# 3.23: Untitled Page 49

## Chapter 3

available at http://www.monolake.org, and another web site located at

http://www.worldsat.ca/image_gallery/aral_sea.html will provide information about a similar problem in the Aral Sea. The demise of Mono Lake was apparently secured in 1970 with the completion of a second barrel of the already-existing Los Angeles aqueduct from the southern Owens Valley. This allowed for a 50% increase in the flow, and most of this water was supplied by increased diversions from the Mono Basin. To be definitive, assume that the export of water from the Mono Basin was increased to 110,000 acre‐feet per year in 1970.

Given the conversion factor

3

1 acre‐foot  43,560 ft

one finds that

9

3

4 . 79  10 ft of water are being removed from the Mono Basin each year. In 1970 the surface area of the lake was 6

2

185  10 m and the

maximum depth was measured as 50 m. If the lake is assumed to be circular with the configuration illustrated in Figure 3.9a we can deduce that the tangent

of  is given by

3

tan  (

h t) r( t)  6 52

.

10 .

Figure 3.9a. Assumed Mono Lake profile

In this problem you are asked to determine the final or steady‐state condition of the lake, taking into account the flow of water to Los Angeles. The control volume to be used in this analysis is illustrated in Figure 3.9b and one needs to know the rate of evaporation in order to solve this problem. The rate of evaporation from the lake depends on a number of factors such as water temperature, salt concentration, humidity and wind velocity, and it varies considerably throughout the year. It appears that the rate of evaporation from

Single component systems

83

Mono Lake is about 36 inches per year. This represents a convenience unit and in order to determine the actual mass flux, we write

mass flow rate owing

surface area

m

 

  

 

2

H2O

 to evaporation

 of the lake 

in which  is the convenience unit of inches per year. This parameter should be thought of as an average value for the entire lake, and for this problem  should be treated as a constant.

Figure 3.9b. Fixed control volume for the steady‐state analysis of Mono Lake Section 3.3

3‐10. A cylindrical tank having a diameter of 100 ft is used to store water for distribution to a suburban neighborhood. The average water consumption (stream 2 in Figure 3.10) during pre‐dawn hours (midnight to 6 AM) is 100 m3/h.

From 6 AM to 10 AM the average water consumption increases to 500 m3/h, and then diminishes to 300 m3/hr from 10 AM to 5 PM. During the night hours, from 5 PM to midnight, the average consumption falls even lower to 200 m3/h. The tank is replenished using a line (stream 1) that delivers water steadily into the tank at a rate of 1,120 gal/min. Assuming that the level of the tank at midnight is 3 m, plot the average level of the tank for a 24 hour period.

84