With the above
nondimensional quantities, the governing equations (1) become
where [S.sup.*.sub.ij] = [S.sub.ij]/([mu]W/h) is the
nondimensional shear stress.
The
nondimensional differential dynamics, as seen in (9), is obtained from (6) by the replacement of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [Q.sub.x] = 2[pi][[??].sub.x] x [m.sub.x]/[c.sub.x].
In their analysis, it was found that under the assumptions of long wavelength and low Reynolds number approximation the flow is governed by the following system of partial differential equations in
nondimensional form [13]:
In this paper, by applying the VIM, we solve the
nondimensional dynamic equation of the suspension spring system under the excitation of dropping shock to obtain a firstorder approximate solution and obtain the
nondimensional maximum acceleration expression.
For this purpose the following
nondimensional variables are now introduced:
where [[theta].sub.BT] is
nondimensional temperature at the beginning of fuel injection; A is the factor of fuel properties; a, a1 are diesel engine and fuel injection system structure weightings; [PSI] is assessment factor of the ratio of physical and chemical rates; [[phi].sub.IL] is fuel injection period (using fuel injection system features of real engines 1DH-FTE, GM 6.5L, OM 366 LA), deg.c.r.; [[phi].sub.IK] is the factory fuel injection angles (fuel injection system angles of real engines 1DH-FTE, GM 6.5L, OM 366 LA), deg.c.r.
Therefore, a sound speed that is made
nondimensional using the isothermal sound speed of the vapor, as shown in the equation below, approaches unity.
The stresses in the part are to be expressed in a
nondimensional form, in order to show the effect of the shape of the part on the stresses in it.
In an effort to add further fluid dynamical underpinnings to navigational strategies, I suggest how simple
nondimensional categorization of behavior in relation to flow may aid in identifying the forces underlying common elements, even across animals of seemingly disparate size and scale.
t* =
nondimensional time (Fourier number), dimensionless