Pipe Area, Velocity, Slope, Friction, Manning-Style Concepts, and Travel Time
Key Takeaways
- Use Q = A x V for direct flow calculations; area must be in square feet and velocity in ft/sec when the answer is cfs.
- Gravity sewer capacity is controlled mainly by pipe diameter, slope, and roughness, with slope providing the driving head.
- Manning-style questions often test concepts: steeper slope increases velocity, rougher pipe decreases velocity, and larger hydraulic radius increases capacity.
- A common self-cleansing target is about 2 ft/sec, while a gravity sewer consistently running full suggests surcharge or downstream restriction.
- Travel time is distance divided by velocity, but the time unit must be converted from seconds to minutes or hours.
Gravity Sewer Flow Basics
Gravity sewers normally flow partly full. The pipe is not supposed to act like a pressurized force main during ordinary operation. On the exam, full-pipe or consistently high-depth conditions usually point to surcharge, inadequate capacity, a downstream obstruction, or excessive wet-weather flow.
The most direct flow equation is:
Q = A x V
Where:
- Q = flow, usually in cubic feet per second (cfs)
- A = flow area, in square feet
- V = velocity, in feet per second
If the problem asks for gpm or MGD, calculate cfs first and then convert.
Worked Example: Velocity-Area Flow
An 8-inch sewer is flowing half full. The problem gives the half-full flow area as 0.175 sq ft. The measured velocity is 2.2 ft/sec. Find flow in gpm.
- Q = A x V = 0.175 sq ft x 2.2 ft/sec = 0.385 cfs.
- Convert cfs to gpm: 0.385 x 448.8 = 173 gpm.
If the same question asks for MGD, use 1 cfs = 0.646 MGD: 0.385 x 0.646 = 0.249 MGD.
Slope Setup
Slope is rise or drop divided by horizontal distance. It may be shown as ft/ft, percent, or feet per 100 ft.
| Form | Example | Meaning |
|---|---|---|
| ft/ft | 0.004 ft/ft | 0.004 ft drop per 1 ft run |
| percent | 0.4% | 0.4 ft drop per 100 ft run |
| ft per 100 ft | 0.4 ft/100 ft | Same as 0.4% |
| ft per 1,000 ft | 4 ft/1,000 ft | Same as 0.004 ft/ft |
Worked example: A sewer drops 2.8 ft over 700 ft. Slope = 2.8 / 700 = 0.004 ft/ft = 0.4% = 0.4 ft per 100 ft.
Manning-Style Concepts
The Manning equation is commonly written for U.S. units as:
V = (1.486 / n) x R^(2/3) x S^(1/2)
Where:
- V = velocity, ft/sec
- n = Manning roughness coefficient
- R = hydraulic radius, ft
- S = slope, ft/ft
You may not need to perform a full Manning calculation on an entry-level exam, but you should understand the relationships.
| If This Changes | Hydraulic Effect |
|---|---|
| Slope increases | Velocity and capacity increase |
| Slope decreases | Velocity and capacity decrease; solids may settle |
| Pipe roughness n increases | Friction increases and velocity decreases |
| Pipe roughness n decreases | Pipe is smoother and velocity increases |
| Pipe diameter increases | Area increases and hydraulic radius generally increases |
| Pipe runs full unexpectedly | Surcharge/backwater/capacity concern |
A frequently tested target is self-cleansing velocity. About 2 ft/sec is commonly used so grit and organic solids stay moving rather than settling in the pipe.
Friction and Roughness in Plain Language
Friction is energy lost as wastewater rubs against the pipe wall, passes deposits, changes direction, or moves through rough joints. New smooth PVC has lower roughness than old deteriorated concrete, brick, or heavily tuberculated pipe. More roughness means more head loss for the same flow, or less capacity at the same slope.
Travel Time
Travel time is another distance-rate-time problem:
Travel time = distance / velocity
Use feet and ft/sec first, then convert seconds.
Example: Flow travels 1,800 ft at 2.5 ft/sec.
- Time = 1,800 ft / 2.5 ft/sec = 720 sec.
- Convert to minutes: 720 / 60 = 12 minutes.
Common trap: Do not multiply distance by velocity. Velocity already contains distance per time.
A sewer segment has a measured flow area of 0.60 sq ft and an average velocity of 2.5 ft/sec. What is the flow in gpm?
A 500-ft sewer drops 1.5 ft between manholes. What is the slope expressed as percent?
In Manning-style gravity sewer hydraulics, what is the most likely effect of heavy deposits and a rough deteriorated pipe wall?