Dimensionless time

In order to make time dimensionless we again make use of the results at the simple crossing point. When fcu = 0 we found that the natural frequency of... 

Fig. 51. A log—log diagram of the velocity autocorrelation function for a Brownian particle in nitrogen as at two different pressures. Both axes are scaled to make the velocity autocorrelation function normalised and the time dimensionless. The pressures were O, 0.1 MPa ", 1.135PMa. At short times, the experimental data fit an exponential...

However, if q is to be varied, Eq. (12) will not do, because q appears also in the dimensionless time r. Thus k must be used to make time dimensionless, for instance, r = kt. Da is still the Damkohler number, but the equation is now... 

The introductory example may be reworked using the Gamma distribution, since the special case given there is n = 1. Let c(x, 0) = Cogn( ) where C0 is the total initial concentration. Let the first order rate constant be k(x) = kx and make time dimensionless as kt. This reaction time or intensity of reaction—severity of reaction as the oil people have it—is really the Dam-kohler number, Da, for the reactor, with t the time of reaction if it is a batch reactor or the residence time if a PFTR. Thus... 

R S V characteristic reaction time dimensionless velocity vector... 

Injection time Dimensionless time Cycle time... 

The constant A is used to render the time dimensionless. In case the kinetic constants /3, are fixed and we consider only one reference composition, there are only two parameters p and k and these are separated in the sense that p is associated with the integral F whilst K is associated with the temperature policy. 

Time differential perturbed angular correlation spectroscopy, 353 Time, dimensionless, 535 Time resolved laser induced fluorescence spectroscopy, 349, 350 Titanates... 

Keywords Flow pattern Circulation time Dimensionless mixing time Froude number Non-Newtonian behavior Pneumatic agitation... 

Shear stress or particle relaxation time Dimensionless particle relaxation time Rate of deposition Particle flux Particle volume... 

For the two-heated-tank process of Example 7.7, the two transfer functions were given in Eq. (7.92). The steady-state gain between the inlet temperature Tg and the output T2 is found to be 1°F/°F when s is set equal to zero. This says that a 1° change in the inlet temperature raises the outlet temperature by 1°, which seems reasonable. The steady-state gain between Tj and the heat input Q is 1/2160 °F/Btu/min. You should be careful about the units of gains. Sometimes they have engineering units, as in this example. At other times dimensionless gains are used. We discuss this in more detail in Chapter 8. 

Ratio between characteristic diffusion and deformation time Dimensionless parameter Deformation rate of a filament (1/s) Solubility parameter [(J/m ) ]... 

---