Library / Hydraulics, open channels and fluid power / HYD-08
Hydraulics, open channels and fluid power
Kinetic-energy correction factor from sampled velocities
Kinetic-energy correction factor for a profile described by two subareas with representative velocities.
- Ref
- HYD-08
- Rev
- v1
- Field
- Hydraulics, open channels and fluid power
- Result
- α
When the velocity across a pipe is not uniform, the true kinetic energy flow exceeds that of the mean velocity by the factor α = Σ(Aᵢuᵢ³)/(A U³), with the mean U = Σ(Aᵢuᵢ)/A. A uniform profile gives α = 1, and fully developed laminar pipe flow gives 2. This calculator uses two subareas, so set one subarea to a small value to approximate a single area.
Kinetic-energy correction factor for a profile described by two subareas with representative velocities. The mean velocity U is the area-weighted mean, so a uniform profile gives 1 and a laminar pipe profile gives 2.
Calculator
- Area-weighted mean velocity, U2 m/s
- Total area2 m²
- Momentum correction factor, Σ Aᵢuᵢ²/(A U²)1.25
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.
- With velocities of 1 and 3 m/s over equal parts, the mean is 2 m/s and the kinetic energy is 1.75 times that of the mean velocity.
- The more uneven the profile, the larger α: equal velocities would give exactly 1.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| u1 Representative velocity in subarea 1 | 0.01 to 50 m/s | 1 | 3.96 | 2.96 | +10% | −6.04 % |
| u2 Representative velocity in subarea 2 | 0.01 to 50 m/s | 1.003 | 3.882 | 2.879 | +10% | +6.19 % |
| A1 Subarea 1 | 0.001 to 100 m² | 1.001 | 2.257 | 1.256 | +10% | +2.74 % |
| A2 Subarea 2 | 0.001 to 100 m² | 1.01 | 2.257 | 1.247 | +10% | −2.7 % |
Sweep of Representative velocity in subarea 2
| Representative velocity in subarea 2 (m/s) | Kinetic-energy correction factor |
|---|---|
| 0.01 | 3.882 |
| 0.029 | 3.671 |
| 0.08409 | 3.141 |
| 0.2438 | 2.109 |
| 0.7071 | 1.088 |
| 2.05 | 1.356 |
| 5.946 | 2.521 |
| 17.24 | 3.378 |
| 50 | 3.769 |
Sweep one variable
Variables and how each one contributes
Kinetic-energy correction factor
What the equation gives you. Everything else feeds it.
Subarea 1
The area of subarea 1, in m². A larger first area gives it more weight in the mean and in the cubic sum. Raising it by 10 % (to 1.1) moves the result by +2.74 %, from 1.75 to 1.798.
Subarea 2
The area of subarea 2, in m². A larger second area gives it more weight in the mean and in the cubic sum. Raising it by 10 % (to 1.1) moves the result by −2.7 %, from 1.75 to 1.703.
Representative velocity in subarea 1
The representative velocity in subarea 1, in m/s. A larger u₁ raises the spread of velocities, so α changes. Raising it by 10 % (to 1.1) moves the result by −6.04 %, from 1.75 to 1.644.
Representative velocity in subarea 2
The representative velocity in subarea 2, in m/s. A larger u₂ changes the spread of velocities, so α changes. Raising it by 10 % (to 3.3) moves the result by +6.19 %, from 1.75 to 1.858.
Worked example with the values above
- Mean velocity: (1 × 1 + 1 × 3) / 2 = 2 m/s.
- Cubic sum: Σ Aᵢuᵢ³ = 28; A U³ = 16.
- α = 1.75.
Assumptions and limits
- Steady, fully developed laminar flow of a Newtonian liquid with no slip at the walls.
- Smooth, straight geometry, and no body force other than gravity where stated.
Common mistakes
- Using the plain average of the velocities in place of the area-weighted mean.
- Using zero-area subareas.
- Using the velocity at the centre as the mean velocity.
Statistics and uncertainty
These laminar formulas are exact for their model, so the uncertainty comes from the inputs. Gap and film thickness enter with the third power, so a 1 % error in thickness gives about a 3 % error in flow.
Where it is used
- Lubrication films, coating, sealing gaps and thin-film runoff.
- Checking viscous pipe flow and wall shear from measured pressure drops.
Maths you need
- Viscosity: μ, the shear stress per unit velocity gradient
- No-slip condition: the liquid moves with the wall at the wall
- Reynolds number: the ratio of inertial to viscous forces