Calculation Result
| Item | Value | Unit |
|---|
Calculator Inputs
Example Data Table
| Case | Diameter | Upstream Depth | Flow Rate | Tailwater | Use |
|---|---|---|---|---|---|
| Storm pipe outlet | 1.20 m | 0.22 m | 1.35 m³/s | 0.75 m | Check if a jump forms inside the conduit. |
| Culvert barrel | 4.00 ft | 0.80 ft | 46.00 cfs | 2.50 ft | Compare sequent depth with available tailwater. |
| Drainage pipe | 0.90 m | 0.18 m | 0.72 m³/s | 0.52 m | Estimate energy loss and jump length. |
Formula Used
Circular segment area:
A = r² cos⁻¹((r - y) / r) - (r - y) √(2ry - y²)
Top width:
T = 2 √(2ry - y²)
Hydraulic depth and Froude number:
Dₕ = A / T and Fr = V / √(gDₕ), where V = Q / A.
Specific force for a circular section:
M = Q² / (gA) + A z̄
Here, z̄ is the distance from the water surface to the centroid of the wetted area.
Sequent depth:
M(y₂) = M(y₁)
Specific energy loss:
ΔE = (y₁ + V₁² / 2g) - (y₂ + V₂² / 2g)
Estimated jump length:
Lⱼ = K(y₂ - y₁)
This tool assumes open-channel flow in a partially full circular pipe. It is not for pressurized full-pipe flow.
How To Use This Calculator
- Select the unit system.
- Enter the pipe inside diameter.
- Enter the upstream water depth before the jump.
- Enter the flow rate through the pipe.
- Add tailwater depth if you want a support check.
- Keep the default gravity value, or edit it for special cases.
- Choose a jump length factor for conservative planning.
- Press the calculate button.
- Review Froude number, sequent depth, energy loss, and warnings.
- Download the CSV or PDF report for records.
Understanding Hydraulic Jump In Pipe Flow
A hydraulic jump is a sudden rise in water depth. It happens when fast, shallow flow changes into slower, deeper flow. In a pipe, this condition is important when the conduit is not running full. Designers often review it in storm drains, culverts, and outlet barrels. The jump can dissipate energy. It can also create turbulence, vibration, air entrainment, and local pressure changes.
Why The Result Matters
The most important value is the upstream Froude number. A value above one shows supercritical flow. That means a jump can form when enough downstream depth exists. The sequent depth estimates the downstream depth needed to balance momentum. If the available tailwater is lower, the jump may move downstream. If tailwater is much higher, the jump may drown and move upstream.
Pipe Shape Effects
A circular pipe is different from a rectangular channel. Area, top width, and centroid depth change with the water level. This calculator uses circular segment properties. It then solves the momentum equation to estimate the paired depth. The approach gives a better pipe check than a simple rectangular shortcut. It still assumes open-channel flow, steady discharge, and a clear free surface.
Reading The Outputs
Velocity shows how quickly water enters the jump. Energy loss estimates the head removed by turbulence. Power loss converts that head into a rate of dissipation. Jump length gives a planning distance, not an exact boundary. The pipe fill warning helps you see whether the estimated downstream depth can physically fit inside the selected diameter.
Design Use
Use the result as a screening tool during early design. Check whether the sequent depth fits inside the pipe. Review energy loss to understand outlet protection needs. Compare jump length with the space available in the barrel or downstream structure. Try several discharges, because wet weather pipes often operate over a wide range. Also compare site tailwater after storms, debris blockage, and outlet submergence. These checks reveal sensitivity before detailed modeling begins. Record the controlling case in your design notes. For final construction, confirm results with local standards, field data, and a qualified hydraulic review. Keep assumptions visible for every reported scenario.
FAQs
1. What is a hydraulic jump in a pipe?
A hydraulic jump is a rapid depth increase in partially full pipe flow. It changes supercritical flow into subcritical flow and removes energy through turbulence.
2. Can a hydraulic jump happen in a full pipe?
No. This calculator is for open-channel flow with a free surface. A full pressurized pipe needs different pressure-flow analysis methods.
3. What does Froude number mean?
Froude number compares flow velocity with wave speed. Values above one indicate supercritical flow, where a hydraulic jump can occur if tailwater supports it.
4. What is sequent depth?
Sequent depth is the downstream depth paired with the upstream depth by momentum balance. It estimates the depth after a stable jump.
5. Why does tailwater matter?
Tailwater controls where the jump forms. Low tailwater may sweep the jump downstream. High tailwater may drown it or push it upstream.
6. Is jump length exact?
No. Jump length is an estimate. It depends on turbulence, air entrainment, geometry, slope, roughness, and downstream conditions.
7. Why use circular section formulas?
A pipe has changing area and top width as water depth changes. Circular formulas give better estimates than simple rectangular assumptions.
8. Can I use the export files in reports?
Yes. The CSV and PDF downloads summarize the entered data, computed depths, energy loss, jump length, and key warnings for documentation.