1.1. In Example 1.1: (a) Estimate the pressure drop required. (b) Estimate the pumping power required. See any fluid mechanics textbook for methods of making these estimates. Eyample 1.1. The area of the Los Angeles basin is 4083 square miles. The heavily nolluted air layer is assumed to be 2000 ft thick on average. One solution to Los Angeles' problems would be to pump this contaminated air away. Suppose that we wish to pump out the Los Angeles basin every day and that the air must be purnped 50 miles to the desert near Palm Springs. (We assume the residents of Palm Springs won't complain.) Assume also that the average velocity in the pipe is 40 ft/s. Estimate the required pipe diameter. The flow rate required is АН 4083 mi? 2000 ft (5280 ft/mi)? ft3 2.63 10° At 24 h 3600 s/h = 7.46 · 107 and the required pipe diameter is 4Q D = 4 2.63 10° ft/s = 9158 ft 2791 m I. 40 ft/s This is about three times the height of the tallest man-made structure, and far beyond our current structural engineering capabilities. Similar calculations (Problem 1.1) show that the power required to drive the flow exceeds the amount of electrical power generated in the Los Angeles basin. We are unlikely to solve our air pollution problems by pumping away the polluted air, although this solution is still frequently proposed. Instead, we must deal with those problems by reducing emissions, the principal subject of the rest of this book.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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For part (a), use conservation of energy equation (Bernoulli equation with losses) and assume the blower is just outside the control volume. Assume loss coefficients of 0.5 and 1.0 for entrance and exit, and that a plastic pipe is used (roughness = 0). Use the Colebrook or Haaland equation to approximate the friction factor. Also assume that the sum of the static pressure head and elevation head doesn't change significantly between the entrance and exit. In other words, although the elevation head will increase, the pressure head will decrease to compensate. This assumes the atmospheric pressure change is γ*Δz, which is a decent estimate for elevation changes less than ~1000 ft or so).
- For part (b), use textbook equation 1.4 and assume a 100% efficient blower. Also, compare the power needed to power the blower with the world's largest non-hydro power plant in the world.
https://en.wikipedia.org/wiki/List_of_largest_power_stations_in_the_world#Top_20_largest_power_producing_facilities

1.1. In Example 1.1:
(a) Estimate the pressure drop required.
(b) Estimate the pumping power required.
See any fluid mechanics textbook for methods of making these estimates.
Evample 1.1. The area of the Los Angeles basin is 4083 square miles. The heavily
nolluted air layer is assumed to be 2000 ft thick on average. One solution to Los
Angeles' problems would be to pump this contaminated air away. Suppose that we
wish to pump out the Los Angeles basin every day and that the air must be pumped
50 miles to the desert near Palm Springs. (We assume the residents of Palm Springs
won't complain.) Assume also that the average velocity in the pipe is 40 ft/s. Estimate
the required pipe diameter.
The flow rate required is
АН
4083 mi? · 2000 ft (5280 ft/mi)?
ft3
At
2.63 · 10°
%3D
24 h
3600 s/h
3
m
= 7.46 · 107
and the required pipe diameter is
4Q
4 2.63 10° ft/s
D =
= 9158 ft = 2791 m
JI 40 ft/s
This is about three times the height of the tallest man-made structure, and far
beyond our current structural engineering capabilities. Similar calculations (Problem
1.1) show that the power required to drive the flow exceeds the amount of electrical
power generated in the Los Angeles basin. We are unlikely to solve our air pollution
problems by pumping away the polluted air, although this solution is still frequently
proposed. Instead, we must deal with those problems by reducing emissions, the
principal subject of the rest of this book.

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