are the same for both starting conditions, obtained by zeroing the derivatives in Eqs. (1) and (2). Then... 

Where is nonzero only for tray N, y and x refer to the light component only such that the corresponding mole fractions for the heavy component are (1 — y) and (1 — x), L and are the initial steady-state values, and P is a constant that depends on tray hydraulics. 

In certain cases, where a long delay may be necessary for the protective scheme to operate, it may be desirable to use the maximum steady-state short-circuit current V2 /j, for a more appropriate setting, rather than the maximum transient current i2 /, as by then the fault current will also fall to a near steady-state value, /sKr.m s.i-... 

In the event of an expander trip, the regenerator pressure decreases by 46 mbar, and then increases to overshoot the steady-state value by 16 mbar. This constitutes a substantial improvement over the previously described process, but still did not meet the specifications of the end-user. 

A fuel treatment system will effeetively eliminate eorrosion as a major problem, but the ash in the fuel plus the added magnesium does eause deposits in the turbine. Intermittent operation of 100 hours or less offers no problem, sinee the eharaeter of the deposit is sueh that most of it sheds upon refiring, and no speeial eleaning is required. However, the deposit does not reaeh a steady-state value with eontinuous operation and gradually plugs the first-stage nozzle area at a rate of between 5% and 12% per 100 hours. Thus, at present, residual oil use is limited to applieations where eontinuous operation of more than 1,000 hours is not required. 

Various theoretical and empirical models have been derived expressing either charge density or charging current in terms of flow characteristics such as pipe diameter d (m) and flow velocity v (m/s). Liquid dielectric and physical properties appear in more complex models. The application of theoretical models is often limited by the nonavailability or inaccuracy of parameters needed to solve the equations. Empirical models are adequate in most cases. For turbulent flow of nonconductive liquid through a given pipe under conditions where the residence time is long compared with the relaxation time, it is found that the volumetric charge density Qy attains a steady-state value which is directly proportional to flow velocity... 

When the damping eoeffieient C of a seeond-order system has its eritieal value Q, the system, when disturbed, will reaeh its steady-state value in the minimum time without overshoot. As indieated in Table 3.4, this is when the roots of the Charaeteristie Equation have equal negative real roots. 

Find the value of K to give the system a elosed-loop time eonstant of one seeond. What is the steady-state value of ujoit) when V[ t) has a value of 10 V. 

The reverse-time ealeulations are shown in Figure 9.3. Using equations (9.29) and (9.30) and eommeneing with P(A ) = 0, it ean be seen that the solution for K (and also P) settle down after about 2 seeonds to give steady-state values of... 

Figure 9.13 indicates the burner temperature time response The temperature falls from its initial value, since the gas valve is closed, and then climbs with a response indicated by the eigenvalues in equation (9.93) to a steady-state value of 400 °C, or a steady-state error of 50 °C. 

Continue the recursive steps until the solution settles down (when k = 50, or kT = 5 seconds) and hence determine the steady-state value of the feedback matrix K(0) and Riccati matrix P(0). What are the closed-loop eigenvalues ... 

The fractional conversions in terms of both the mass balance and heat balance equations were calculated at effluent temperatures of 300, 325, 350, 375, 400, 425, 450, and 475 K, respectively. A Microsoft Excel Spreadsheet (Example6-ll.xls) was used to calculate the fractional conversions at varying temperature. Table 6-7 gives the results of the spreadsheet calculation and Eigure 6-24 shows profiles of the conversions at varying effluent temperature. The figure shows that die steady state values are (X, T) = (0.02,300), (0.5,362), and (0.95,410). The middle point is unstable and die last point is die most desirable because of die high conversion. 

C (0). The analytieal solution to Equation 9-34 is rather eomplex for reaetion order n > 1, the (-r ) term is usually non-linear. Using numerieal methods, Equation 9-34 ean be treated as an initial value problem. Choose a value for = C (0) and integrate Equation 9-34. If C (A.) aehieves a steady state value, the eorreet value for C (0) was guessed. Onee Equation 9-34 has been solved subjeet to the appropriate boundary eonditions, the eonversion may be ealeulated from Caouc = Ca(0). 

Washout oeeurs when eells are removed from the reaetor at a rate (D that is just equal to the maximum rate at whieh they ean grow. As the flowrate u inereases, D inereases and eauses the steady state value of C., to inerease and the eorresponding value of C, to deerease, respeetively. When D approaehes beeomes zero, and... 

Itisveryinterestingtonotethatthenumericalvaluesoftimearerealuntilwereachavalue of 100 and then they depart for the complex plane. We can start to see why if we compute the steady-state value of y directly from the differential equation forthese parameter... 

So this solution approaches the correct steady state value but we do not know if the time-dependenceiscorrect.Wemightwonderhowandwherethissolutionwasderived. 

Now with Hx turned off, the induced magnetization must relax to its steady-state value. This is the free induction decay phase. Figure 4-9C shows an intermediate stage in the FID is increasing ftom zero toward Mq, and My is decreasing toward zero. As we have seen, relaxes with rate constant l/Ti, and My relaxes with rate constant l/T 2. 

Attenuation zone (decreasing loss rate to a steady-state value). 

For reven sible systems, evolution almost always leads to an increase in entropy. The evolution of irreversible systems, one the other hand, typically results in a decrease in entropy. Figures 3.26 and 3.27 show the time evolution of the average entropy for elementary rules R32 (class cl) and R122 (class c3) for an ensemble of size = 10 CA starting with an equiprobable ensemble. We see that the entropy decreases with time in both cases, reaching a steady-state value after a transient period. This dc crease is a direct reflection of the irreversibility of the given rules,... 

Variable, deviation The difference between dependent variable and steady state value. 

Schemes II and III can be solved only if [I] can be approximated at the steady-state value. If that approximation is not valid, then neither [A], nor [P], has a closed-form solution. Schemes II and III have a fixed stoichiometry, this being 2A = P for Scheme II and A + B = P + Q for Scheme III. Scheme I, on the other hand, has a variable stoichiometry, intermediate between the extremes A = P (when it fe tB]) and A + B = Q (when k k2[B]).

Then let us examine the rate relaxation time constant x, defined as the time required for the rate increase Ar to reach 63% of its steady state value. It is comparable, and this is a general observation, with the parameter 2FNq/I, (Fig. 4.13). This is the time required to form a monolayer of oxygen on a surface with Nq sites when oxygen is supplied in the form of 02 This observation provided the first evidence that NEMCA is due to an electrochemically controlled migration of ionic species from the solid electrolyte onto the catalyst surface,1,4,49 as proven in detail in Chapter 5 (section 5.2), where the same transient is viewed through the use of surface sensitive techniques. 

The NEMCA time constant, t, is defined1,4 as the time required for the rate increase Ar to reach 63% of its steady-state value during a galvanostatic transient, such as the one shown in Fig. 4.13 and 4.14. Such rate transients can usually be approximated reasonably well by ... 

At t=0 a constant anodic current I=5mA is applied between the Pt catalyst film and the counter electrode. The catalyst potential, Urhe, reaches a new steady state value Urhe=1.18 V. At the same time the rates of H2 and O consumption reach, within approximately 60s, their new steady-state values rH2-4.75T0 7 mol/s, ro=4.5T0 7 mol/s. These values are 6 and 5.5 times larger than the open-circuit catalytic rate. The increase in the rate of H2 consumption (Ar=3.95T0 7 mol H2) is 1580 % higher than the rate increase, (I/2F=2.5T0 8 mol/s), anticipated from Faraday s Law. This shows clearly that the catalytic activity of the Pt catalyst-electrode has changed substantially. The Faradaic efficiency, A, defined from ... 

There is an additional important observation to be made in Fig. 9.25 regarding the magnitude of the relaxation time constant, x, upon current imposition Electrochemical promotion studies involving both solid electrolytes and aqueous alkaline solutions have shown that x (defined as the time required for the catalytic rate increase to reach 63% of its final steady-state value upon current application) can be estimated from ... 

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