EngiMetric Arena / Engineering Trade-off
Choose a gravity pipe diameter that keeps velocity in range
Competency Constraints and trade-offs primary Quantitative reasoning supporting
What you should take away: Evaluate a pipe diameter against velocity and head-loss criteria, and recognise that a range of standard sizes can satisfy the same design.
The situation
What is happening
A gravity sewer carries 1,260 m3/h (350 L/s) over a 250 m reach at a Hazen-Williams C of 130. The project requires a self-cleansing velocity of at least 0.75 m/s, a maximum velocity of 1.5 m/s, and a head loss no greater than 1.0 m per 100 m. Specify a standard diameter from 500, 600, 700 or 800 mm.
Given
| Quantity | Value | Unit | Note |
|---|---|---|---|
| Design flow | 1 260 | m3/h | Equivalent to 350 L/s. |
| Reach length | 250 | m | Gravity section. |
| Hazen-Williams C | 130 | - | Pipe roughness coefficient. |
| Minimum velocity | 0.75 | m/s | Self-cleansing limit. |
| Maximum velocity | 1.5 | m/s | Scour limit. |
| Maximum head loss | 1.0 | m/100 m | Hydraulic gradient limit. |
Assumptions this challenge makes
- The pipe runs full at the design flow.
- Hazen-Williams friction is used, with the stated C.
- Only the four listed standard diameters are available for this reach.
Limits this decision must satisfy
| Limit | Requirement | If it is breached |
|---|---|---|
| Velocity | not more than 1.5 and not less than 0.75 m/s | Below the minimum the pipe silts; above the maximum the invert and joints are exposed to scour. |
| Head loss | not more than 1 m/100 m | Above the hydraulic-gradient limit the reach needs a steeper fall or a larger diameter. |
Choose one of 500, 600, 700 or 800 mm. More than one standard size satisfies the stated limits.
Your call
Your answer
Hints
- Velocity is flow divided by area. A smaller diameter raises velocity; a larger one lowers it.
- Check the smallest and largest candidates first. One may scour, the other may fall below the self-cleansing velocity.
- Head loss is a separate check from velocity. A diameter that passes one can still fail the other.
Your answer Engine result
Where that comes from
Each limit, checked
Why
- At 600 mm the velocity is about 1.24 m/s and the head loss about 0.224 m/100 m. Both limits are satisfied.
- At 700 mm the velocity is about 0.91 m/s and the head loss about 0.106 m/100 m. Both limits are satisfied as well.
- At 500 mm the velocity rises to about 1.78 m/s, above the 1.5 m/s scour limit. At 800 mm it falls to about 0.70 m/s, below the 0.75 m/s self-cleansing limit.
- So 600 mm and 700 mm are both defensible. The smaller pipe is cheaper and easier to lay but runs faster; the larger pipe has more hydraulic margin but higher capital cost.
- The design choice between them depends on cost, available fall and future flows, not on a single hydraulic optimum.
What this challenge does not establish
- The pipe is assumed to run full; part-full flow and the actual depth-discharge relationship are not modelled.
- Hazen-Williams is an empirical friction model; the stated C is an assumption for this pipe material and condition.
- Sediment transport, minimum shear stress and surcharge conditions are not assessed.
- Only four standard diameters are considered; the actual catalogue and constructability may differ.