CONSERVATION: MASS, MOMENTUM, AND ENERGY BALANCES - Biomass as a Sustainable Energy Source for the Future - page 92

3.5
3.0
2.5

2.0
1.5

1.0

0.5
0

0 0.05 0.10 0.15 0.20 0.25

y (m)

FIGURE 3.5 Velocity in x-direction as a function of the liquid height y.

Boundary conditions: y = H, and then τ y = 0 and thus

τ y = d p

d p
dx H

dx y

−

Now, as the liquid is Newtonian and given the boundary condition y = 0, v x =0

s −1 (no slip condition at the bottom of the duct), it follows that m

1
2

d p

dx y 2 + 1

d p
dx Hy

v x = −

η η

s −1 ].
A sketch of the velocity profile in y-direction is given in Figure 3.5.

Check whether the units of the right-hand side terms result in [m

CHAPTER SUMMARY AND STUDY GUIDE

This chapter deals with the formulation of mass, species, energy, and momentum bal-
ances. Setting up these equations for closed and open-flow systems and simplifying
them as much as possible are a prerequisite for understanding any bioenergy conver-
sion system.

KEY CONCEPTS

Systems: open and closed
Balances: mass, energy (both nonreaction and reaction systems), and momentum.
Microscopic versus macroscopic balances (differential vs. control volume approach)
Chemical conversion, selectivity, and yield