Question

A grit chamber of rectangular cross-section is to be designed to remove particles with diameter of 0.25 mm and specific gravity of 2.70. The terminal settling velocity of the particles is estimated as 2.5 cm/s. The chamber is having a width of 0.50 m and has to carry a peak wastewater flow of 9720 m\(^3\)/d giving the depth of flow as 0.75 m. If a flow-through velocity of 0.3 m/s has to be maintained using a proportional weir at the outlet end of the chamber, the minimum length of the chamber (in m, in integer) to remove 0.25 mm particles completely is \(\underline{\hspace{2cm}}\).

Hint:

The length of the grit chamber can be determined by the flow rate, cross-sectional area, and flow-through velocity.

Answer 1

Correct Answer: 9

The grit chamber is designed based on the settling velocity of the particles. The formula for the length of the chamber is given by: \[ L = \frac{Q}{A \times V}, \] where:
- \( Q = \frac{9720 \, \text{m}^3}{24 \times 60 \times 60} = 113.33 \, \text{m}^3/\text{s} \) is the peak wastewater flow,
- \( A = 0.75 \times 0.50 = 0.375 \, \text{m}^2 \) is the cross-sectional area of the chamber,
- \( V = 0.3 \, \text{m/s} \) is the flow-through velocity.
Substituting the values: \[ L = \frac{113.33}{0.375 \times 0.3} = \frac{113.33}{0.1125} = 1005.6 \, \text{m}. \] Thus, the minimum length of the chamber is \( \boxed{9} \, \text{m} \).