Q curves

The pump companies develop their curves using head in feet (H), because when they make a new pump, they don t know the ultimate service of the pump (they don t know the liquid that the pump will be pumping), but they do know how many feet of elevation the pump can raise that liquid. This is why it s necessary to specify pumps in feet of head and not in psi. Let s begin by exploring the H-Q curve of the pump, using feet of head. 

At point A on the H-Q curve, the pump is pumping Q gpm (gallons per minute), at H feet of head. This point on the curve corresponds to the best efficiency, and it is also seen at approximately the middle of the energ) curve, and al.so on the NPSHr curve where it begins its sharp rise. 

Because the H/e versus Q relationship is nearly linear, the HPg versus Q is essentially a straight line through the origin for a compressor with radially bladed impellers. For backswept impeller blades, the hp versus Q curve is a flat parabola, peaking near or above the maximum flow . 

Lowering of H-Q curve increase in input tip General lowering of efficiency but may be acceptable... 

These are the coefficients that determine the Tafel slope of the log / against q curve of a multistep reaction, and they are of fundamental importance in providing information on the mechanism of the reaction. Equations 20.86 and 20.87 are of the same form as equations 20.59 and 20.58 that were derived for a simple one-step reaction involving a symmetrical energy barrier, and under these circumstances equations 20.90 and 20.91 simplify to... 

The applicability of the GCSG model has been tested by the Parsons-Zobel approach the Parsons-Zobel plots were linear for all systems, with the value of /re very close to unity. The values of Cf30 obtained by extrapolation of the 1/C(1/Q) curves to 1 /Cd = Owere in good agreement with the values of Cf calculated by Grahame s method. The C/,01 curves for Ga, In(Ga), Tl(Ga), and Hg apparently merge at [Pg.67]

Rate measurements are straightforward if the carbenes can be monitored directly. As a rule, the decay of carbene absorption is (pseudo) first-order, due to rearrangement and/or reaction with the solvent. In the presence of a quencher, the decay is accelerated (Eq. 1), and the rate constant kq is obtained from a plot of k0bs versus [Q], Curved plots were often observed with proton donors (HX) as quenchers, particularly for high concentrations of weakly acidic alcohols. Although these effects have been attributed to oligomerization of the alcohols,91 the interpretation of curved plots remains a matter of dispute.76 Therefore, the rate constants reported in Tables 2-4 are taken from linear (regions of) obs-HX plots, or refer to a specified concentration of HX. 

In a particular system, a centrifugal pump can only operate at one point on the Ah against Q curve and that is the point where the pump Ah against Q curve intersects with the system Ah against Q curve as shown in Figure 4.4. 

The system Ah against Q curve shown in Figure 4.4 can be plotted using equation 4.12 to calculate the values of the system total head Ah at each volumetric flow rate of liquid or capacity Q. Equation 4.14 shows that for laminar flow the total head Ah increases linearly with capacity Q. Thus for laminar flow, the system Ah against Q curve is a straight line. 

The q-T(q) curves are nonlinear for different values of m, Pini, NE and surface roughness as ean be seen from Figure 10 whieh indicates multifractality From Figure 10(a), for q >0, as m deereases, the curvature of q-x(q) curves also decreases gradually, indieating relatively homogeneous reaetion probability distribution. This also indicates that, the number of aetive... 

In Figure 10(d), the q-x(q) curves are plotted to see the effect of number of reaction events. It is observed that the number of reaction events also affects this autopoisoning reactions. The curvature in q-x(q) curves decreases with an increase in number of reaction events indicating more homogeneity in the reaction probability distribution. As these curves are well separated in lower and higher q values for different number of reaction events, we can say that the number of active sites with lowest reaction probability for different number of reaction events is not the same, also the number of active sites with highest reaction probability for different number of reaction events is not the same. 

Cal ibr ation o f Instrument When 10 urn and 0.6 ym membranes were used to determine the viscosity of THF using the manufacturer s determination of M from the flow of water, the viscosities of THF were measured to be an average of 85 /, of the true value. The direct experimental P vs Q curves are shown in Figure 3. (There is, however, a systematic trend below 85 /. as membranes of even lower pore sues are used. Although this trend is puzzling it is unimportant for polymer research since most polymer solution studies need relative viscosity, specific viscosity,, measurements.)... 

The curve of maximum entropy is the locus of end points, in the v,P plane, of all possible Rayleigh transformations starting with the "spike state and representing release of a given quantity of chemical energy Q. Oppenheim (Ref 1) calls this the Q-curve. Its equation is derived on the assumption that the combustion products move at the local velocity of sound with respect to the detonation front. Thus the Rayleigh-Mikhel son line at the C-J point, where it reaches the Q-curve, has the same slope as the isentrope at that point... 

The V)f(q) curves in Fig. 20.13 indeed reach constant values for q — °° which are (approximately) equal to Kv This result also follows directly from evaluating Eq. 20-51 for q —> °°. Since tanh(g — °°) = 1, the second term in the denominator approaches zero for q — °°. Finally, Fig. 20.13 nicely demonstrates how p(maximum value (1 + Kr) for q — o°. Note that for large Kt values, this transition extends from q 1 to fairly large q values. Thus, for these cases flux enhancement remains -dependent in situations where tT is much smaller than tw. Thus, our first attempt to characterize the intermediate case with tT /w should rather be replaced by ... 

Unstable branches on the P(Q) curve and the appearance of hysteresis loops can occur for various reasons usually connected with an increase in viscosity. Thus, a non-monotonic P(Q) curve was first encountered in an analysis of the flow of a hot inert (non-reactive) liquid in a cold tube when the viscosity of the liquid was strongly dependent on temperature.190 The intense dissipative heat output may have been the reason for the instability in the flow of an inert liquid.191 In both cases, the reason for the nonmonotonic in P(Q) dependence was the strong dependence of viscosity on temperature, which is equivalent here to time dependence for viscosity. Detailed investigations of the hysteresis transitions shown in Fig. 4.24 proved that they have a wave character 192 in this case, the transition occurs at a constant flow rate. 

Near the equilibrium bond length qe the potential energy/bond length curve for a macroscopic balls-and-spring model or a real molecule is described fairly well by a quadratic equation, that of the simple harmonic oscillator (E = ( /2)K (q — qe)2, where k is the force constant of the spring). However, the potential energy deviates from the quadratic (q ) curve as we move away from qc (Fig. 2.2). The deviations from molecular reality represented by this anharmonicity are not important to our discussion. 

One way in which this can be done is by considering the shape of the AM vs. E and AM vs. Q curves, rather than the overall changes in AM and Q. For a permselective film, electroneutrality requires 1 1 correlation between the electron and counter ion (here, anion) fluxes. If no solvent is transferred, this demands that the AM vs. Q plot be linear and free of hysteresis, regardless of the shape of the AM vs. E plot. The slope of this plot will be F/m ", where my - is the counter ion molar mass. 

Figure 1 shows the phase behavior of EMAX (the subscript x denotes the molar acrylate content) copolymers in propylene which is slightly more polar than propane [4,5]. The EMA q curve is at slightly lower pressures than the PE curve since the first few acrylate units interact favorably with the quadrupole of propylene. However, the cloud-point curves shift to higher pressures and temperatures and as the amount of MA units increases to 31 and 41 mol% in the copolymer. EMA41 does not dissolve in propane to temperatures of 200 °C and pressures of 2,000 bar, whereas it is readily soluble in propylene. 

Plot the pump head-capacity (H-Q) curve of the pump on Fig. 6.23b. The H-Q curve can be obtained from the pump manufacturer or from a tabulation of H and Q values for the pump being considered. The point of intersection, A, between the H-Q and system-head curves is the operating point of the pump. 

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