Statistics for Environmental Engineers

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The data come from a quiescent batch settling test. At the beginning of the test, the concentration is uniform over the depth of the test settling column. The mass of solids in the column initially is M = C0ZA, where C0 is the initial concentration (g/m3), Z is the water depth in the settling column (m), and A is the cross-sectional area of the column (m ). This is shown in the left-hand panel of Figure 38.1.

After settling has progressed for time t, the concentration near the bottom of the column has increased relative to the concentration at the top to give a solids concentration profile that is a function of depth at any time t. The mass of solids remaining above depth z is M = AjC(z, t)dz. The total mass of solids in the column is still M = C0ZA. This is shown in the right-hand panel of Figure 38.1.

M = C0ZA





Solids profile at settling time t = 0

M = A” C(z, t) dz

Solids profile at к settling time t




0 C( z, t)

0    C 0

FIGURE 38.1 Solids concentration as a function of depth at time. The initial condition (t = 0) is shown on the left. The condition at time t is shown on the right.

The fraction of solids removed in a settling tank at any depth z, that has a detention time t, is estimated as:

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