Library / Hydraulics, open channels and fluid power / HYD-26
Hydraulics, open channels and fluid power
Specific energy in a rectangular channel
Energy per unit weight measured from the channel bed, for flow per unit width q at depth y in a rectangular channel with hydrostatic pressure and unit velocity coefficient.
- Ref
- HYD-26
- Rev
- v1
- Field
- Hydraulics, open channels and fluid power
- Result
- E [m]
Specific energy is the energy per unit weight relative to the channel bed, E = y + V²/(2g). With q = V y, it becomes E = y + q²/(2g y²). For a given q there are two depths with the same energy, one subcritical and one supercritical, and a minimum E at the critical depth. It assumes a mild slope, hydrostatic pressure and unit velocity coefficient.
Energy per unit weight measured from the channel bed, for flow per unit width q at depth y in a rectangular channel with hydrostatic pressure and unit velocity coefficient.
Calculator
- Mean velocity, q/y3 m/s
- Froude number, q/(y√(g y))1.355
- Velocity head, q²/(2g y²)0.4587 m
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- At 0.5 m depth with 1.5 m²/s the specific energy is 0.9587 m, with a Froude number of 1.35.
- The flow is supercritical (Fr > 1): the depth is below critical, and the energy would rise if the depth fell further.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| q Discharge per unit width | 0.01 to 50 m²/s | 0.5 | 510.2 | 509.7 | +10% | +10 % |
| y Water depth | 0.02 to 10 m | 0.9295 | 286.7 | 285.8 | +10% | −3.09 % |
| g Gravitational acceleration | 1 to 30 m/s² | 0.65 | 5 | 4.35 | +10% | −4.35 % |
Sweep of Water depth
| Water depth (m) | Specific energy (m) |
|---|---|
| 0.02 | 286.7 |
| 1.268 | 1.339 |
| 2.515 | 2.533 |
| 3.763 | 3.771 |
| 5.01 | 5.015 |
| 6.258 | 6.26 |
| 7.505 | 7.507 |
| 8.752 | 8.754 |
| 10 | 10 |
Sweep one variable
Variables and how each one contributes
Specific energy
What the equation gives you. Everything else feeds it.
Water depth
The water depth, in m. Changes the energy, in opposite directions on the two sides of the critical depth. Raising it by 10 % (to 0.55) moves the result by −3.09 %, from 0.9587 to 0.9291 m.
Discharge per unit width
The discharge per unit width, in m²/s. A larger flow raises the velocity head and so the energy. Raising it by 10 % (to 1.65) moves the result by +10 %, from 0.9587 to 1.055 m.
Gravitational acceleration
The gravitational acceleration, in m/s². Lowers the velocity head in inverse proportion. Raising it by 10 % (to 10.79) moves the result by −4.35 %, from 0.9587 to 0.917 m.
Worked example with the values above
- Velocity: q/y = 1.5 / 0.5 = 3 m/s.
- Velocity head: 3² / (2 × 9.81) = 0.45872 m.
- E = 0.5 + 0.45872 = 0.95872 m.
Assumptions and limits
- A prismatic rectangular channel with hydrostatic pressure and a uniform velocity profile.
- For jumps: a horizontal channel, negligible friction across the jump and momentum coefficient 1.
Common mistakes
- Using total discharge where discharge per unit width is needed.
- Applying the jump relation when Fr₁ is below 1, where no jump forms.
- Measuring the energy from the wrong datum.
Statistics and uncertainty
Depths near the critical depth are very sensitive: a small change in energy gives a large change in depth. Jump relations are also sensitive to the upstream Froude number, so errors in the measured depth and discharge matter.
Where it is used
- Locating control sections and finding whether flow is subcritical or supercritical.
- Sizing stilling basins and tracing backwater and drawdown curves.
Maths you need
- Froude number: Fr = V/√(g D), the ratio of flow speed to wave speed
- Specific energy: energy per unit weight measured from the bed
- Momentum conservation: force balance across the jump