WASTEWATER TREATMENT –I

SOLUTION

1.      Design a grit chamber of rectangular cross-section.  Following information is provided: Flow (Q): 50 MLD; Minimum particle diameter to be completely removed (d) = 0.20 mm; Specific Gravity of particles (Ss): 2.65; Horizontal mean flow velocity (V): 0.30 m/s; Theoretical depth (D): 1.0 m; Calculate the dimensions and slope of the grit chamber. While designing the actual grit chamber, add 25 percent to the depth for grit collection, and 0.25m freeboard.  Also add 50 percent to the theoretically calculated length.

Stoke’s law:           ;     Manning’s Formula:

Dynamic viscosity (m) = 1.002 N.s/m2.  Density of water (r) = 1000 Kg/m3, Density of particles (rs) = Ss.r; g = 9.81 m/s2; S is the slope of the chamber expressed in m/m; Value of Manning’s ‘n’ is 0.20; R (= A/P) is the hydraulic radius of the channel in m, where A is the flow area in m2 and P the wetted perimeter in m.                                (6)

Using Stoke’s Law:

Theoretical depth of flow (D) = 1 m

Required detention time (T) =  = 1000 / 35.89 = 27.86 s

As per design conventions, provide a detention time of 45 s

Velocity of Flow (V) = 0.30 m/s

Theoretical length of channel (L) = V.T = 0.30 x 45 = 13.5 m

Flow (Q) = 50 MLD = 50000 / 86400 = 0.5787 m3/s

Area of flow (A) = = 0.5787 / 0.30 =1.929 m2

Width of the Channel =  = 1.929 / 1 = 1.929 m

Whetted Perimeter (P) = (1 + 1.929 + 1) = 3.929 m

Using Manning’s equation:

,          Where, S = Channel slope, m/m

Using this equation, S was calculated to be 9.29 x 10-5

Thus,          Design Length (L’) = 1.5.(13.5) = 20.25 ~ 21 m

Design Depth (D’) = (0.25 + 1 + 0.25) = 1.5 m

Slope = 1.95 mm / 21 m

2.      Derive the expression:         , which relates microbial growth with substrate utilization, from first principles.  Where, m is the specific growth rate (per day), q is the specific substrate utilization rate (per d), YT is the ‘yield coefficient’ (mg/mg) and Kd is the endogenous coefficient (per day).                                  (4)

Microbial growth can be represented by the following expression:

Where,

Dividing by X, the biomass concentration:

, Where,

Also,                    and,

Thus,

Substituting in the original equation: