Scaled distance equations used for estimating peak particle velocity have been developed by some researchers. The most widely used equation among these is the equation developed by Duvall and Fogelson. However,
center of the pipe to any point in the fluid, a the mean radius of the pipe, c the sound velocity in the fluid inside the pipe, ω the radian frequency of the sound, x the longitudinal distance from the disturbance to any point in the fluid, and zt the impedance of the pipe such ...
where ψ is the electrical potential, F is the Faraday constant, R is the universal gas constant, T is temperature, v is the average velocity of convective solvent flow, and Ci, x, zi and Di are, respectively, the concentration, position in the membrane, valence of charge and diffusion ...
Suppose a body started with some initial velocity \(\overrightarrow u \) and has a uniform acceleration \(\overrightarrow a \) and due to this acceleration, the final velocity after time \(t\) becomes \(\overrightarrow v \). Thus integrating and putting in the limits we get, \(\in...
For a state to state transfer, we derive a family of control fields depending upon two free parameters, which allow us to adjust the efficiency, the time and the robustness of the control process. As an illustrative example, we consider the quantum analog of the tennis racket effect, which ...
An apparent time dependence of the Hubble constant was deduced from the linear correlation between the recession velocity of galaxies and the traveled distance of their photons under the assumption of the space expansion being homologous. The time dependence of the space expansion velocity at early ...
The SIMPLE algorithm is used for coupling between the velocity and pressure fields. The second-order central difference scheme (CDS) is applied for the discretization of the diffusive terms in all equations and of convective terms in 〈U, V, W, T〉 equations (T-RANS, LES and HYBRID ...
If the actions of the floor in constraining the normal velocity of the sound field to zero, and in exerting reaction forces on the air, are to be represented by ‘sources’ acting on this plane in free space, instead of by a boundarycondition on a bounded space, they must appear on ...
Given the work-energy theorem, relating force F and the differential distance Δx over which it acts give differential kinetic energy ΔK: (38)ΔK=FΔx. Substitution into Eq. 38 for the change of kinetic energy ΔK in terms of change in potential energy ΔV of Eq. 37 gives (39)F=...
where ρ¯ is the density and u˜i is the velocity component. Sm is the mass source term from the evaporating droplets to the gas (gm unit volume−1 s−1). Care has to be taken in this calculation to allow for the volume occupied by the droplets themselves. Momentum Conservation...