13.7.1.2: Acceleration Pressure Loss
- Page ID
- 878
The acceleration pressure loss can be estimated by
\[
-\left. \dfrac{dP}{dx} \right|_a = \dot{m} \, \dfrac{dU_m} {dx}
\label{phase:eq:accPL}
\]
\[
-\left. \dfrac{dP}{dx} \right|_a =
\dot{m}\, \dfrac{d} {dx} \left( \cfrac{\dot{m}} {A\,\rho_m} \right)
\label{phase:eq:accPLa}
\]
Or in an explicit way equation (36) becomes
\[
-\left. \dfrac{dP}{dx} \right|_a =
{\dot{m}}^2 \left[
\overbrace{\dfrac{1}{A} \, \dfrac{d} {dx} \left( \dfrac{1} {\rho_m} \right)}
^{\text{pressure loss due to density change}} +
\overbrace{\dfrac{1}{\rho_m\,A^2} \dfrac{dA} {dx}}
^{\text{pressure loss due to area change}}
\right]
\label{phase:eq:accPLae}
\]
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 and Attributions
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.