Some empirical equations

In the following the equations introduced previously are summarised and supplemented by further equations. 

Laminar film condensation on vertical or inclined plates, and on the inside or outside of a vertical tube. 

According to Nusselt s film condensation theory, from (4.13a), under the assumption QG Qi, the heat transfer coefficient follows as 

If the wall is inclined at an angle 7 to the vertical then the acceleration due to gravity g has to be replaced by its component parallel to the wall g cos 7 with 0 7 7r/2. The equation also holds for condensation of quiescent vapours on the inside or outside of a vertical tube, if the diameter of the tube is large in comparison to the film thickness. The width b has to be replaced by b = ir d. If a deviation of 1 % from the values from Nusselt s film condensation theory is permitted, then the equation is valid up to a Reynolds number 

According to (4.15a), with C gL, the mean heat transfer coefficient is 

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Some empirical equations to predict cyclone pressure drop have been proposed (165,166). One (166) rehably predicts pressure drop under clean air flow for a cyclone having the API model dimensions. Somewhat surprisingly, pressure drop decreases with increasing dust loading. One reasonable explanation for this phenomenon is that dust particles approaching the cyclone wall break up the boundary layer film (much like spoiler knobs on an airplane wing) and reduce drag forces. 

A comparison between some empirical equations of state for polymers with regard to their standard deviations was made by Kamal and Levan (1973). 

There are also some empirical equations for describing the yields of products formed in the cracking reactions of polymers. One of them is the Atkinson and McCaffrey kinetic model, which derives the weight loss of polymer for their initial degree of polymerization, weight of sample and reaction rate. As a matter of fact the reaction rate constant is calculated by using a first-order kinetic equation [33, 34]. 

Some empirical equations for heat and mass transfer in external forced flow... 

The stability of embankments on soft clay can be calculated by some empirical equations as functions of the increased shear strength during construction (Suzuki and Yasuhar, 2007). The increased shear strength needs to be determined by in situ measurements such as excess pore pressures, tip resistance of cone penetration tests, and field vane shear strengths, etc. 

In order to capture the time evolution of die swell, some empirical equations have been proposed for annular die geometries. The diameter (B,) and thickness swell (B2) are made time dependent via an exponential function by including a characteristic time (p. This leads to expressions of the form ... 

The concentration dependence of the experimental thermal conductivities for some selected aqueous solutions along various isotherms and isobars is shown in Figure 5.11. As the figures show, the thermal conductivity of most solutions monotonically decreases with composition. Furthermore, the composition dependence of the thermal conductivity exhibits a small curvature, especially at high concentrations (x > 20 mass.%). Some empirical equations employed for the correlation of the thermal conductivity with concentration will be briefly presented here. 

Most paint formulations consist of a mixture of suspension particles (pigments) and emulsion droplets (latex particles that are liquid-like at room temperature) referred to as suspoemulsions. The continuous medium with viscosity Po maybe simply an aqueous phase in which several ingredients are dissolved or could be nonaque-ous (oil) that may consist of two or more miscible oils. For non-Newtonian systems (which is the case with paint systems) some empirical equations can be established to relate the plastic viscosity qpi and yield value Op to the volume fraction of the disperse phase c ) [49]... 

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