Physics calculator

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 Engine tested · Source checked · 5/5 tests · Production surface contract 1/1 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 5/5 tests · Production surface contract 1/1 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: ISO 9826 — Measurement of liquid flow in open channels — Parshall and SANIIRI flumes — Parshall flume
USBR Water Measurement Manual — Parshall flumes, 1–8 ft
ISO 80000-4 — Mechanics — Volume flow rate
Sources
Evidence: 5 property · Production surface contract 1/1 · Artifact integrity PASS
Production: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-18T02:44:05.986Z
Semantic contract: PASS

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

Enter throat width W

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

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.

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

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

Engine tested 5/5 tests · Production surface contract 1/1
Named expert review Not performed
Calculation version 1.0.0

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 · 5/5 tests · Production surface contract 1/1 · 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: ISO 9826 — Measurement of liquid flow in open channels — Parshall and SANIIRI flumes — Parshall flume
Supports: Parshall geometry and free-flow rating; not a thin-plate or broad-crested weir
USBR Water Measurement Manual — Parshall flumes, 1–8 ft
Supports: Q_cfs = 4 W_ft Ha_ft^n with n = 1.522 W_ft^{0.026}
ISO 80000-4 — Mechanics — Volume flow rate
Supports: Q is volume flow; W and Ha are lengths
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: Broad-crested weir, Thin-plate weir, Manning formula, Flow rate, Critical depth, Cutthroat flume .

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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.