Dimensionless pressure

Starting with equation (11.20) we multiply both sides by D and Introduce a dimensionless pressure tt such that p = p ir. Then... 

Fig. 6.6 Dependence of dimensionless wall superheat Ar Qj g = AroNs/Argi g on dimensionless pressure = Ps/ s- Hsu (1962), 2 Bergles and Rohsenow (1964), 3 Thom et al. (1965), 4 Jens and Lottes (1951)...

Fig. 13 —Dimensionless pressure distribution of the gas film within the two-rail slider. Lx slider length Ly. slider width.

Table 5 gives the comparisons of the calculated load carrying capacity F, the pitch moment M (moment around Y axis), the maximum and minimum dimensionless pressures Pmax. Pmin the Speed of 9.57557 m/s, with and without consideration of the rarefaction effect. All of the absolute values of F, M, min become lower when the rar-... 

Fig. 15—Dimensionless pressure distributions of the gas film in the Q type slider under several different pitch angle conditions, (a) Pitch angle 0=0 /jirad, calculated floating force F=17.83g (b) Pitch angle 0=1O iirad, calculated floating force F=9.76g (c) Pitch angle 6 = 300 yurad, calculated floating force F = -0.75 g (d) Pitch angle 0=3,000 u,rad, calculated floating force F = 3.64 g.

Fig. 18—Dimensionless pressure distributions with two different mesh sizes.

A separated flow model for stratified flow was presented by Taitel and Dukler (1976a). They indicated analytically that the liquid holdup, R, and the dimensionless pressure drop, 4>G, can be calculated as unique f unctions of the Lockhart-Martinelli parameter, X (Lockhart and Martinelli, 1949). Considering equilibrium stratified flow (Fig. 3.37), the momentum balance equations for each phase are... 

Figure 8. Experimental data of the dimensionless pressure drop per bubble as a function of capillary number for 1 and 2 mm diameter glass capillaries. The solid line denoted by E - 0 gives the theory of Bretherton.

L/pj-A)(S/psA), liquid-solids velocity ratio, dimensionless Number of heat-transfer stages, dimensionless = hdp/kg, Nusselt number, dimensionless Pressure drop, gm-wt/cm2 = Cpu kg, Prandtl number, dimensionless = dpiipj U, Reynolds number, dimensionless S Mass velocity of solids, gm/cirf sec... 

O Dimensionless pressure drop in accelerative particle motion... 

Omega Method Model for Compressible Flows The factored momentum balance, Eq. (23-42), can be analytically integrated after first relating the dimensionless specific volume 8 to the dimensionless pressure ratio r. A method to do this, designated the omega method, was suggested by Leung (1986) ... 

First-principle calculations of the thermodynamic properties are more or less hopeless enterprise. One of the most famous phenomenological approaches was suggested by van der Waals [6, 8, 9]. Using the dimensionless pressure it = p/pc, the density v = n/nc and the temperature r = T/Tc, the equation of state for the ideal gas reads it = 8zzr/(3 -u) — 3zA Its r.h.s. as a function of the parameter v has no singularities near u = 1 v = it = t = is the critical point) and could be expanded into a series in the small parameter 77 = [n — nc)/nc with temperature-dependent coefficients. Solving this... 

More recently, Brauer (B18) carried out a detailed analysis of the flow of smooth films and gas streams inside vertical tubes this work was subsequently extended by Feind (F2). In this treatment, all the possible cases of film/gas flow (countercurrent, upward cocurrent, and downward cocurrent) are dealt with in a unified manner by plotting the calculated results in the form of / as a function of NRe, . Here / is the absolute value of the dimensionless pressure drop in the gas stream ... 

Fig. 14. Dimensionless pressure as a function of dimensionless time at four points of the mould for plastisol I with gelatination taken into account upon moulding into a preheated mould. Solid lines calculated dotted measured...

For a power law solution the equation, of motion is non-dimensionalized in a similar manner as with the Newtonian solution, except that dimensionless pressure is defined as... 

Figure 6.41 Dimensionless pressure distribution for various power law indices.

Figure 6.60 presents the dimensionless pressure flow velocity profile for various positive values of Cl. It should be noted that negative values of Cl lead to symmetric velocity profiles as the one generated by the positive values. 

Dimensionless pressure flow velocity profile for various dimensionless temperature... 

Solve for the pressure distribution for the two previous problems and compare them to each other. On the same graph, plot the dimensionless pressure p/pmax for both cases. 

Langmuir (1918) laid down a systematic and theoretically grounded adsorption isotherm, the well-known Langmuir isotherm, which has served as a basis for a number of future isotherms, such as the BET isotherm, described in 1.4.1.3. The basic assumptions of the Langmuir adsorption model include monolayer coverage, localized adsorption (i.e., the specific adsorption sites exist and the interactions are between a specific molecule and the site), and homogeneous materials. In addition, the heat of adsorption is independent of coverage. He proposed that the rate of adsorption is proportional to the dimensionless pressure of the adsorbate, p/po (= p ), where po is the saturated vapor pressure, and the... 

---