Stage Step function

In-house correlation of pumps should be made using gpm vs. cost with head as a parameter. These should result in step functions, since one size pump with different impellers can serve several flow rates and heads. Different correlations should be made for each type of pump. The price of a vertical multistage pump may be quite different from a horizontal splitcase multistage pump. A sump pump with a 15-ft drive shaft would cost more than a single-stage horizontal pump with the same gpm and head. 

The first three stages can be performed in a single reaction vessel, although the overall yield of the sequence can be improved by isolating the P-hydroxy sulfone at the second stage and functionalizing the hydroxy group in a separate step. Purification of intermediates is not normally required. 

The three stages of the conductometric titration curve were expressed as an exponential step function with the requisite parameters. ... 

Figure 1 Hypothetical collection efficiency of a stage of an impactor. Fraction deposited plotted against particle size. The step function indicates the theoretical deposition, and the curve indicates the practical characteristics.

Thus, the magnetic field in an insulator, as well as the dipole moment, presents itself as the step function (t Tq), and it is natural here to distinguish three successive stages. Until moment t = Tq = R/v the field is absent at the point with coordinates R,0). Due to the instant change of the dipole moment the signal front is described by the -function and its derivative. Only at this moment the electric field is not equal to zero. After arrival of the signal t > Tq) the magnetic field instantly becomes constant in the same way as the dipole moment while the electric field vanishes. 

On the other hand, at great times currents induced in a medium due to the step function excitation are located relatively far away from the dipole, and for this reason a field measured relatively close to the dipole is almost uniform. It means that the main information about the late stage of a transient response is contained in the integrand mjC i(mi, 7712,7713) when the variable of integration m is small. 

The number of theoretical separation stages is determined based on the operating line and the equilibrium curve with the corresponding construction of the step function between both lines. For the example shown in Figure 3.3.30, we get four theoretical stages. The number of stages decreases with increasing liquid-to-gas... 

The step function, starting from the point (0, 0.0089) to the point where X=Xout = 0.00075 yields the number of separation stages as about 4. Finally, we calculate the volume rate of water... 

In some cases, a pseudo-equilibrium stage is reached in the moisture uptake, which is then followed by a secondary uptake process. This is illustrated in O Fig. 31.13a. This type of behavior indicates that the absorbed moisture has triggered an additional moisture uptake mechanism. For example, differential hygroscopic expansion may lead to cracking and moisture uptake by capillary action. In order to model the moisture uptake shown in Fig. 31.13a, Mubashar et al. (2009b) proposed a dual Fickian model with a Heaviside step function. This model was termed the delayed dual Fickian model, where the secondary uptake is modeled by a power law. The mass uptake by a delayed dual Fickian model is, hence, given by ... 

Imagine for a moment that the exploration activities carried out in the previous section have resulted in a successful discovery well. Some time will have passed before the results of the exploration campaign have been evaluated and documented. The next step will be the appraisal of the accumulation, and therefore at some stage a number of additional appraisal wells will be required. The following section will focus on these drilling activities, and will also investigate the interactions between the drilling team and the other E P functions. 

The process whereby aldehydes are produced from arylmethyl (also alkyl and other) halides by the action of hexamine is known as the Sommelet reaction. The reaction is essentially the conversion of an amine into an aldehyde the hexamine serves the dual role of converting the halide into the amine and the amine into the aldehyde, but its function is different in the two steps. When starting from a halide, the reaction proceeds in three stages —... 

The steps may be so chosen as to correspond to consecutive points on the experimental isotherm. In practice it is more convenient to divide the desorption process into a number of standard steps, either of relative pressure, or of pore radius, which is of course a function of relative pressure. The amount given up during each step i must be converted into a liquid volume i , (by use of the normal liquid density) in some procedures the conversion is deferred to a late stage in the calculation, but conceptually it is preferable to undertake the conversion at the outset. As indicated earlier, the task then becomes (i) to calculate the contribution dv due to thinning of the adsorbed film, and thus obtain the core volume associated with the mean core radius r by the subtraction = t ... 

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