. Under similar geometrical conditions, the scale of time can be described as
(2) Kinematic Similarity
. It means that, in the prototype and model, the corresponding kinematic parameters, such as the velocity and acceleration, are in the same direction and are proportional; then the time-scale ratio is as follows:
2) kinematic similarity
: this means that the observed geometry of vector field rate is similar;
A model is said to have similitude with the real application if the two applications share geometric similarity, kinematic similarity and dynamic similarity, as follows: 1) geometric similarity--the engineered model is the same shape as the application, but usually scaled; 2) kinematic similarity--fluid flow of both the model and real application must undergo similar time rates of change motions--(fluid streamlines are similar); and 3) dynamic similarity--ratios of all forces acting on corresponding fluid particles and boundary surfaces in the two systems are constant.
These can be listed as follows: 1) calibration traits of the artifacts (original prototypes) transferred to the meter (provided that the CNC-machining tolerances and body dimensions are valid between devices) offering minimum dynamic calibration; 2) meter turndown can be determined after manufacture to suit the application and controlled (this will be discussed later in this article); 3) concentricity of the meter and subsequent area ratio (beta) changers controlled at a high tolerance level; 4) tap design, position and repeatability of design; and finally 5) surface roughness control by CNC machining--very important for dynamic and kinematic similarity.
Thus Geometric, Dynamic and Kinematic Similarity is satisfied by the precision machining and manufacturing process.
This is due to the fact that topological equivalence, also called conjugacy, as well as kinematic similarity, preserves the inner structures of the solutions of differential equations.
then it follows that [PHI](t) = V(t) [U.sup.-1](t), and therefore [PHI](t) gives the required kinematic similarity.