The available direct gas dynamic tables provide the area ratio and the Prandtl-Meyer(P-M) angle of isentropic expansion of gas as functions of the Mach number. But finding the value of the Mach number in terms of area ratio or P-M angle requires an inverse function. Currently, the Mach number is determined by either interpolation from the direct gas dynamics tables, or the application of non-linear equation solvers using numerical methods. Both methods are approximate. In this paper inverse functions for Mach number in the form of Taylor’s series expansions are reported to develop the so-called inverse tables. The advantage of this approach is that the Mach number with a greater accuracy, referred to as nearly exact can be obtained by reading from the inverse table. In the presentation, the necessary equations and new tables that can be used by the scientific community will be disseminated. The data and computer programs are made available on GitHub through https://github.com/anillals/Inverse-gas-dynamic-tables- and-codes. A paper describing the complete mathematical steps in the derivation of the equations can be found at https://rdcu.be/dgrlf

The computing power of smartphones has not received considerable attention in the mainstream education system. Most of the education-oriented smartphone applications (apps) are limited to general purpose services like Massive Open Online Courses (MOOCs), language learning, and calculators (performing basic mathematical calculations). Greater potential of smartphones lies in educators and researchers developing their customized apps for learners in highly specific domains. In line with this, we present Fluid Dynamics, a highly accurate Android application for measuring flow properties in compressible flows. This app can determine properties across the stationary normal and oblique shock, moving normal shock and across Prandtl $-$ Meyer expansion fan. This app can also measure isentropic flows, Fanno flows, and Rayleigh flows. The functionality of this app is also extended to calculate properties in the atmosphere by assuming the International Standard Atmosphere (ISA) relations and also flows across the Pitot tube. Such measurements are complicated and time-consuming since the relations are implicit and hence require the use of numerical methods, which give rise to repetitive calculations. The app is an efficient semi-implicit solver for gas dynamics formulations and uses underlying numerical methods for the computations in a graphical user interface (GUI), thereby easing and quickening the learning of concerned users. The app is designed for the Android operating system, the most ubiquitous and capable surveillance platform, and its calculations are based on JAVA based code methodology. In order to check its accuracy, the app's results are validated against the existing data given in the literature.

We review a modern differential geometric description of the fluid isotropic motion and featuring it the diffeomorphism group structure, modelling the related dynamics, as well as its compatibility with the quasi-stationary thermodynamical constraints. There is analyzed the adiabatic liquid dynamics, within which, following the general approach, there is explained in detail, the nature of the related Poissonian structure on the fluid motion phase space, as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product. We also present a modification of the Hamiltonian analysis in case of the isotermal liquid dynamics. We study the differential-geometric structure of the adiabatic magneto-hydrodynamic superfluid phase space and its related motion within the Hamiltonian analysis and invariant theory. In particular, we construct an infinite hierarchies of different kinds of integral magneto-hydrodynamic invariants, generalizing those before constructed in the literature, and analyze their differential-geometric origins. A charged liquid dynamics on the phase space invariant with respect to an abelian gauge group transformation is also investigated, some generalization of the canonical Lie-Poisson type bracket is obtained.