Recent content by Mr. Cosmos

  1. M

    Force Produced from Fluid Motion

    But it is certainly possible to have a flow situation in a closed volume where the velocity vectors do not sum to zero.
  2. M

    Force Produced from Fluid Motion

    Dear all, I have a question that has eluded explanation in fluid mechanics textbooks and even some of my colleagues. Suppose we have a general control volume. The application of linear momentum conservation will yield an equation of the form, $$\frac{\partial}{\partial t} \int_{V\llap{-}} \rho...
  3. M

    I Vector Calculus?

    Thanks for the quick response. I now see my mistake. Thanks!
  4. M

    I Vector Calculus?

    So I have a quick question that will hopefully yield some clarification. So the divergence of a dyadic ##\bf{AB}## can be written as, $$\nabla \cdot (\textbf{AB}) = (\nabla \cdot \textbf{A}) \textbf{B} + \textbf{A} \cdot (\nabla \textbf{B})$$ where ##\textbf{A} = [a_1, a_2, a_3]## and...
  5. M

    Atomic Conservation in Ionized Hydrogen Gas

    Dear all, So I have a question concerning atomic conservation in an ionized hydrogen gas. So imagine we have ## H_2 ## initially. Later the gas is taken to an appreciable temperature such that at equilibrium the following species are present, ## e^-, \ H, \ H^+, \ H_2, \ H^-, \ \text{and} \...
  6. M

    Specific Heat Capacity for Gas

    Thanks for the quick reply. I guess my confusion was with the appropriate definitions of the heat capacities being state variables. In my textbook the heat capacities are declared as non-state variables, and the same is said here, https://www.grc.nasa.gov/www/k-12/airplane/specheat.html However...
  7. M

    Specific Heat Capacity for Gas

    So I have a question regarding the specific heat capacities in thermodynamics. In general the specific heat capacities for a gas (or gas mixture in thermo-chemical equilibrium) can be expressed as, ## c_p = \left(\frac{\partial h}{\partial T}\right)_p \qquad \text{and} \qquad c_v=...
  8. M

    How to convert Euler Equations to Lagrangian Form?

    So I played around with the equations and with the aid of my fluid mechanics book I figured it out. One must realize that the Lagrangian time derivative is related to the Eulerian time derivative by, \left(\frac{\partial f}{\partial t}\right)_L = \left(\frac{\partial f}{\partial t}\right)_E +...
  9. M

    How to convert Euler Equations to Lagrangian Form?

    I am not entirely sure how to convert the conservation of mass and momentum equations into the Lagrangian form using the mass coordinate h. The one dimensional Euler equations given by, \frac{\partial \rho}{\partial t} + u\frac{\partial \rho}{\partial x} + \rho\frac{\partial u}{\partial x} = 0...
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