General Pressure Drop in One-Dimensional Flow

The role of the pressure gradient may be shown in the momentum equation of a gas-solid mixture. Consider a steady pipe flow without mass transfer and with negligible interparticle collisions. From Eq. (5.170), the momentum equations for the gas and particle phases can be given by 

For one-dimensional horizontal pipe flows without electrostatic effects, using Gauss s theorem, Eq. (11.5) yields 

---