Effect of sewer size on flow velocity and deposition: Which statement is correct for gravity sewers carrying the same discharge?

Introduction / Context:
Gravity sewer hydraulics often involve partially full flow. For a fixed discharge and slope, cross-sectional size influences flow area, hydraulic radius, and consequently velocity. Understanding this relationship helps avoid deposition problems.

Given Data / Assumptions:

• Compare sewers under the same slope and the same discharge.
• Manning equation applies: V ∝ (R^(2/3) * S^(1/2)) / n, and Q = A * V.

Concept / Approach:
For a given Q, increasing size generally increases area A. If slope and roughness are unchanged, the needed velocity V to carry Q reduces because Q = A * V. Lower V increases the risk of deposition unless the sewer runs at a depth that optimizes hydraulic radius and maintains self-cleansing conditions.

Step-by-Step Solution:
1) Hold Q and S constant; increase diameter.2) Since A increases with size, V = Q / A decreases.3) Lower V makes it harder to keep solids in suspension, promoting deposition if below self-cleansing velocity.4) Therefore, a larger sewer for the same flow tends to have lower velocity and greater deposition risk.

Verification / Alternative check:
Design guidelines always check for minimum self-cleansing velocities; oversizing pipes is discouraged precisely because of the velocity drop at low flows.

Why Other Options Are Wrong:
Option A: Velocity does not increase merely due to larger size under the same Q.Option B: Smaller size generally increases velocity for the same Q (within capacity limits).Option C: Larger size does not guarantee freedom from deposition; it often worsens it at low flow.Option E: Velocity depends on both area and hydraulic radius; it is not independent of size.

Common Pitfalls:

• Equating larger size with better performance without checking velocity.
• Ignoring partial-flow hydraulics and self-cleansing criteria.

Final Answer:
For a larger sewer carrying the same flow and slope, velocity tends to be lower, encouraging deposition.