Rapid sand filter design – under-drain laterals: For the lateral pipes in a rapid sand filter under-drain system, the ratio of lateral length to its diameter (L/D) should not be greater than which limiting value to avoid excessive headloss and maldistribution?

Introduction / Context:
Under-drain systems in rapid sand filters distribute backwash water and collect filtered water. An appropriate geometry of laterals (length and diameter) ensures uniform velocities, acceptable headloss, and even cleaning of the bed. A practical limit on the length-to-diameter (L/D) ratio of laterals is used in design handbooks to avoid maldistribution.

Given Data / Assumptions:

• Conventional rapid sand filter with a manifold and perforated laterals.
• Backwash and filtration both pass through the under-drain.
• Headloss uniformity and velocity limits control sizing.

Concept / Approach:
As L/D increases, friction losses along the lateral cause flow to decline toward the closed end, creating uneven distribution. Design uses a maximum L/D to keep headloss variation small. A commonly taught conservative limit for many exam problems is L/D about 20 for laterals, with additional checks on orifice loss versus pipe friction loss to maintain a desired ratio (often orifice loss several times pipe friction loss).

Step-by-Step Solution:
Set design objective: maintain near-uniform discharge along lateral.Recognize that excessive L/D raises friction loss, reducing uniformity.Adopt limiting L/D value used in standard practice problems.Select the closest upper bound from choices: 20.

Verification / Alternative check:
Checking orifice headloss to pipe loss ratio and computing head distribution along the lateral with L/D = 20 typically yields acceptable uniformity (e.g., within ±10%).

Why Other Options Are Wrong:

• 10, 15: Overly restrictive; not necessary for uniformity in typical designs.
• 25: Higher L/D risks noticeable maldistribution and larger end loss.

Common Pitfalls:

• Ignoring that under-drain design must satisfy both filtration and backwash modes.
• Letting lateral spacing and perforation layout substitute for proper L/D control.

Final Answer:
20