V-Notch (Triangular) Weir Flow Rate
V-Notch (Triangular) Weir Flow Rate
A V-notch weir is one of the most accurate and widely used devices for measuring small to moderate flows in open channels, laboratories, and treatment plants, because its triangular opening makes the discharge extremely sensitive to head at low flows — far more sensitive than a rectangular weir would be. That sensitivity is exactly what makes it a good flow meter: small flow changes produce measurable changes in head. Because the discharge depends on head raised to the 5/2 power, small errors in reading the upstream head translate into disproportionately larger errors in the computed flow, so the head gauge must be placed and zeroed carefully upstream of the drawdown zone for the measurement to be trustworthy.
The V-notch weir equation is Q = (8/15)*Cd*sqrt(2g)*tan(theta/2)*H^(5/2). where C_dw is the weir discharge coefficient, g_w is gravitational acceleration, theta_w is the full notch angle in radians, and H_w is the head measured above the notch vertex.
Inputs
C_dw := 0.58=0.58
g_w := 9.81 m/s^2=9.81 m/s^2
theta_w := 1.5708=1.57
H_w := 0.3 m=300 mm
The tangent of the half-angle captures how the flow area widens as water rises up the V shape, and the head is raised to the 5/2 power because both the flow area and the velocity grow with head.
Q_weir := (8/15)·C_dw·sqrt(2·g_w)·tan(theta_w/2)·H_w^(5/2)=0.07 m^3/s
Results
A 90-degree V-notch at 0.3 m of head gives a modest, easily-measured flow typical of lab or small-channel monitoring; because Q scales with H^2.5, a 10% error in the head reading produces roughly a 25% error in the computed flow, far larger than the same error on a rectangular weir. This strong head sensitivity is precisely why the V-notch is favored for low-flow measurement, provided the head gauge is read accurately.
Assumptions & limitations
- Sharp-crested notch with fully aerated (ventilated) nappe.
- Approach velocity assumed negligible.
- Discharge coefficient assumed constant over the head range used.
- Notch angle theta must be expressed in radians for this formula.