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Parshall Flume Calculator

Compute USBR 1–8 ft Parshall flume free-flow discharge from throat width W and gage head Ha. Runs locally. Not a thin-plate weir, not a broad-crested weir, not Manning, not Q=Av, and not an orifice.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · USBR 1–8 ft Parshall free flow Q_cfs=4 W_ft Ha_ft^n, + O3 mpmath tabulated Q.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
USBR 1–8 ft Parshall free flow Q_cfs=4 W_ft Ha_ft^n, + O3 mpmath tabulated Q.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (flow, alias, awkward, wide, invalid-domain) · Matrix
Deferred
Not submerged Hb, not Manning n input, not thin-plate/broad crest, not orifice, not cutthroat L_f.
Numerical scope
O2: USBR 1–8 ft Parshall free flow vs a separate-module identity (≤2 ULP). Not submerged Hb, not Manning n input, not weir H/L, and not orifice. ≤2 ULP vs O3 applies only to the published tabulated Parshall vectors. Not submerged Hb, not Manning n input, not weir H/L, and not orifice.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
USBR 1–8 ft Parshall flume free-flow discharge or gage head. SI W, Ha, Q.
Scope
USBR 1–8 ft Parshall free flow: Q_cfs = 4 W_ft Ha_ft^n, n=1.522 W_ft^{0.026}; SI W, Ha, Q; n is reported, not an input
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · USBR 1–8 ft Parshall free flow Q_cfs=4 W_ft Ha_ft^n, + O3 mpmath tabulated Q.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision
2026-09-26.o2-o3 · 1/1 property · digest 14b291406a58
Legacy regression
6/6 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
4/4 golden · 1/1 CVP boundary · 3/3 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
Sources
Evidence
1 legacy golden · legacy regression suite · 4/4 oracle-backed golden · 3/3 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

USBR free flowQ_cfs = 4 W_ft Ha_ft^n
Exponentn = 1.522 W_ft^{0.026}
iSI. Convert with 1 ft = 0.3048 m and 1 cfs = 0.028316846592 m³/s. Envelope W∈[0.3048 m, 2.4384 m], Ha∈[0.03048 m, 1.6764 m]. 1–9 in sizes and submerged flow are out of scope. Do not send query v — that is calculation_version.

How to use

1

Enter throat width W

Parshall throat in metres, 1–8 ft. This is not weir span b or crest L.

2

Enter gage head Ha or discharge Q

Give one, not both. Ha is the specified-gage head, not weir H.

Example calculations

Common configurations with formula and result.

ϟ

1 ft throat, 1 ft Ha

W=0.3048 m, Ha=0.3048 m

Q_cfs = 4 (1) (1)^{1.522}
Q=4 cfs ≈ 0.11327 m³/s
ϟ

Invert Ha from that Q

W=0.3048 m, Q≈0.11327 m³/s

Ha_ft = (Q_cfs / 4 W_ft)^{1/n}
Ha=0.3048 m

Parshall Flume calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
USBR 1–8 ft Parshall flume, free flow. Q_cfs = 4 W_ft Ha_ft^n with n = 1.522 W_ft^{0.026}. Inputs and result are SI (W, Ha in m, Q in m³/s). Ha is the specified-gage upstream head, not weir crest head H. n is reported, not an input. Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not broad-crested (2/3)^{3/2} b √g H^{3/2}, not Manning n, not Q=Av, not orifice, not submerged Hb.
What it calculates
USBR 1–8 ft Parshall flume free-flow discharge or gage head. SI W, Ha, Q.
Inputs
  • mode?
  • W
  • Ha | Q
Outputs
  • Q
  • Ha
  • W
  • n
  • mode
  • model
Formula
Q_cfs = 4 W_ft Ha_ft^n; n = 1.522 W_ft^{0.026}
Assumptions
  • USBR 1–8 ft Parshall free flow: Q_cfs = 4 W_ft Ha_ft^n, n=1.522 W_ft^{0.026}; SI W, Ha, Q; n is reported, not an input
  • Ha is the specified-gage upstream head, not weir crest head H; W∈[0.3048 m, 2.4384 m]; Ha∈[0.03048 m, 1.6764 m]; free nappe only
  • Not thin-plate (2/3) C_d L √(2g) H^{3/2}, not broad-crested (2/3)^{3/2} b √g H^{3/2}, not Manning n, not Q=Av, not orifice, not submerged Hb
Units
  • SI; W and Ha in m; Q in m³/s; n dimensionless
Boundary conditions
  • missing W, Ha, or Q when required → MISSING_REQUIRED_INPUT
  • Ha and Q together, weir H/L/b, Manning n/R/S, orifice A/d/D/Δp, Q=Av v, yc/q/Fr/g, Cd, Hb, W_ft, L_f → MIXED_INPUT_ENCODING
  • W outside [0.3048, 2.4384] m or Ha outside [0.03048, 1.6764] m → VALUE_OUT_OF_RANGE
  • mode=rectangular|thin-plate|broad-crested or unknown mode → MIXED_INPUT_ENCODING or INVALID_MODE
Example
W=0.3048 Ha=0.3048 → Q≈0.11327
Validation cases

4 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence

  • W=0.3048 Ha=0.3048 → Q = 4 cfs ≈ 0.11327 m³/s
  • W=0.3048 Ha=0.3048 H=0.3048 → MIXED_INPUT_ENCODING
  • W=0.15 Ha=0.3048 → VALUE_OUT_OF_RANGE
  • mode=rectangular W=0.3048 Ha=0.3048 → MIXED_INPUT_ENCODING
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute Parshall flume free-flow discharge from throat width and specified-gage head.

Supported and not supported

Supported — USBR 1–8 ft free-flow Q from W and Ha · invert Ha from Q · API physics.fluid.parshall_flume

Not supported — thin-plate weir, broad-crested weir, Manning n, Q=Av, orifice, 1–9 in Parshall C tables, submerged Hb/Ha, SANIIRI

Agent / API notes

Capability id: physics.fluid.parshall_flume · tool id: parshall-flume · pin 1.0.0.

{ "W": 0.3048, "Ha": 0.3048 }

Invert: { "mode": "head", "W": 0.3048, "Q": 0.11327 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/parshall-flume. There is no /calc/fluid.

Other calculators in this family: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator . Explore all Fluid Mechanics.

→ Alternate Depth Calculator Compute both rectangular depths at the same specific energy from E, Q, and width b. Runs locally. Not specific energy from y+v; not specific force M; not hydraulic jump y2; not critical depth yc as the product. › → Bernoulli Equation Calculator Incompressible Bernoulli along a streamline: solve P2, v2, or h2. Runs locally in your browser. › → Broad-Crested Weir Calculator Compute rectangular broad-crested weir discharge Q = C_d (2/3)^{3/2} b √g H^{3/2}. Default C_d=0.85. Runs locally. Not a thin-plate weir, not Manning, not Q=Av, and not an orifice. › → Cavitation Number Calculator Compute the cavitation number σ = (p − p_v) / (½ ρ v²). Runs locally. Not NPSH, not Thoma NPSH/H, not Weber, and not Euler Eu=Δp/(ρ v²). › → Chezy Formula Calculator Compute open-channel mean velocity V = C √(R S). Runs locally. Not Manning n, not Q=Av, not Hazen–Williams, and not Darcy. › → Colebrook Friction Factor Calculator Solve the Colebrook–White equation for Darcy friction factor f from Re and ε/D. Turbulent pipes Re≥4000. Runs locally. Not laminar 64/Re and not a Moody-chart lookup. › → Concentric Reducer Calculator Compute concentric-reducer loss h = K v₂² / (2g) with K = 0.5 (1 − A₂/A₁) referenced to the downstream speed. Runs locally. Not sudden expansion, not gradual contraction α, not vena-contracta C_c, not catalog K, and not Q=Av. › → Critical Depth Calculator Compute rectangular critical depth yc = (q²/g)^{1/3}. Runs locally. Not a Froude wrap, not specific energy, not a hydraulic jump, and not Q=Av. ›

Frequently asked questions

Key distinctions behind the calculation.

Is this a thin-plate weir?

No. Thin-plate Q=(2/3) C_d L √(2g) H^{3/2} is /calc/physics/weir-discharge. Sending H or L here is MIXED_INPUT_ENCODING.

Is this a broad-crested weir?

No. Rectangular broad-crested Q=C_d (2/3)^{3/2} b √g H^{3/2} is /calc/physics/broad-crested-weir. Sending b, H, Cd, or g here is MIXED_INPUT_ENCODING. The USBR exponent is ≈1.52, not 3/2.

Is this the Manning formula?

No. Manning is uniform open-channel flow from n, A, R, and S at /calc/physics/manning-formula. Sending n, R, or S is MIXED_INPUT_ENCODING. This page reports the USBR exponent n; it is not an input.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. Sending A or v is MIXED_INPUT_ENCODING.

Is this an orifice?

No. A hole under head or a pipe orifice plate is /calc/physics/orifice-discharge. Sending d, D, or Δp is MIXED_INPUT_ENCODING.

Can I send submerged Hb?

No. This seed is free flow only. Submerged Hb/Ha is MIXED_INPUT_ENCODING.

Is this a cutthroat flume?

No. A cutthroat has no diverging section, so flume length L_f is independent. That is /calc/physics/cutthroat-flume. Sending L_f here is MIXED_INPUT_ENCODING.

Is this a sluice gate?

No. A free-flow undershot sluice with Swamee C_d from a/y1 is /calc/physics/sluice-gate. Sending kind=sluice here is MIXED_INPUT_ENCODING.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine parshallFlume wrapper.