Recent content by c0der

From the Eulerian form of the continuity equation, where x is the Eulerian coordinate: \frac {\partial \rho}{ \partial t } + u \frac {\partial \rho}{\partial x} + \rho \frac { \partial u}{\partial x} = 0 The incremental change in mass is, where m is the Lagrangian coordinate: dm = \rho dx...

I read the part in your link on the first law. Ok I see, I have confused the temperature dependence, which I missed in your link. I think I will just leave it at that to avoid more confusion, thank you for your time.

Thanks Chet, that makes sense about the restricted first law and reversible processes. I will post my understanding, please let me know of any flaws: For a reversible process, we can use two variables to define the state of the system (choosing temperature T and specific volume v in this...

Thanks, that makes sense. Fair enough, whether or not the volume is constant does not affect the change in internal energy. Given this, for any process (volume not constant), we can write the first law as above: c_v dT+pdV=dq Given that the internal energy is a function of temperature...

If c_v is the specific heat at constant volume, authors substitute this into the first law as follows: c_v d\theta + pdv = dq How can one deduce that equation for any case? Since the specific heat at constant volume is used, the equation would be valid only where there is no expansion i.e...

Matlab's simplifier was the problem, I verified the solution by hand, thanks for the help.

Thanks for checking. It strikes me as odd that Matlab cannot solve this ODE and that the above procedure I used does not turn out to be a solution when back substituting for u and du/dx: >> syms u(x) >> dsolve(diff(u,x)/(1+u^2)^(3/2)==1) Warning: Explicit solution could not be found. > In...

Thanks for your replies. Zondrina: I believe that's the same answer, just in a different form as 1 = [1 - (x + C)^2] / [ 1 - (x+C)^2 ] ? Mark44: I evaluated the integral in mathematica and matlab, and the same answer is given. I am integrating 1/(1+u^2)^(3/2) over u not x?

Homework Statement Solve the following equation: v is the dependent variable, x is the independent variable Homework Equations \frac{d^2v/dx^2}{(1+\frac{dv}{dx}^2)^{3/2}}=1 The Attempt at a Solution Hi, I am trying to solve the following equation...

Thank you, stupid me.

Homework Statement Verify Stokes' theorem for the following: F=[y^2, x^2, -x+z] Around the triangle with vertices (0,0,1),(1,0,1),(1,1,1) Homework Equations \int\int_S(curlF)\cdot ndA=\int_C F\cdot r' ds The Attempt at a Solution [/B] For the LHS: curlF\cdot n=2x-2y \int\int_S(curlF)\cdot...

I see: x=rcos\theta, y=rsin\theta where 0<=r<=z Thanks a lot

Homework Statement Find the moment of inertia of a solid cone about its longitudinal axis (z-axis) The cone: x^2+y^2<=z^2, 0<=z<=h I_z = \int\int\int_T(x^2+y^2)dxdydzHomework Equations Representing the cone in cylindrical coords: x=zcos\theta y=zsin\theta z=z The Attempt at a Solution...

(c2 / (x2 + c1x)) * y

Thank you, I have done this however as follows: Equating coefficients of x0 gives: a0=0 For x1: a2 = c2/2c1 Equating coefficients of xm: am+1 = [ c2 - (m-1)m ] / [ c1m(m+1) ] am for m>=2 Then: a3 = [ (c2 - 2) / 3!2!c12 ] a1 a4 = [ (c2 - 6)(c2 - 2)c2 / 4!3!c13 ] a1 a5 = [ (c2 - 12)(c2 -...