Estimate of the energy spectrum characteristics of shock processes in a fluid

Conclusions

It follows from the results obtained that the upper frequency of possible local pulsations in a fluid is determined by two factors: the quantityα, which depends on the kinematic viscosity of the fluid Υ, the mean velocity of the nonstationary flow v_av, the tube diameter d, and the relative depth of the shock process characterized by the parameter$(\sqrt 3 /8)(\mu c/v_{av} ) \simeq 0.2\tilde v/v_{av}$.

The energy spectrum characteristic of nonstationary processes of limiting rapidity can be computed from the equations

$$\begin{gathered} c_L (f) = 1 - 2\pi \frac{{\sqrt 3 }}{8}\frac{{\mathop \upsilon \limits^ \sim }}{{\upsilon _{av} }}\sqrt {\frac{f}{a}} + 2\pi ^2 \frac{3}{{64}}\left( {\frac{{\mathop \upsilon \limits^ \sim }}{{\upsilon _{av} }}} \right)^2 \frac{f}{a},f< 0.43a\left( {\frac{{\upsilon _{av} }}{{\mathop \upsilon \limits^ \sim }}} \right)^2 ; \hfill \\ c_f = 0.6\exp \left( { - 0.56\left( {\frac{{\mathop \upsilon \limits^ \sim }}{{\upsilon _{av} }}} \right)^2 \frac{f}{a}} \right), \hfill \\ 0.43a\left( {\frac{{\upsilon _{av} }}{{\mathop \upsilon \limits^ \sim }}} \right)^2< f< 3.2a\left( {\frac{{\upsilon _{av} }}{{\mathop \upsilon \limits^ \sim }}} \right)^2 ; \hfill \\ c_H f = \frac{{1/9}}{{1 + \frac{{\pi ^2 }}{{256}}\left( {\frac{{\mathop \upsilon \limits^ \sim }}{{\upsilon _{av} }}} \right)^4 \left( {\frac{f}{a}} \right)^2 }}, \hfill \\ 3.2a\left( {\frac{{\upsilon _{av} }}{{\mathop \upsilon \limits^ \sim }}} \right)^2< f. \hfill \\ \end{gathered} $$

The smaller the amplitude of the nonstationary perturbation in the fluid, the more it can, in principle, contain hf harmonics. Energy spectra of nonstationary processes of sufficiently small amplitude can be arbitrarily close to a white noise spectrum.

On the basis of the investigations presented, the problem of estimating the optimum fast response of an IMS can be solved as a function of the specific realization of a random process, which is determined on the basis of the energy spectrum characteristics found for the parameter being measured and the interference.