Let us consider the steady isothermal motion of a stream of material particles and air in a straight chute of the uniform cross-section area Sch. To this effect, at x distance to the chute inlet (Figure 3.1), we select a unit prism of ∆x length, the lateral faces of which are the chute walls. The coordinates’ origin is placed in the entry section; the X-axis is directed along the chute centerline toward the bulk material particle motion. Without pulsation, the equations for component mass ow rates will appear as:
G v dS Sch
1 1 1 1= ∫ β ρ , (3.1) G v dS
2 2 2 2= ∫ β ρ . (3.2) The momentum conservation equation for the material and air conned in the selected element ∆ ∆x S Vch ch⋅ = projected on the chute centerline will appear as follows:
β ρ β ρ β1 1 1 1 1 1 1 1v v dS M dV V RdV S pVch ch
∫ ∫ = −∆Vch∫ , (3.3)
∫ ∫ = + ∏ + ∫∫
where S Vch∆ is the selected element surface ∆Vch; and ∏2 is OX-projection of surface forces.