Wastewater from a small town is treated in a trickling filter which is preceded by a screen, sand-removal and primary clarification. The maximum hydraulic capacity, or peak flow, of the treatment plant is 1,500 m³/h. The dry weather flow (Qdwf) amounts 7,500 m³/day, with a BOD concentration of 300 mg/l.
The maximum scouring velocity or slip velocity is 0.3 m/s and the maximum surface load or Hazen velocity is 40 m/h.
Calculate the liquid velocity during Qdwf (in m/s) in the channel.
To calculate the liquid velocity during the dry weather flow (Qdwf) in the channel, we can use the formula for channel flow:
Q = A * V
Where:
Q = Flow rate (m³/s)
A = Cross-sectional area of the channel (m²)
V = Velocity of the liquid in the channel (m/s)
First, let's convert the dry weather flow (Qdwf) from m³/day to m³/s:
Qdwf = 7,500 m³/day
= 7,500 m³/day * (1 day / 24 hours) * (1 hour / 60 minutes) * (1 minute / 60 seconds)
= 5.21 m³/s
Next, we need to determine the cross-sectional area of the channel (A).
Assuming the channel is rectangular, we can use the formula for the area of a rectangle:
A = Width * Depth
To determine the values for width and depth, we need to consider the maximum surface load or Hazen velocity. The Hazen velocity (Vh) is given as 40 m/h. We know that:
1 m/h = 0.2778 m/s
So, the maximum Hazen velocity is:
Vh = 40 m/h * 0.2778 m/s
= 11.11 m/s
The maximum Hazen velocity represents the maximum allowable velocity in the channel. To determine the cross-sectional area, we need to find the width. We can assume the depth of the channel is 1 meter (m).
A = (Qdwf / Vh) * Depth
= (5.21 m³/s / 11.11 m/s) * 1 m
= 0.47 m²
Now that we have the cross-sectional area (A) of the channel, we can calculate the liquid velocity during the Qdwf. Rearranging the formula for channel flow (Q = A * V), we have:
V = Q / A
= 5.21 m³/s / 0.47 m²
= 11.06 m/s
So, the liquid velocity during the dry weather flow (Qdwf) in the channel is approximately 11.06 m/s.