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Which of the following sewer sections has the least perimeter for a given cross- sectional area?
Rectangular sewer
Egg-shaped sewer
Parabolic sewer
Circular sewer
Circular sewer
Among all geometric shapes of equal cross-sectional area, the circle has the minimum perimeter. In sewer design, this property minimizes the material required for the pipe wall and maximizes hydraulic efficiency by reducing frictional resistance.
CPHEEO Manual on Sewerage and Sewage Treatment
Among all geometric shapes of equal cross-sectional area, the circle has the minimum perimeter. In sewer design, this property minimizes the material required for the pipe wall and maximizes hydraulic efficiency by reducing frictional resistance.
P=╧АD тАФ Perimeter of a circular sewer
A=4╧АD2тАЛ тАФ Area of a circular sewer
R=4DтАЛ тАФ Hydraulic radius for a full circular sewer
The hydraulic efficiency of a sewer is determined by the hydraulic radius, defined as R=PAтАЛ, where A is the area and P is the wetted perimeter. Since the flow velocity V is directly proportional to R via the Manning or Chezy equation, minimizing the perimeter P for a given A results in a larger R and consequently higher flow velocity and self-cleansing capacity.
Circular sections provide the most efficient hydraulic performance due to the minimum wetted perimeter.
Higher hydraulic radius R leads to better self-cleansing properties.
Circular pipes are structurally superior for resisting external earth pressures.
Circular sections are the most economical to manufacture and install.
Minimal material consumption due to least perimeter
Excellent structural stability under external load
Higher velocity at partial depths compared to non-circular shapes
Ease of manufacturing and standardized installation
Fixed capacity may be problematic for highly variable flow conditions
Difficult to maintain self-cleansing velocity during extremely low flow
General municipal sewerage systems
Stormwater drains
Small to medium scale drainage networks
Egg-shaped sewers are used in combined sewerage systems where flow fluctuates significantly, providing better velocity at low flows.
Parabolic sewers are rarely used in practice due to construction difficulties.
Rectangular sewers are typically reserved for large, open-top storm drains or specific site constraints.
D is correct тАФ The circular section provides the minimum wetted perimeter for a given cross-sectional area, resulting in maximum hydraulic efficiency.
Remember that while circular sections are most efficient for gravity flow, egg-shaped sections are the preferred alternative when dealing with highly variable discharge to maintain velocity.
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