Comparison between flow formulae

Clearly the factor A2 p /v is common to all three expressions, and we may examine the differences in predicted flow by considering (he behaviour of the flow functions  

The numerical behaviour of these flow functions is shown in tabular and graphical forms below. Table 5.1 shows three instances for the general, polytropic case  

TabI 5.1 Tabulation of values of the various flow functions 

A number of points can be deduced from the graph and the table. 

Kearton, W.J. (1922, 1958). Steam Turbine Theory and Practice, Pitman and Sons. 

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Comparison of results between the various empirical steam flow formulas suggests the Babcock equation as a good average for most design purposes at pressure 500 psia and below. For lines smaller than 4 inches, this relation may be 0-40 percent high [56]. 

Owing to the great theoretical and experimental difficulties, it is possible only to make a qualitative comparison between the results in models dis- -playing Brownian motion and the formulas. According to these, the viscosity rises as required, both with the axial ratio and the concentration, and does so more rapidly even if moderate Brownian motion occurs. An effect of flow gradient is also appreciable. If, in addition, the above statement on the restriction of the region of dilution is true, a fortiori, the special result of these experiments with rigid models may be summed up... 

Yao et al. [10] studied an electroosmotic pump made from porous silicon membranes having straight circular pores. Tortuosity is unity and ifr was measured directly from SEM images of the cross-section. Zeta potential is calculated by using the formula for the ratio 2max/Jmax and the measured data of Qmax and /max- Comparison between theory and experiment is good for the plots Qmax versus V and Jmax versus V. There was considerable deviation for the prediction of Apmax and Yao et al. attributed this discrepancy to the problem in the zeta potential measurement and non-uniform distribution of the pore size. At a lower flow... 

Instead of nodal lines in closed systems we are interested in the statistics of NPs for open chaotic billiards since they form vortex centers and thereby shape the entire flow pattern (K.-F. Berggren et.al., 1999). Thus we will focus on nodal points and their spatial distributions and try to characterize chaos in terms of such distributions. The question we wish to ask is simply if one can find a distinct difference between the distributions for nominally regular and irregular billiards. The answer to this question is clearly positive as it is seen from fig. 3. As shown qualitatively NPs and saddles are both spaced less regularly in chaotic billiard in comparison to the integrable billiard. The mean density of NPs for a complex RGF (9) equals to k2/A-k (M.V. Berry et.al., 1986). This formula is satisfied with good accuracy in both chaotic and integrable billiards. 

Comparisons of precision using Eqs. 5.220 and 5.221 and Blasius s formula (Table 5.8) in which the diameter of circular duct 2a is replaced by hydraulic diameter 4b, b being the halfspace between two plates, have been conducted by Bhatti and Shah [45]. In the range of 5000 < Re < 3 x 104, Eq. 5.220 is recommended otherwise, Eq. 5.221 should be used to obtain the friction factor for fully developed turbulent flow in a parallel plate duct. However, use of the hydraulic diameter to substitute for the circular duct diameter in the Blasius equation is reasonable for the prediction of the fraction factor [45]. 

In order to estimate the water flow into tunnel with horseshoe cross-section, based on the exsting analytical solution and numerical method, we attempt to establish a relationship between water inflow and the corresponding boundary conditions. Interestingly, by making a comparison of existing analytical solutions and other empirical formulas (Li et al., 2010), it could be found that all solutions can be expressed in the following general form ... 

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