2. Determine the surface area of a primary settling tank sized to handle a maximum hourly flow of 0.570 m3/s at an overflow rate of 60.0 m/d. If the effective tank depth is 3.0 m, what is the effective theoretical detention time

The surface area of the primary settling tank is 0.0095 m^2.

The effective theoretical detention time is 0.05 s.

Explanation:

The surface area of the tank is calculated by dividing the volumetric flow rate by the overflow rate.

Volumetric flow rate = 0.570 m^3/s

Overflow rate = 60 m/s

Surface area = 0.570 m^3/s : 60 m/s = 0.0095 m^2

Detention time is calculated by dividing the volume of the tank by the its volumetric flow rate

Volume of the tank = surface area * depth = 0.0095 m^2 * 3 m = 0.0285 m^3

Detention time = 0.0285 m^3 : 0.570 m^3/s = 0.05 s

Given Information:

overflow rate = v = 60 m/d

volumetric flow rate = Q = 0.570 m³/s

depth of tank = h = 3 m

Required Information:

detention time = θ = ?

Answer:

detention time = θ = 3 days or 1.2 hours or 72 minutes or 4.32x10³ seconds

Explanation:

We know that the detention time is given by

θ = V/Q

Where V is the volume of tank and Q is the volumetric flow rate of the tank.

To find out the volume of tank, first we have to find the surface area of the tank.

As we know the volumetric flow rate is given by

Q = Av

A = Q/v

Where A is the surface area of tank and v is the over flow rate and Q is the volumetric flow rate.

First convert the overflow rate from m/d into m/s

1 day has 24 hours, each hour has 60 minutes, each minute has 60 seconds.

v = 60 / (24*60*60)

v = 6.94x10⁻⁴ m/s

A = Q/v

A = 0.570/6.94x10⁻⁴

A = 821.32 m²

The volume of tank is given by

V = A*h

V = 821.32*3

V = 2463.97 m³

Finally, the detention time is

θ = V/Q

θ = 2463.97/0.570

Detention time in seconds:

θ = 4.32x10³ seconds

Detention time in minutes:

θ = 4.32x10³/60 = 72 minutes

Detention time in hours:

θ = 72/60 = 1.2 hours

Detention time in days:

θ = 1.2/24 = 0.05 days