Weir Head Calculator
Design Philosophy
(Source: Reprint from CPHEEO Manual on Water Supply and Treatment, 2013)
A weir is a flow-measuring and flow-control structure placed transversely across an open channel. The relationship between the upstream head over the weir crest and the volumetric discharge is governed by the principle of critical flow over the weir crest. The CPHEEO Manual on Water Supply prescribes specific formulas for each standard weir profile, all of which take the general form:
where,
Q : Volumetric discharge (m³/s)
C : Coefficient of discharge (dimensionless)
L : Effective crest length (m)
H : Head above the weir crest (m)
n : Exponent depending on weir geometry
Sharp-Crested Rectangular Weir (Francis Formula)
For rectangular weirs with end contractions suppressed, the CPHEEO Manual on Water Supply recommends the Francis Formula. This is the most commonly used weir type in water treatment plant inlet structures and distribution chambers.
V-Notch Weir — 90° (Thomson Formula)
For a V-notch weir at a fixed notch angle of 90°, the CPHEEO Manual recommends the Thomson formula. The V-notch geometry is particularly suited for measuring low flows, where a rectangular weir would produce insufficient head to be read accurately.
Broad-Crested Weir
For a broad-crested weir, the CPHEEO Manual prescribes the following formula with a default discharge coefficient (Cd) of 0.848. The designer should adjust Cd for site-specific approach velocity and weir profile conditions.
Cipolletti (Trapezoidal) Weir
The Cipolletti weir has side slopes of 1H:4V. The trapezoidal geometry partially compensates for end contractions, making the effective crest length approximately equal to the base width.
Ogee Weir
For an Ogee-profile weir, the CPHEEO Manual prescribes the following formula. The coefficient of discharge (Cd) typically ranges from 0.623 to 0.750, depending on the weir profile and approach velocity. The default value used in this calculator is 0.700.
Calculator
(Note – all Yellow are user defined value, all white are fixed values, all green are calculated value, all orange is calculated not to be shown)
Instructions
Enter values highlighted in the Yellow
Green highlights are the results
In case of any invalid result of non-functioning of the calculator, please write to us at design@swaenviro.com. We will try and help you with your sizing and calculation
INPUT
| Parameter | Values | Units | Remarks |
|---|---|---|---|
| Sharp-Crested Rectangular Weir | |||
| Discharge (Q) | Enter discharge value and select unit from dropdown | ||
| Crest Length (L) | m | L = effective crest length in metres | |
| Discharge | 0.12 | cum/s | |
| Head H | 0.05 | m | H = (Q / 1.84×L)^(2/3) | Francis Formula | CPHEEO Manual on W/S |
| Head H | 54.09 | mm | |
| V-Notch Weir (90°) | |||
| Discharge (Q) | Enter discharge value and select unit from dropdown | ||
| Discharge | 0.12 | cum/s | |
| Head H | 0.37 | m | H = (Q / 1.417)^(2/5) | Thomson Formula | CPHEEO Manual on W/S | Angle fixed at 90° |
| Head H | 367.15 | mm | |
| Broad-Crested Weir | |||
| Discharge (Q) | Enter discharge value and select unit from dropdown | ||
| Crest Length (L) | m | L = effective crest length in metres | |
| Cd (coeff. of discharge) | 0.848 | Default Cd = 0.848 as per CPHEEO Manual on W/S. Adjust if site conditions differ | |
| Discharge | 0.115740 | cum/s | |
| Head H | 0.0635 | m | H = (Q / 1.705×Cd×L)^(2/3) | CPHEEO Manual on W/S |
| Head H | 63.52 | mm | |
| Cipolletti (Trapezoidal) Weir | |||
| Discharge (Q) | Enter discharge value and select unit from dropdown | ||
| Crest Length (L) | m | L = base crest length in metres | Side slopes fixed at 1H:4V | |
| Discharge | 0.115740 | cum/s | |
| Head H | 0.0537 | m | H = (Q / 1.859×L)^(2/3) | Cipolletti Formula | CPHEEO Manual on W/S |
| Head H | 53.72 | mm | |
| Ogee Weir | |||
| Discharge (Q) | Enter discharge value and select unit from dropdown | ||
| Crest Length (L) | m | L = effective crest length in metres | |
| Cd (coeff. of discharge) | 0.7 | Default Cd = 0.700 | CPHEEO range: 0.623–0.750 | Adjust based on weir profile and approach velocity | |
| Discharge | 0.115740 | cum/s | |
| Head H | 0.1030 | m | H = (Q / Cd×L)^(2/3) | CPHEEO Manual on W/S |
| Head H | 103.03 | mm | |