اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدApplication of Gauss Law in Acoustics
430
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Practical application of Gauss law in acoustics is not a very well known method. However, any inverse square law behavior can be formulated in the way similar to Gauss law, which allows us to extend the same principle to sound waves propagation. We show in this paper how the acoustic power of sound source can be related to the sound intensity flow through a given surface by means of the Gauss law. Several different sound-source shapes, important in practical applications, are analyzed by means of the Gauss law. A suitable choice of the Gaussian surface allows us to obtain the simple and straightforward method for calculating the sound intensity distribution in space.
قيم البحث
اقرأ أيضاً
We consider linear and nonlinear waves in a stratified hydrostatic fluid within a channel of variable area, under the restriction of one-dimensional flow. We derive a modified version of Riemanns invariant that is related to the wave luminosity. This
quantity obeys a simple dynamical equation in linear theory, from which the rules of wave reflection are easily discerned; and it is adiabatically conserved in the high-frequency limit. Following a suggestion by Lighthill, we apply the linear adiabatic invariant to predict mildly nonlinear waves. This incurs only moderate error. We find that Lighthills criterion for shock formation is essentially exact for leading shocks, and for shocks within high-frequency waves. We conclude that approximate invariants can be used to accurately predict the self-distortion of low-amplitude acoustic pulses, as well as the dissipation patterns of weak shocks, in complicated environments such as stellar envelopes. We also identify fully nonlinear solutions for a restricted class of problems.
The contact angle that a liquid drop makes on a soft substrate does not obey the classical Youngs relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact ang
les different from that predicted by Neumanns law, which applies when the drop is floating on another liquid. Here we derive an elasto-capillary model for contact angles on a soft solid, by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of vanishing elastic modulus yields Neumanns law or a slight variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit (Young) to the soft limit (Neumann) appears when the length scale defined by the ratio of surface tension to elastic modulus $gamma/E$ reaches a few molecular sizes.
The 4/5-law of turbulence, which characterizes the energy cascade from large to small-sized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up to R_lambda ~
1640. The result is corroborated by high-resolution simulations of Landau-Tiszas two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3 % but with a lower Reynolds number of order R_lambda ~ 100. Although the Karman-Howarth equation (including a viscous term) is not valid emph{a priori} in a superfluid, it is found that it provides an empirical description of the deviation from the ideal 4/5-law at small scales and allows us to identify an effective viscosity for the superfluid, whose value matches the kinematic viscosity of the normal fluid regardless of its concentration.
How to determine accurately and efficiently the aerodynamic forces of the aircraft in high-speed flow is one of great challenges in modern aerodynamics. In this Letter we propose a new similarity law for steady transonic-supersonic flow over thin bod
ies. The new similarity law is based on the local Mach number frozen principle. It depends on both the specific heat ratio and the free-stream Mach number. The new similarity law enables one to determine the lift and drag coefficients of the aircraft from that of a reference state which is more reachable. The validity of the new similarity law has been confirmed by the excellent agreement with numerical simulations of both two-dimensional airfoil flows and three-dimensional wing flows.
The four-fifths law for third-order longitudinal moments is examined, by the use of direct numerical simulation data on three-dimensional forced incompressible magnetohydrodynamic (MHD) turbulence without a uniformly imposed magnetic field in a perio
dic box. The magnetic Prandtl number is set to one, and the number of grid points is $512^3$. A generalized Karman-Howarth-Kolmogorov equation for second-order velocity moments in isotropic MHD turbulence is extended to anisotropic MHD turbulence by means of a spherical average over the direction of $textbf{r}$. Here, $textbf{r}$ is a separation vector. The viscous, forcing, anisotropy and nonstationary terms in the generalized equation are quantified. It is found that the influence of the anisotropic terms on the four-fifths law is negligible at small scales, compared to that of the viscous term. However, the influence of the directional anisotropy, which is measured by the departure of the third-order moments in a particular direction of $textbf{r}$ from the spherically averaged ones, on the four-fifths law is suggested to be substantial, at least in the case studied here.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
