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If the test is being conducted at elevation other than zero or one atmosphere of barometric pressure, the [Cos] obtained from Table 9.1 must be corrected for the pressure of the test. Thus, during the performance of the experiment, the barometric pressure at the location should be recorded. Also, the barometric pressure at the test location may be obtained using the barometric equation. This equation relates the barometric pressure Pb with altitude z in the troposphere, and from fluid mechanics, this equation is

Pb = Pbo (1-^" = 101325(1-^)981/[(2869)(00065)]

where Pbo = barometric pressure at z = 0 (= 101325 N/m ); B (the temperature lapse rate) = 0.0065° K/m for the standard atmosphere; To = temperature in °K at z = 0; g = 9.81 m/s ; and R (gas constant for air) = 286.9 N • m/kg • °K. As written, Pb has the unit of N/m . The equation assumes that the temperature varies linearly with altitude. Therefore, if the elevation where the test is conducted and the temperature at mean sea level are known, the corresponding barometric pressure can be found. Because [Cos] varies directly as the pressure and if the condition of test is at barometric pressure, the [Cos] at test conditions will be

Ps where [C0SjSp] is the [Cos] from Table 9.1 at the standard pressure of Ps = Pbo = 760 mm Hg.

Pressures corresponding to [Cos]. In sizing aerators, what pressure to use to determine [Cos] depends upon the type of aeration device used. For apron, cascade and surface aerators and for spray and plate towers, the corresponding pressure should be taken as barometric. For aerators that are submerged below the surface of water such as the bubble-diffusion and turbine type aerators, since the point of release of the air is submerged, the pressure must correspond to the average depth of submergence. If the submergence depth is Zd, the corresponding average pressure P is

where y is the specific weight of the water or the mixed liquor, in the case of the activated sludge process tank. The equation for [Cos] is then revised to

Example 9.4 An environmental engineer performs an experiment for the purpose of determining the value of ¡3 of a particular wastewater. The [Cos,J of the wastewater after shaking the jar thoroughly is 7.5 mg/L. The temperature of the wastewater is 25°C. Calculate ¡3.

Solution:

Therefore,

Example 9.5 An environmental engineer performs an experiment for the purpose of determining the value of ß of a particular wastewater in the mountains of Allegheny County, MD. On a normal day, what is the prevailing barometric pressure, if the temperature of the air on the Chesapeake Bay is 30°C?

Solution:

In Allegheny, z = 756 m above the Chesapeake Bay, consulting the county topographical map

Pb = 101325f 1 - °.0065(75;6)1526 = 92,975 N/m2 Ans b \ 30 + 273 J

Example 9.6 An activated sludge reactor is aerated using a turbine aerator located 5.5 m below the surface of the mixed liquor. What is the pressurizing pressure if the prevailing barometric pressure is 761 mm Hg and the water temperature 20°C?

Solution:

P = 0.761 (13.6)(1000)(9.81 ) + (5j5](997)(9.81) = 128, 426.14 N/m2 Ans

Example 9.7 An activated sludge reactor is aerated using a turbine aerator located 5.5 m below the surface of the mixed liquor. What is [Cos] if the prevailing barometric pressure is 761 mm Hg and the water temperature 20°C?

Solution: From the previous example, P = 128,426.14 N/m . From Table 9.1, [Cos] = 9.2 mg/L at 20°C and 1 atm pressure.

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