Rise curves

Nozzle Static Pressure Loss Overall nozzle static pressure loss (SPN) was tested for all of the experimental LVHV nozzles.Experimental testing has confirmed what would be expected, that nozzle shape and size variation can cause great differences in overall static pressure loss, especially at high airflow velocities. Figure 10.25l/ compares SPN versus Vq (cm Hg versus m s" inch Hg versus fpm) characteristics for five circular nozzles. The plain wedge had the steepest rising curve, followed by the plain circular nozzle. Both of... 

A plotted curve as shown on Figure 3-59 [33] show s that at point A a rise of 20°F on the temperature rise curve corresponds to a flow of 47 GPM minimum safe for the pump handling 220°F, with NPSH of 18.8 feet. 

Equation (35) describes the line in Fig. 10, which is a semilog plot of Cp versus time for an orally administered drug absorbed by a first-order process. The plot begins as a rising curve and becomes a straight line with a negative slope after 6 hours. This behavior is the result of the biexponential nature of Eq. (35). Up to 6 hours, both the absorption process [exp(—kat) and the elimination process [exp( keil)] influence the plasma concentration. After 6 hours, only the elimination process influences the plasma concentration. 

Pressure rise curve for X52 steel during high-pressure hydrogen permeation measurement. The measured pressure is normalized to the charging pressure on the upstream side. Here, the hydrogen charging pressure is 510 psi and the test temperature is 165°C. 

From the pressure rising curve, the diffusivities of X52 and X65 can be calculated. Figure 10.9 shows the calculated diffusivities as compared to the diffusivity data compiled by Alefeld and Volkl [22] from open literature. It is seen that the measured X52 and X65 diffusivities [9] under both low- and high-pressure conditions are significantly lower than those collected by Alefeld and Volkl. The causes of this difference may be attributed to the presence of a passive... 

Fig.9 Variation of the rate of polymerization of PUA with the rate at which temperature rises (curve a ) and with the temperature at which (Rp) is measured (curve b A). (Film thickness 10 pm).

Detailed studies reveal that apart from an initial large phase, the rise-curve is exponential. Thus the measured concentration C as a function of time, t, is given hy Eq. 2. 1, where and Q are the concentrations at the steady state and at time c. 

A plot of log Ct against time takes the generic form of Fig. 2.IS. The value of IT,/, is calculable directly from the slope of the Hnear portion of the plot. The initial nonexponential part of the plot is termed the lag phase i and is expressed numerically as the value of the intercept of the Hnear portion on the time axis. The fall-curve structure is the inverse of that of the rise-curve. 

In the continuous processing of discrete samples in the AutoAnalyzer system, the reaction-time is held constant by the manifold design, and because the rise-curve is exponential the degree of attainment of steady-state conditions is independent of concentration. Consequently it is unnecessary for the analytical reaction to proceed to completion for Beer s Law to be obeyed. This confers a considerable advantage upon the AutoAnalyzer approach and one which is frequently emphasized. The relationship between degree of attainment of steady state and IT,/, can be generaHzed in the semi-logarithmic plot of Fig. 2.16 [10], where time is expressed in units of IT,/,. 

The shape and position of the curve describes the potency of the drug. A steeply rising curve indicates that a small change in dose produces a large change in drug effect, for example, a loop diuretic. By contrast, the dose-response curve for the thiazide diuretics plateau at lower doses, and increasing the dose produces no additional diuretic effect. 

Bhaumik (148) measured the rise time of the red fluorescence in some europium chelates. His data were collected with a stroboscopic instrument having a time-resolution capability of around 0.2 /xsec. Figure 40 shows the fluorescence-rise curve of the sDq- >1F2 transition in the piperidine adduct of the four-ligand europium dibenzoylmethide chelate. Data were collected at 77°K. 

The formulation was intensively mixed for 15 s in a cylindrical vessel of 9.5 cm diameter and 10 cm height. A copper-constantan thermocouple was centered, and the signal continuously monitored. Figure 5.16 shows adiabatic temperature rise curves for different catalyst concentrations. The adiabatic temperature rise was estimated as 155°C. 

Figure 5.17 Fit of the adiabatic temperature rise curve for the formulation containing the highest catalyst amount. Points are experimental values while the full curve represents the best regression. (Reprinted from Aranguren and Williams, 1986, Copyright 2001, with permission from Elsevier Science)...

Figure 5.20 shows a plot of the experimental temperature decay for run 1, after t = 60 min. An excellent linear regression was obtained, which means that U can be regarded as a constant value. The adiabatic temperature rise curves were calculated using Eq. (5.77) (plots are shown in Fig. 5.19). The adiabatic curves are now ready for a kinetic analysis.

Figure 7.10 Typical (steady-state) viscosity rise curve for the free-radical copolymerization of mono- and multiunsaturated monomers, correlated with the steps of the reaction mechanism.

The first-order rate constant can be evaluated from the decay curves of 3C o and the rise curves of Qo and the donor radical cation [125,154], The observed electron transfer rate constants for C6o are usually in the order of 109-1010 dm3 mol-1 s-1 and thus near the diffusion controlled limit which depends on the solvent (e.g., diffusion controlled limit in benzonitrile -5.6 X 109 M-1 s-1) [120,125,127,141,154-156],... 

The open-ring isomer was excited with a 355 nm laser pulse (fwhm 22 ps) and the formation of the closed-ring isomer was followed at 560 nm in hexane. A rapid spectral evolution in a few tens of picoseconds was observed, and attributed to the photocycliza-tion reaction. The rise curve was reproduced by taking into account the pulse duration and the time constant of formation (t = 8 ps). Taking the rather long pulse duration into account, it was concluded that the switching time is shorter than 10 ps. 

The more steeply rising curve is the longitudinal or compression mode. The less steep curve at — 0 is the torsional mode. The quadratic curves at 9 = 36 are beam bending modes. The dashed curve is the dispersion obtained after taking into account the coupling to water. 

Related Calculations. Use this procedure for any centrifugal pump handling any liquid in any service—power, process, marine, industrial, or commercial. Pump manufacturers can supply a temperature-rise curve for a given model pump if it is requested. This curve is superimposed on the pump characteristic curve and shows the temperature rise accompanying a specific flow through the pump. 

Equation (5.11) represents a straight line in the diagram of fractional temperature rise versus reactor feed temperature. We show three such lines in Fig. 5.21. All lines intersect the temperature rise curve at least once (at a low temperature not shown in Fig. 5.21). It therefore appears that the reactor FEHE can have one, two, or three steady-state solutions for this particular set of reaction kinetics. Furthermore, the intermediate steady state, in the case of three solutions, is open-loop unstable due to the slope condition discussed in Chap. 4. This was verified by Douglas et al. (1962) in a control study of a reactor heat exchange system. 

Estimated horn A(t) in Figure 9.10a as a single exponential rise curve. 

The sole use of a trimerization catalyst, such as potassium 2-ethylhexanoate, shows two-step rise curves. In the initial stage the catalyst slowly accelerates urethane linkage formation, and then, after the reaction exotherm rises, trimerization begins. 

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