Open Channel Flow Calculator — Manning, Weir & Culvert
Enter the channel geometry, the bed slope, and the lining — the calculator returns discharge, velocity, hydraulic radius, and the Froude number with its flow state, live on every keystroke. Weir and culvert tabs sit one click away for cross-checks.
The Open Channel Flow Calculator
Live results — nothing leaves your browser
Try a worked example
Velocity exceeds ~1.5 m/s — a typical scour threshold for earth and natural channels. Plan lining or grade control, and confirm the permissible velocity for your soil.
Flow area A (m²)
1.600
Wetted perimeter P (m)
3.600
Hydraulic radius R (m)
0.444
Top width T (m)
2.000
Hydraulic depth D (m)
0.800
D = A / T
Mean velocity V (m/s)
1.647
V = Q / A
Discharge Q
2.636 m³/s
n = 0.025 · Q = (1/n)·A·R2/3·S1/2
Froude number Fr = V / √(g·D)
0.588
Engineering-use notice
Preliminary estimates for planning and education. Stormwater, sewer, and culvert design must follow local drainage codes and a licensed civil engineer. This page explains the method so you can prepare for that conversation — it does not replace the stamped drawing.
💡 Where this fits in the toolset
This open channel flow calculator covers gravity flow, where the water finds its own depth. When your conduit runs full and pressurized, the main flow rate calculator on the homepage takes over, and the full calculator hub lists every dedicated tool — sized so one survey feeds both engines.
Open Channel vs Pressurized Pipe Flow: What Changes
In a pressurized pipe the water fills the bore completely, and a pressure gradient — supplied by a pump or an elevated tank — drives the flow. Geometry is fixed, so once you know the cross-section and the velocity, the discharge follows from Q = A·v. That is the job the homepage flow engine does: hand it a diameter and a velocity and it returns the flow, the Reynolds regime, and the friction bill.
An open channel obeys a different contract. The water touches a free surface, the driving force is gravity acting on the bed slope, and the depth is not a constant you control — it is a result the flow settles into. The same channel can carry the same discharge at two different depths, so “velocity” is a poor input: nobody hands you one in the field. What you can survey reliably is the geometry, the fall of the bed, and the lining material.
That is the gap this page fills. Where the homepage FAQ describes forward calculation from a known cross-section and a known velocity, the Manning equation replaces the velocity input with slope and roughness: you supply b, y (and z), S, and n, and the equation returns the discharge the channel will actually carry, plus the velocity and the Froude state that the flow settles to. Depth, not pressure, is the free variable — and everything downstream of that difference changes with it.
Practical consequence: a partially full pipe is an open channel. A storm sewer running half-full obeys Manning, not Darcy–Weisbach. When the water rises to the crown, the regime flips to pressurized — and the pipe sizing calculator becomes the right tool. The boundary between the two is exactly where this page warns you off (see the crown-depth branch in the SOP below).
Free surface, self-chosen depthPhoto: UnsplashHow the Manning Equation Works
Robert Manning published the form in 1889, and it has survived because it compresses a century of channel behaviour into five terms you can survey with a tape and a level. The calculator on this page evaluates it live in both unit conventions — the SI form with coefficient 1.0 and the US customary form with coefficient 1.486, which converts feet and seconds into the same physical answer:
Q = (1/n) · A · R2/3 · S1/2
US customary: Q = (1.486/n) · A(ft²) · R2/3(ft) · S1/2 → ft³/s
The Equation, Term by Term
A — flow area
The wetted cross-section. Capacity scales linearly with it, which is why doubling depth can double Q even before the shape term gets involved. For rectangular channels A = b·y; for trapezoidal A = (b + z·y)·y; for a partially full pipe the segment formula A = r²(θ − sin θ)/2 with θ = 2·acos((r−y)/r).
R — hydraulic radius (A/P)
The shape-efficiency term, raised to the 2/3 power. Water near a boundary is slowed by friction, so a section that packs its area deep — large R — moves faster than a wide, shallow one of equal area. The 2/3 exponent dampens but preserves that ranking.
S — bed slope (√)
The driving force per unit weight of water. It enters under a square root: doubling the slope multiplies Q by only √2 ≈ 1.41. Gravity is forgiving here — a survey error in S of ±10% moves Q by about ±5%, the gentlest lever in the equation.
n — roughness (1/n)
Everything the formula cannot see: lining material, weeds, silt, slumps, age. It enters inversely and linearly, which makes it the sharpest and least observable lever in the whole equation — and the reason Step 02 of the SOP below carries a data-required warning.
How Each Input Moves the Result
The levers are not equal, and knowing their ranking tells you where to spend measurement effort. Roughness passes through nearly linearly: at a fixed depth, a 20% error in n would push Q almost 20% the other way. In a real channel the depth also adjusts — a rougher bed makes the water pile up deeper, which enlarges A and R and claws some of the loss back — field comparisons put the net discharge error closer to 15% for that same 20% n mistake. The R2/3 term is the buffer, and it is also the amplifier of shape: two channels with identical areas but different shape efficiencies differ in Q by their R ratio raised to the two-thirds power.
Depth compounds because it acts on both A and R at once: P grows slower than A as y rises, so R climbs, and Q rises faster than the depth does. That is why a stage reading has to be accurate — a few centimetres of misread depth in a small channel is a double-digit Q error. Slope is the gentlest lever (square-root response), but it must be the water-surface or bed fall over a straight, uniform reach — a slope measured across an bend or a backwater pool does not describe the reach you are computing.
💡 Tip — build R into your survey: when you can choose where to measure, pick the straightest, most uniform reach and measure depth at three stations, then average. Hydraulic radius rewards uniformity; a single depth read at a scoured pool or a shoal biases both A and P in the same wrong direction.
Slope → Flow Quick Reference
Generated from the equations on this page (Manning, rectangular section) — a 1 m wide concrete-lined channel (n = 0.015) with 0.5 m of water. The same numbers reproduce in the calculator above.
| Bed slope S | Q (m³/s) | Q (ft³/s) | V (m/s) | V (ft/s) |
|---|---|---|---|---|
| 0.1% | 0.209 | 7.39 | 0.418 | 1.37 |
| 0.5% | 0.468 | 16.5 | 0.935 | 3.07 |
| 1% | 0.661 | 23.4 | 1.323 | 4.34 |
| 2% | 0.935 | 33.0 | 1.871 | 6.14 |
| 4% | 1.323 | 46.7 | 2.646 | 8.68 |
⚠️ Read the velocity column before the flow column: from S = 2% upward the lining is what keeps this channel alive. At 1.87 m/s an earth bank of the same geometry would already be eroding — a typical scour threshold for erodible channels sits near 1.5 m/s. The full formula reference for pressurized equivalents lives on the homepage formulas section.
Survey first, compute secondPhoto: UnsplashStep-by-Step: Measuring and Computing Channel Flow
Treat this as the standing procedure for the moment you are standing at a channel with a tape, a level, and this page open. Each step feeds the next, and the two places where estimates go wrong — roughness selection and flow-state verification — carry explicit warning tags. Tick the boxes as you go; the tracker keeps your place.
Measure the geometry — verify channel shape & depth
Confirm which section you actually have before touching a formula: rectangular (measure bed width b and depth y at the same station), trapezoidal (bottom width, side slope z as horizontal run per 1 vertical, depth), or circular pipe (true inside diameter — a nominal label is not a dimension — plus the depth at the centreline). Measure on a straight, uniform reach; verify the depth reading at a second station within the reach before accepting it. Record the units you surveyed in — the calculator converts, but only if you tell it the truth.
Select the Manning n — never copy it from another channel
⚠️ Do not borrow n from a neighbouring ditch, a textbook sketch, or last year’s survey without re-inspecting the lining. Roughness is condition-sensitive: weeds, silt, slumped banks, and age move n far more than material alone. A 20% error in n produces roughly a 15% error in Q — the linear 1/n pass-through is partially buffered by the R2/3 term as depth adjusts, but nothing cancels it.
Photograph the reach, derive n from the reference table below (Chow’s typical values), and — this is the backup discipline — compute the estimate twice: once with the low bound of the material’s range, once with the high bound. Quote the bracket, not a single number, whenever the lining is heterogeneous or the reach is weedy.
Compute the discharge Q
Assemble A and P from the geometry, take R = A/P, and apply Q = (1/n)·A·R2/3·S1/2 — the calculator does this live, but audit its unit convention: SI data with the 1.486 coefficient, or feet data with the 1.0 coefficient, silently inflates or deflates the answer by the 1.486 factor. Run the units check by hand once per project: if Q comes out in units of length² per second, something upstream never got converted.
Check the Froude number and the flow state
Compute top width T, hydraulic depth D = A/T, and Fr = V/√(g·D), then make the number agree with what the water is doing: subcritical reaches show ripples travelling upstream and smooth mirror surfaces; supercritical reaches show broken white water and standing waves. A computed state that contradicts the observed one means an input is wrong — usually depth or slope — and no design decision should be taken on the contradiction.
The state decides which answers the channel respects: in subcritical flow, downstream controls (a weir, a culvert entrance) set the upstream depth; in supercritical flow nothing propagates upstream and the control moves to the head of the reach. Getting this backwards inverts your whole backwater reasoning.
Cross-validate with an independent method
Convergence test: compare the Manning estimate against a physically independent reading — a weir or flume gauge, a salt-dilution slug in a small creek, a current meter traverse, or at minimum a timed float over a measured reach (correct surface-float speeds down toward the mean, ×0.8–0.9). Agreement within ±10% counts as convergence; a wider gap is not noise, it is a suspect input. Re-examine n first (Step 02’s bracket tells you how wide the honest uncertainty is), then the slope, then the depth. Only when the bracket and the independent reading still disagree should you question the section survey itself.
Branching Rules: When the Procedure Changes Course
Fr lands in 0.85–0.95
Near-critical flow makes the water surface unstable: standing waves, noisy stage readings, depths that wander minute to minute. Densify the verification — repeat the depth measurement at two stations and time-average, and treat any single reading as provisional. Design decisions made on a near-critical depth inherit its instability.
V > 1.5 m/s in an earth channel
About 1.5 m/s is the typical scour threshold for erodible linings: fine-grained earth banks start shedding sediment, beds incise, banks slump. The channel does not merely carry the flow you computed — it starts to rebuild itself until n rises and your calculation stops describing reality. Plan lining or grade control, and verify the permissible velocity for the specific soil.
y approaches the pipe crown
As y → D, top width T → 0, hydraulic depth → ∞, and the Froude number stops describing anything. The pipe is transitioning to pressurized flow and the open-channel logic is invalid beyond this point. Switch to full-pipe hydraulics — the pipe sizing calculator covers the pressurized regime with velocity and friction tools.
How to Trust the Number (Not a Mirage of It)
A computed Q can be arithmetically perfect and physically worthless — the equation faithfully amplifies whatever you fed it. Four checks separate a real discharge from a confident-looking artefact:
- Two-depth consistency. Re-measure the depth an hour later (or 20 m downstream on a uniform reach). Q should reproduce within its honest n-bracket; a large drift means the reach is not uniform or the flow is changing.
- Two-formula comparison. Where a small weir exists, compute Q from both the rectangular and the V-notch formula (or the weir against Manning). Two independent formulas agreeing beats one formula computed precisely.
- R-sensitivity audit. When R falls below ~0.3 m, n uncertainty dominates the answer — the R2/3 term can no longer buffer the roughness spread. Quote the bracket, and say so in the deliverable.
- Unit audit. Convert the final Q by hand once (m³/s ↔ ft³/s ↔ GPM) and check the number survives round-trip. Unit-mixed inputs produce plausible-looking garbage that no downstream review catches.
Verify, then trustPhoto: Unsplash❌ Don’t — skip Step 04 because “the number already looks right”: a plausible Q with an unverified flow state is the most expensive shortcut in channel work. The counter-example below shows exactly what it costs. State verification is one division and one glance — cheaper than any repair it pre-empts.
Froude Number and Flow States
The Froude number answers a question the discharge alone cannot: who is in control of the water surface? Fr = V/√(g·D) compares the flow speed V against the speed at which a surface gravity wave travels, √(g·D) — where D is the hydraulic depth A/T, not the hydraulic radius. That distinction matters: hydraulic radius tunes the velocity through friction; hydraulic depth tunes wave celerity, and wave celerity is what the Froude number is really about.
The mechanism is worth holding onto. Below Fr = 1 the wave outruns the current, so any disturbance — a rock, a sill, a culvert entrance — sends its influence upstream, and downstream controls set the depths: this is subcritical flow, the settled state of canals and lowland rivers. Above Fr = 1 the current outruns its own waves: disturbances sweep downstream only, control moves to the upstream end, and wherever the flow must decelerate it does so abruptly, through a hydraulic jump that concentrates energy dissipation — and scour — in one place. Near Fr = 1 both statements half-apply at once, which is precisely why the surface there is unstable.
The calculator’s badge uses design bands around the physical boundary: Subcritical below 0.9, Transitional between 0.9 and 1.1, Supercritical above 1.1. The extra margin keeps decisions out of the twitchy zone rather than sitting exactly on it.
| Fr range | Flow state | Engineering meaning |
|---|---|---|
| Fr < 0.9 | Subcritical | Decelerating waves travel upstream — downstream structures set backwater depths. Measuring flumes and gentle channels live here; depths are stable and readable. |
| 0.9 – 1.1 | Transitional | Near-critical: unstable surface, standing waves, erratic stage readings. Avoid designing here; expect noisy verification and re-measure before trusting any depth. |
| Fr > 1.1 | Supercritical | Shooting flow on steep gradients — no upstream influence, control at the reach head, energy must be dissipated where flow slows. Expect scour at the jump and need for lined transitions. |
💡 Tip — read Fr before you read Q: the Froude state tells you which direction information travels in the reach, so it decides whether your downstream structure (weir, culvert, flume) will actually set the depth you computed with. Compute Q first if you like, but qualify it with the state badge before quoting it.
Weir Flow Calculations
A weir turns discharge into a single depth measurement. Water backing up behind the crest accelerates over it, passes through critical depth, and falls as a nappe — and because the flow at the crest is critical, the discharge depends only on the head H above the crest and the geometry of the opening. That is the whole trick: no velocity measurement, no slope survey, one staff gauge reading.
The exponent encodes the geometry. A rectangular crest spills a sheet whose width contributes linearly, so Q ∝ H1.5; a 90° V-notch trades width for a wedge whose effective opening grows with the head itself, so Q ∝ H2.5 — the steeper exponent resolves tiny flows finely, which is why V-notches guard the low end of hydrographs. For a rectangular crest that does not span the full channel, each end contraction pinches the sheet; the Francis approximation subtracts 0.1·n·H from the crest length (n = number of contracting edges) before multiplying — an approximation, labeled as one everywhere it appears on this page.
Weir Formulas and Coefficients
SI and US coefficient sets are separate conventions (metres→m³/s, feet→cfs); each is unit-consistent with its own inputs. Standard approximations — verify against a local rating curve before operational use.
| Weir type | Formula (SI) | Coefficient SI / US | Applies when | Data nature |
|---|---|---|---|---|
| Suppressed rectangular (full-width) | Q = 1.84·L·H1.5 | 1.84 m³/s · 3.33 cfs | Crest spans the full channel; free ventilated nappe; negligible approach velocity | Francis-type standard approximation |
| Contracted rectangular (n edges) | Q = 1.84·(L−0.1·n·H)·H1.5 | 1.84 m³/s · 3.33 cfs | Crest narrower than channel; each side edge pinches the nappe | Francis approximation — treat as estimate |
| 90° V-notch triangle | Q = 1.38·H2.5 | 1.38 m³/s · 2.50 cfs | Small discharges; fully developed nappe; crest level and ventilated | Standard approximation (Cone-type coefficient) |
⚠️ Submerged weirs invalidate everything above: when tailwater rises above the crest and drowns the nappe, the free-discharge formulas silently under-read. Check that the downstream level sits below the crest and that air reaches under the nappe; if it does not, the reading needs a submergence correction beyond this page’s scope.
💡 Tip — measure the head where the water is flat: read H upstream of the surface drawdown (several times H back from the crest), from a stilling well or the channel side. A head read in the drawdown curve itself reads low, and since Q grows with H1.5–H2.5, a small bias compounds. Logging head readings over a storm turns the weir into a hydrograph; to convert storage volumes from that hydrograph into filling or drain-down times, the tank fill time calculator picks the job up from there.
One head reading → one dischargePhoto: UnsplashCulvert Screening Estimates
Culvert hydraulics is a discipline of its own — the FHWA’s HDS-5 manual runs inlet control against outlet control and takes the governing case, with barrel length, slope, tailwater, and bend losses all in the ledger. But a first screening question has a one-line answer: treating the inlet as an orifice, the discharge a submerged entrance passes is
Q ≈ Cd · Afull · √(2g·h)
Cd ≈ 0.6 · Afull = full-bore area π·D²/4 · h = head at the inlet
The coefficient bundles entrance and contraction losses into one number; the square root of the head does the driving, exactly as in orifice flow. The preset on this page — a 24-inch culvert with 1 ft of head — evaluates to roughly 0.43 m³/s (≈ 15 ft³/s ≈ 6,800 GPM), which is the order-of-magnitude a screening answer is good for.
❌ Don’t — size a road culvert from this tab: the screening estimate ignores tailwater submergence, outlet control, barrel friction, and inlet-edge geometry — any of which can halve the real capacity. An undersized road culvert does not fail quietly: it overtops the road and erodes the embankment. Screening ranks options; HDS-5 analysis by a drainage engineer seals the choice.
💡 Tip — use the culvert tab as the independent reading in Step 05:where a field reach discharges through a culvert under known head, the screening value is a physically independent cross-check against the Manning estimate — often the fastest convergence test available on a roadside survey.
Manning n Reference Table
Ven Te Chow’s 1959 Open Channel Hydraulics assembled the roughness coefficient tables engineers still reach for first. The values below are the typical mid-range figures the calculator’s dropdown uses — Chow’s source lists a range for each material (roughly ±0.008 around these), and condition — weeds, silt, age, alignment — decides where in the range reality sits. For verifiable institutional context on streamflow measurement, the USGS Office of Surface Water maintains the techniques and records behind professionally gauged streams.
| Lining material | n (typical) | Typical application |
|---|---|---|
| PVC / HDPE pipe | 0.010 | Smooth plastic storm and sewer pipes at partial depth |
| Concrete pipe | 0.013 | Precast concrete culverts and storm sewers |
| Cast iron | 0.013 | Cast-iron flumes and aqueduct remnants |
| Concrete lined channel | 0.015 | Trowel-finished lined flood channels and ditches |
| Corrugated metal | 0.024 | Corrugated steel pipe and pipe-arch culverts |
| Earth channel, straight | 0.025 | Freshly cut drainage ditch, straight and uniform |
| Natural stream, clean | 0.030 | Gravel-bottom creek, stable banks, no vegetation |
| Earth channel, winding | 0.035 | Dredged channel with mild bends and some weeds |
| Natural stream, weedy | 0.050 | Sluggish reach, irregular banks, dense summer weeds |
⚠️ These are typical values, not guarantees: a composite reach (concrete invert, weedy banks) deserves an n between its parts — weighted toward the segment that dominates the wetted perimeter. When the answer matters, bracket the value as in Step 02 rather than defending one number.
Common Mistakes in Channel Flow Estimates
❌ Borrowing n across sites
The single most common and most costly habit. n is condition-driven — the same material moves 0.022 → 0.033 between a clean and a weedy earth channel. Always re-derive it for the reach in front of you (Step 02).
❌ Percent slopes entered as decimals (or the reverse)
S = 0.5 entered where 0.005 belongs inflates Q tenfold via the square root. The % chip in the calculator converts for you, but hand arithmetic needs the same discipline: know which convention your number is in.
❌ Mixing unit conventions
Feet data with the SI coefficient (or metres with 1.486) skews every answer by the 1.486 factor — about 49% in Q. The tab is labeled precisely because this error survives every plausibility glance.
❌ Nominal pipe size taken as inside diameter
A 24-inch corrugated pipe does not measure 24.0 inches inside. Survey the true ID, or your A_full, R, and every downstream number inherit the gap.
❌ Depth assumed full for a partly full pipe
Enter the actual water depth, not the diameter. Half-full a pipe carries barely 40% of its full-bore Manning flow — the difference between a design number and a fiction.
❌ Head read in the weir drawdown
The staff gauge belongs upstream of the drawdown curve. Read it in the depressed zone and Q comes out low — increasingly so as the H exponent rises for V-notches.
Counter-Example: Skipping the State Check, Designing the Weir Anyway
An engineer computes Q for a steep reach with Manning’s equation, gets a plausible number, and — skipping Step 04 — designs a downstream overflow weir assuming subcritical flow, because that is the only regime where a downstream weir sets the upstream depth and the computed backwater elevation means what it says.
The reach, however, is supercritical (Fr > 1.1): information cannot travel upstream, so the weir does not set the approaching depth at all. The flow plunges onto the crest from shooting depth, and the hydraulic jump — the violent deceleration the design never budgeted for — forms not at the structure but wherever the tailwater happens to force it: sometimes on the loose rock protection, sometimes 15 metres upstream, in the middle of an unprotected erodible bend.
The failure shows up within the first major storm as scour at the jump’s foot, undermining the weir’s foundation and the adjacent bank — a repair measured in re-pouring structure, not in re-running one division to check Fr. The state check costs seconds; the jump’s relocation costs the project.
Worked Example: A 2 m Concrete-Lined Channel
Every figure below reproduces in the calculator above — the first preset button loads the inputs. The channel: rectangular, bottom width b = 2 m, water depth y = 0.8 m, slope S = 0.005 (0.5%), roughness n = 0.025 — the high end of the concrete range, appropriate for an aged, roughened lining of the cement-rubble family (Chow’s range for such linings reaches 0.030). Worked in SI with the coefficient 1.0:
Result
Q ≈ 2.63 m³/s · V ≈ 1.65 m/s · Fr ≈ 0.59 → Subcritical
In US units: ≈ 92.9 ft³/s (cfs) ≈ 41,700 GPM. The calculator, which carries full precision, reports Q = 2.636 m³/s (≈ 93.1 ft³/s) — the example’s 2.63 comes from rounding R to 0.444 m en route; both are the same answer to working accuracy.
What the state badge buys here: Fr ≈ 0.59 puts the reach comfortably in the subcritical band, so a downstream control — a measuring weir, a culvert entrance — would set the upstream depth and a backwater check on it would be meaningful. Had the slope been four times steeper (S = 2%), the same section would flow near 1.86 m/s and Fr would cross 1 — changing which end of the reach controls, without changing the area at all.
💡 Tip — reuse the worked example as your sanity baseline: load the preset before any new survey. If your real channel’s results land wildly far from this scale of number for a similar geometry, suspect a unit or decimal slip before believing the hydrology.
Data Sources & References
This page states where every number it publishes comes from, and how fresh the convention behind it is. Flow Calculator maintains the same editorial standard across the toolset — the about page documents the site-wide method and the standards every calculator page is held to.
- Manning equation — standard open-channel friction law (Manning, 1889; modern form per Chow). Geometry formulas (rectangular, trapezoidal, circular segment, top width) are the classical closed forms reproduced on this page; g = 9.80665 m/s² is shared with the site’s main engine.
- Manning n values — typical mid-range values after Chow (1959), Open Channel Hydraulics, roughness-coefficient tables. Labeled “typical”; Chow’s per-material ranges are wider. Cross-check techniques and gauged records via the USGS Office of Surface Water.
- Weir coefficients — Francis-type coefficients for rectangular weirs (1.84 SI / 3.33 cfs) with the 0.1·n·H end-contraction correction, and the standard 90° V-notch pair (1.38 SI / 2.50 cfs). Textbook-standard approximations: verify against a local rating curve before operational discharge quotes.
- Culvert screening — orifice analogy Q ≈ Cd·A_full·√(2g·h) with Cd ≈ 0.6. Screening-level only; the governing design methodology is FHWA Hydraulic Design of Highway Culverts (HDS-5).
- Scour threshold ~1.5 m/s — typical permissible-velocity figure for erodible channels; confirm against local soil data and the applicable drainage code before design use.
Pair the reading with practice: the guide library covers the velocity-area field method, unit conversions, and the pressurized-flow counterparts of every formula on this page.
Open Channel Flow FAQ
How does the Manning equation calculate flow rate?▼
Manning is an empirical friction law for gravity-driven water. It multiplies the wetted cross-sectional area A by a velocity term assembled from the hydraulic radius R raised to the 2/3 power, the bed slope S raised to the 1/2 power, and a roughness coefficient n that absorbs everything the formula cannot see — lining material, weeds, silt, and age. In SI units the leading coefficient is exactly 1; in US customary units it becomes 1.486 to reconcile feet and seconds. The equation answers “what flow does this channel carry at this depth and slope?” rather than “what velocity should I assume?” — which is exactly the situation in an open channel, where the water chooses its own depth.
What is hydraulic radius?▼
Hydraulic radius is the wetted cross-sectional area divided by the wetted perimeter — the length of bed and banks the water actually touches (R = A/P). Despite the name it is not a radius; it is a shape-efficiency score. A deep, narrow section has a large R because proportionally less of its water rides against friction, so it passes more flow than a wide, shallow section of the same area. Keep it apart from hydraulic depth (A/T, area over top width): hydraulic radius feeds the Manning velocity, while hydraulic depth feeds the Froude number. Swapping the two is a classic silent error.
What does the Froude number tell me?▼
The Froude number compares how fast the water moves with how fast a surface gravity wave can travel through it: Fr = V/√(g·D), with D the hydraulic depth. Below 1 the wave outruns the current, so disturbances propagate upstream and downstream water levels control the flow — the subcritical state typical of canals and rivers. Above 1 the current outruns the waves: disturbances cannot travel upstream, the flow shoots, and energy has to be dissipated where the flow slows again — the supercritical state. Between roughly 0.9 and 1.1 the water surface is twitchy and standing waves appear, so any depth measured there is unreliable by nature.
How do I calculate weir flow rate?▼
Pick the weir type first, because each has its own exponent. A rectangular crest follows Q = C·L·H^1.5: discharge grows with crest length L and with the head H raised to the 3/2 power. A 90° V-notch follows Q = C·H^2.5 — the steeper exponent gives fine resolution at small flows. The coefficient C carries the unit convention: 1.84 and 1.38 when you work in metres and cubic metres per second, 3.33 and 2.50 when you work in feet and cubic feet per second. Measure the head upstream of the surface drawdown, confirm the falling sheet (nappe) is ventilated rather than drowned by tailwater, and for a contracted weir subtract the end-contraction allowance from the crest length before multiplying.
How do I estimate culvert flow?▼
A quick screening estimate treats the culvert inlet as an orifice: Q ≈ Cd·A·√(2g·h), where A is the full pipe cross-section, h is the head driving flow through the entrance, and Cd near 0.6 bundles entrance and contraction losses into a single number. It answers “is this pipe plausibly in the right capacity range?” — nothing more. Real culvert design works through inlet-control and outlet-control calculations (the FHWA HDS-5 methodology), which account for barrel length, slope, tailwater submergence, and bend losses, then takes the governing case. Use the screening number to rank options and to know when a proper analysis is worth commissioning.
How do I measure river or creek flow rate?▼
The field method is the velocity-area approach: choose a straight, uniform reach, measure the average depth and width to get the cross-sectional area, then time a float or read a current meter at several points to get a mean velocity, and multiply — Q = A·v. Correct a surface-float velocity downward (commonly ×0.8–0.9), because surface drift runs faster than the depth-averaged current. If a small weir, flume, or V-notch can be installed, a single head reading replaces all the velocity work. When you can only survey geometry and slope, the Manning equation on this page gives a defensible estimate — and the USGS publishes rating curves for many gauged streams that will beat any estimate.
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Run Your Channel Estimate Now
Load a preset, or enter the geometry you surveyed — discharge, velocity, hydraulic radius, and the Froude state arrive on the same keystroke. Free, private, and in-browser.