A V notch weir is to be designed to meter an irrigation channel flow. For ease in reading the upstream water-level gage, a reading H ≥ 30 cm is desired for the design flow rate of 150 m^3/h. What is the appropriate angle θ for the V notch?

Question

A V notch weir is to be designed to meter an irrigation channel flow. For ease in reading the upstream water-level gage, a reading H ≥ 30 cm is desired for the design flow rate of 150 [latex]m^3[/latex]/h. What is the appropriate angle θ for the V notch?

Accepted Answer

• Assumptions: Steady flow, negligible Weber number effect because H > 50 mm.

• Approach: Equation (10.60) applies with, we hope, a notch angle 20° < θ < 100°.

[latex]Q_{V notch} \approx C_d an \frac{ heta}{2}g^{1/2}H^{5/2} Cd \approx 0.44 for 20° < θ < 100°[/latex] (10.60)

• Property values: If surface tension is neglected, no fluid properties are needed. Why?

• Solution: Apply Equation (10.60) to the known flow rate and solve for θ:

[latex]Q = \frac{150 m^3/h}{3600 s/h} = 0.0417\frac{m^3}{s} \geq C_d an \left(\frac{ heta}{2} ight) g^{1/2} H^{5/2} = 0.44 an \left(\frac{ heta}{2} ight) \left(9.81\frac{m}{s^2} ight)^{1/2}(0.3 m)^{5/2}[/latex]

Solve for [latex] an \left(\frac{ heta}{2} ight) \leq 0.613[/latex] or θ ≤ 63° Ans.

• Comments: An angle of 63° will create an upstream head of 30 cm. Any angle less than that will create an even larger head. Weir formulas depend primarily on gravity and geometry. Fluid properties such as (ρ, μ, ϒ) enter only as slight modifications or as correction factors.

Question 10.12: A V notch weir is to be designed to meter an irrigation chan...

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