Downstream Water Level Calculator

Example data table

Formula used

This calculator estimates the downstream water surface elevation by subtracting energy losses along a reach:

• Velocity: V = Q / A
• Hydraulic radius: R = A / P
• Friction slope (Manning): Sf = (n² Q²) / (A² R^(4/3))
• Friction loss: hf = Sf × L
• Local loss: hl = K × V² / (2g)
• Downstream WSE: WSE2 = (Z1 + y1) − (hf + hl)
• Downstream bed elevation: Z2 = Z1 − (S0 × L)
• Downstream depth: y2 = WSE2 − Z2

This is a practical reach-loss estimate. If tailwater is higher than the computed level, backwater can control the downstream depth.

How to use this calculator

1. Select a unit system and a section shape.
2. Enter discharge, roughness, reach length, and bed slope.
3. Provide upstream bed elevation and upstream depth.
4. Fill geometry fields relevant to the chosen shape.
5. Optionally add a local loss coefficient and known tailwater elevation.
6. Click Calculate to show results above the form.
7. Use the CSV or PDF buttons to export the computed report.

Downstream level intent in temporary works

Downstream water level estimates support diversion planning, outlet sizing, and erosion protection during construction. The reported downstream water surface elevation (WSE2) helps verify freeboard, avoid overtopping, and evaluate whether a discharge point will stay stable under design flow. Use it for short reaches where losses dominate and where rapid scenario testing is valuable for field decisions.

Inputs that drive reach losses

The calculator combines friction loss and a local loss term. Friction is driven by discharge, roughness, hydraulic radius, and reach length; local losses represent transitions, bends, culvert outlets, energy dissipators, or temporary structures. When geometry changes, the flow area changes, which shifts velocity and loss magnitude. Keep units consistent and confirm that the selected section shape matches the actual conveyance.

Interpreting computed WSE2 and y2

WSE2 is the estimated water surface at the reach end after subtracting losses from the upstream water surface. The downstream bed elevation (Z2) is based on bed slope and length, and downstream depth (y2) is computed as WSE2 minus Z2. If y2 becomes small or negative, tailwater or controls downstream may govern. Enter a known tailwater WSE to quickly flag potential backwater conditions.

Example scenario for site drainage

For a temporary rectangular channel carrying Q = 2.50 with n = 0.015, length L = 150, and bed slope S0 = 0.001, the calculator typically returns a downstream WSE close to the upstream level minus modest losses. Use the example below to confirm that your setup and units are correct.

Compare the computed WSE2 against a surveyed tailwater elevation to determine whether the reach will experience backwater.

Common checks before issuing reports

Validate roughness against lining type, confirm geometry from as-built dimensions, and test sensitivity by varying n and K. Review velocity to confirm acceptable limits for soil and lining, then verify that downstream depth aligns with any controlling structure. Document assumptions, especially when using short-term, temporary conveyance in active work zones.

FAQs

1) What does the downstream water surface elevation represent?

It is the estimated water surface at the reach end after subtracting friction and local losses from the upstream water surface. It is reported in the same length units as your elevation inputs.

2) When should I enter a tailwater elevation?

Enter tailwater when the outlet discharges into a canal, river, pond, or structure that can control the water level. The comparison highlights whether backwater may raise the downstream level above the computed free-outfall estimate.

3) Why is my downstream depth negative?

A negative y2 indicates that the calculated downstream water surface falls below the computed bed elevation at the reach end. Check geometry, slope direction, units, and whether tailwater or a control structure governs the profile.

4) How should I choose the roughness coefficient?

Select n based on lining and surface condition: smooth pipe, concrete, riprap, or vegetated channels differ significantly. Use conservative values for temporary works, and re-check results with a plausible range to understand sensitivity.

5) What does the local loss coefficient cover?

K represents additional losses from transitions, bends, entrance and exit effects, outlet structures, or energy dissipators. If you do not have detailed coefficients, start with a small allowance and adjust based on expected turbulence and fittings.

6) Can I use this for long rivers or complex backwater profiles?

This tool provides a practical reach-loss estimate. For long systems, variable geometry, or strong backwater effects, use a dedicated gradually varied flow model and surveyed boundary conditions to capture profile changes more accurately.

7) Which output should I put in a field report?

Report WSE2, downstream depth y2, velocity, and the assumed inputs (Q, n, L, slope, K, and geometry). If tailwater is provided, also report the comparison statement so reviewers understand whether backwater is expected.