=(V2)1/2 KπGOO'Consider the dispersion relation of a linear spiral density wave perturbation (equation 4.45 inChapter 3 of the lecture notes). The Toomre's parameter is defined as Qwhere(V2) 1/2 is the root-mean-square turbulent plus thermal velocity, к the epicyclic frequency, σ theunperturbed surface density of the disc and G the gravitational constant. For Q = 1/√2, showthat the spiral pattern is unstable ifК(√2-1)(V²² ) 1/2 < |k| < (√√2+1)where k is the wavenumber of the perturbation.К(V+2)1/2

Answered: Image /qna-images/answer/973953ae-a79e-4b30-a850-fd48ae01b2ad.jpg

Answered: = (V2)1/2 K πGOO ' Consider the…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter2: The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 97CP: Verify the normalization equation 0f(v)dv=1 In doing the integral, first make substitution...

See similar textbooks

Similar questions

2b. Consider that the input to the tank-pipe liquid system is formed of a source pressure pi, the atmospheric pressure pa, and the input flow rate q., whereas the output is the output flow rate q. Derive the corresponding transfer function matrix by means of complex impedances considering that known are the element properties Ci and R. Utilize the transfer function approach using a) matlab and b)Simulink to plot the output flow rate of the liquid system shown. Known are pa = 10 N/m, pi =2.2x10 N/m2, q=0.03 m3/s. d=1.5 m (diameter of the tank). p= 1000 kg/m', d, = 0.020 m (diameter of the pipe). / = 18 m (length of pipe), u=0.001N s/m?. P. Tank Pipe R. Pressure source
A water well is excavated, and has a cylindrical form. The water level in the well is 2 meters from the level ground. What is the absolute pressure experienced by a dipper at a depth of 1.5 meter in the water? (Assume water is at 4 degree Celsius) solve with complete solution, given, figure & fbd
Consider a non-rotating circular thin disc of gas of radius R. The only forces present in the system are pressure forces within the disc and its self-gravity. The disc is surrounded by empty space. In the disc is present a surface density perturbation of the type 01 = 010e (wt-kr) where σ10 is the amplitude of the perturbation, t represents time, r the radial coordi- nate from the centre of the disc, w is the angular frequency of the perturbation and k its wavenumber. Under the influence of the above perturbation, the linear stability of the disc is determined by the following dispersion relation w² = u²k² - 2πGook, where u is the sound speed in the disc, σ the surface density of the disc, and G is the gravitational constant. 1. Using the dispersion relation and appropriate definitions derive an expression of the group velocity of the small perturbations as a function of u, σo and their wavelength. 2. State the criterion for the disc to be stable and then show that the disc is stable…
An incompressible stream function is defined by VCR, 9) = (3ry – y') L? where U and L are (positive) constants. Where in this chapter are the streamlines of this flow plotted? Use this stream function to find the volume flow Q passing through the rectangular surface whose corners are defined by (x, y, z) = (2L, 0, 0), (2L, 0, b), (0, L, b), and (0, L, 0). Show the direction of Q|
Find the mass of the following thin bars. A bar on the interval 0 ... x . 9 with a density (in g>m) given by rx2 = 3 + 2Vx
Q Calculate the velocity of longitudinal and shear elastic waves in a cubical crystal along (111) dire tion.
Consider the dispersion relation of a linear spiral density wave perturbation (equation 4.45 in Chapter 3 of the lecture notes). The Toomre's parameter is (V2)²K defined as Q = = 1/2 лGσ。 , where (V2) 1/2 is the root-mean-square turbulent plus thermal velocity, the epicyclic frequency, σ the unperturbed surface density of the disc and G the gravitational constant. If Q = 0.7, for each of the the following values of the radial wavenumber k choose whether the perturbation makes the spiral pattern stable or unstable. k k = II = 2 4 K K 1/2 stable (1/2 stable (V2)1/2 Κ k = (V unstable 2 1/2 ÷ → k = 2. K (V2)1/2 unstable → k = K (V2)1/2 unstable →
Verify the normalization equation 0f(v)dv=1 In doing the integral, first make substitution u=m2kBTv=vvp. This "scaling" transformation gives you all features of the answer except for the integral, which is a dimensionless numerical factor. You'll need the formula 0x2e x 2dx= 4 to find the numerical factor and verify the normalization.`
When a river flows at a velocity V past a circular pylon of diameter D, vortices are shed at a frequency f. It is known that f is also a function of the water density ρ and viscosity µ, and the acceleration due to gravity, g. (a) Use dimensional analysis to express this information in terms of a functional dependence on nondimensional groups. (b) A test is to be performed on a 1/4th scale model. If previous tests had shown that viscosity is not important, what velocity must be used to obtain dynamic similarity, and what shedding frequency would you expect to see?
The Duffing oscillator with mass m is described by the non-linear second order DE d? 3 + ax + Bx° = y sin (wt), dt? where [x] = L and [t] = T. Calculate the dimensions of , B, y and w. Answer: a [B] = [w] = ||
Solve the following problems Q.1 Derive an expression for plasma oscillation frequency for ions. Q.2 For a simple plasma oscillation with fixed ions and a space-time behavior expli(kx – wt)], calculate the phase ô for Ø1, E1, and v, if the phase of n, is zero. Illustrate the relative phases by drawing sine waves representing n1, Ø1, E1 and v, (a) as a function of x at t = 0, (b) as a function of t at x = 0 for w/k > 0, and (c) as a function of I at x = 0 for w/k < 0. Note that the time patterns can be obtained by translating the x patterns in the proper direction, as if the wave were passing by a fixed observer. Q.3. By writing the linearized Poisson's equation used in the derivation of simple plasma oscillations in the form V . (E E) = 0 derive an expression for the dielectric constant E applicable to high frequency longitudinal motions.
I do not understand how the professor came to the conclusion for the Vcenter equation.

SEE MORE QUESTIONS

Recommended textbooks for you

University Physics Volume 2

Physics

ISBN:

9781938168161

Author:

OpenStax

Publisher:

OpenStax

University Physics Volume 2

Physics

ISBN:

9781938168161

Author:

OpenStax

Publisher:

OpenStax

SEE MORE TEXTBOOKS