**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 (S_{s}):
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/m^{2}. Density of water (r) = 1000 Kg/m^{3},
Density of particles (r_{s}) = S_{s}.r; g = 9.81 m/s^{2}; 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 m^{2}
and P the wetted perimeter in m. **(6)**

**Answer:**

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 m^{3}/s

Area of flow (A) = _{}= 0.5787 / 0.30 =1.929 m^{2}

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), Y_{T}
is the ‘yield coefficient’ (mg/mg) and K_{d}
is the endogenous coefficient (per day). **(4)**

**Answer:**

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:

_{}