Chapter 4 Dispersion page 4-1
Chapter 4 Dispersion
1. Xylene pollution
maximum concentration = M/
R2
c12km
c1200m
200 m
2km
c12km
130 ppm
10 41 ppm
2. Pulse of catalyst
From Fig. 4.4-3, Ez = 2.5*4172.5
0.3 = 34771.2 cm /s = 3.48 m /s
The peak width at the end of pipe is w = 4z = 4 2Ezx/v0 = 13.856 m
The distance between two pulses is x = v0*(1/30) = 1.391 m
These pulses are well overlapped and mixed.
3. Dispersion in an air-lift fermentor
This is a steady state problem. Taking mass balance at a section between z and dz,
Letting dz 0, and combining with Fick’s Law, we have
4. Running a marathon
Assuming the running time of these 3202 runners follows a normal distribution:
f(t) = 1
2 exp
– 1
2
t –
2
Because half of the runners finished in 3hr26min, thus = 3*3600+26*60 = 12360 s
And since 1/4 of the runners finished in 3hr6min, or 11160 s,
Chapter 4 Dispersion page 4-2
11160exp
t – 12360
2dt
5. Dispersion of pheromone
The width of the pheromone “plume” is
6. Harvest ants
7. Muskrats
Based upon this model,
4Ec1
Time (yr) ln(t) Area = r2r2/4t
Chapter 4 Dispersion page 4-3
The regression analysis has R2 = 0.992, F = 127.08, thus this model is significant.
8. Backmixing in a packed-bed reactor
This is similar to chromatography. From eq. 4.4-31,
E = 32
4*3.3*0.206 = 11.754 m /min
9. Shape of moraines
The differential equation becomes
This can be solved numerically to fit experimental data, but seems to us to be curve-fitting.