Nondimensional coordinate

Erom the previous sections it is clear that there are a number of different possible models that can be applied to the contact of an elastic sphere and a flat surface. Depending on the scale of the objects, their elasticity and the load to which they are subjected, one particular model can be more suitably applied than the others. The evaluation of the combination of relevant parameters can be made via two nondimensional coordinates X and P [16]. The former can be interpreted as the ratio of elastic deformation resulting from adhesion to the effective range of the surface forces. The second parameter, P, is the load parameter and corresponds to the ratio of the applied load to the adhesive puU-off force. An adhesion map of model zones can be seen in Figure 2. 

At x = 3 m, which is 10% along the stretch from the river to the wells, the nondimensional coordinates which characterize the transition of the maximum concentration are = 0= 0.1. Thus ... 

Step input. All the conclusions drawn for the pulse input can directly be transferred to the step input. The concentrations, if expressed for the nondimensional coordinates , and 9, are not affected by sorption the shape of the concentration curve along x for a fixed time is independent of sorption. Yet, when the front passes by a fixed location x, the time needed for the concentration to increase from, say, 5% to 95% of the maximum concentration, grows as (/w)-1. This can be directly deduced from Table 25.2, where the duration of the passage of the front is quantified by the nondimensional time interval A0 - 095 -05. This value does not depend on sorption, but after transformation back into real time it does (see Eq. 25-42) ... 

Equation (15) was used to obtain the meniscus height H. As seen in Fig. 27, and (f>i indicate the nondimensional coordinate of the meniscus at the attachment position and the inclination of the test plate, respectively. The gradient of the meniscus curve becomes equal to that of the solid wall (i.e., (f>2 shown in the figure) at C. Hence the coordinate of the contact, zc, can be calculated by using (n—(f)2) instead of ij/ in Eq. (15) as... 

A cylindrical coordinate system is usually used to describe the tank geometry with orthogonal coordinates r, if, z where the origin at the centre of the tank bottom and the z axis is vertical (Fig. 1). The height of the tank to the original of the free surface of the fluid and its radius are denoted by H and R, respectively p is the mass density of the fluid, while the nondimensional coordinates = rjR and C = zlH in the radial direction and along the height of the tank, respectively, are usually considered. 

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