Engineering & Science
Cipolletti Trapezoidal Weir & Parshall Flume Free-Flow Discharge Formulas
Measure irrigation canal and wastewater plant flow rates (m³/s) with Cesare Cipolletti’s 1H:4V end-contraction-compensated weir Q = 1.859*L*H^1.5 and Ralph Parshall’s throat flume Q = C*H_a^n.
Why flaring weir side walls at 1H:4V eliminates Francis end-contraction corrections!
Standard sharp-crested rectangular weirs suffer side-jet contractions that shrink effective crest width as head H rises (L_eff = L - 0.2*H). Italian hydraulic engineer Cesare Cipolletti (1886) angled the side notches outward at 1 horizontal to 4 vertical (14.04 degrees), adding just enough triangular side discharge to cancel end contractions automatically—giving the clean SI formula Q_cip = 1.859 * L * H^1.5 (m^3/s)!
Where sediment or wastewater solids would settle behind a dammed weir crest, Ralph Parshall’s (1926) self-scouring Venturi throat flume accelerates flow to critical depth with minimal head loss, following Q_par = C * H_a^n (for a 1-ft / 0.305-m throat flume in SI units: C = 0.679, n = 1.522)! At upstream head H = 0.32 m and Cipolletti crest L = 1.80 m, Q_cip = 0.6057 m^3/s (rising to 1.1831 m^3/s at H = 0.50 m), while the 1-ft Parshall flume passes Q_par = 0.1199 m^3/s!
| Open-Channel Flowmeter & Head H | Governing SI Equation | Volumetric Flow Rate Q (m³/s) | Primary Field Use |
|---|---|---|---|
| Cipolletti Weir (L = 1.8 m, H = 0.32 m) | 1.859 * L * H^1.5 (H <= L/3) | 0.6057 m³/s (605.7 L/s) | Clean irrigation canals |
| Cipolletti Weir (L = 1.8 m, H = 0.50 m) | 1.859 * 1.8 * 0.50^1.5 | 1.1831 m³/s | High-stage canal turnout |
| 1-ft Parshall Flume (H_a = 0.32 m) | 0.679 * H_a^1.522 | 0.1199 m³/s (119.9 L/s) | Sediment-laden / WWTP influent |
Cipolletti 1:4 Trapezoidal Sharp-Crested Weir Discharge Q_cip (m³/s)
Evaluates 1.859 * L * H^1.5 from crest length B2 (m) and upstream Piezometric head B3 (m), enforcing Cipolletti geometry H <= L / 3.
=IF(OR(B2 <= 0, B3 <= 0, B3 > B2 / 3), "Head Outside Cipolletti H <= L/3 Limit", ROUND(1.859 * B2 * (B3 ^ 1.5), 4))Parshall Throat Flume Free-Flow Discharge Q_par = C * H_a^n (m³/s)
Computes free-flow Parshall discharge from upstream converging-section head H_a (B3, m), throat coefficient C (B4), and exponent n (B5).
=IF(OR(B3 <= 0, B4 <= 0, B5 <= 0), "Invalid Flume Parameters", ROUND(B4 * (B3 ^ B5), 4))Try the example
Use the original values or change them to test your understanding.