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13.7.1.2: Acceleration Pressure Loss

  • Page ID
    1387
  • [ "article:topic" ]

    The acceleration pressure loss can be estimated by
    \[
        -\left. \dfrac{dP}{dx} \right|_a = \dot{m} \, \dfrac{dU_m} {dx}  
         \label{phase:eq:accPL}  \tag{35}
    \]
    The acceleration pressure loss (can be positive or negative) results from change of density and the change of cross section. Equation (35) can be written as
    \[
        -\left. \dfrac{dP}{dx} \right|_a =  
            \dot{m}\, \dfrac{d} {dx} \left( \cfrac{\dot{m}} {A\,\rho_m} \right)  
         \label{phase:eq:accPLa}  \tag{36}
    \]
    Or in an explicit way equation (36) becomes
    \[
        -\left. \dfrac{dP}{dx} \right|_a =  
            {\dot{m}}^2  \left[
                    \overbrace{\dfrac{1}{A} \, \dfrac{d} {dx} \left( \dfrac{1} {\rho_m} \right)}  
                        ^{\text{pressure loss due to density change}} +  
                    \overbrace{\dfrac{1}{\rho_m\,A^2} \dfrac{dA} {dx}}  
                        ^{\text{pressure loss due to area change}}  
            \right]
         \label{phase:eq:accPLae}  \tag{37}
    \]
    There are several special cases. The first case where the cross section is constant, \(\left. dA \right/ dx = 0\). In second case is where the mass flow rates of gas  and liquid is constant in which the derivative of \(X\) is zero, \(\left. dX \right/ dx = 0\). The third special case is for constant density of one phase only, \(\left. d\rho_L \right/ dx = 0\). For the last point, the private case is where densities are constant for both phases.

    Contributors

    • Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.