199/33310–15FE Reference Handbook 10.4 · Hydraulics · Orifices & weirs

Handbook formula

Orifice & Weir Discharge

An orifice converts head into jet velocity with a discharge coefficient C_d < 1. Sharp-crested rectangular weirs use the 3/2 power of head on the weir; triangular (V-notch) weirs use H^{5/2}.

Discharge coefficient
(m)
Head on the weir/orifice
(m)
Effective weir length

Step-by-step solved example

A 50 mm orifice, C_d = 0.62, has 4.0 m of head. Find Q.

HL
Free discharge: orifice √(2gh) or weir C L H^{3/2}.
  1. 1. Area and velocity

    A = 1.963×10⁻³ m². √(2gh) = 8.86 m/s. Q = 0.62×1.963e−3×8.86 = 0.0108 m³/s.

Answer: 0.0108 m³/s (10.8 L/s)

10 practice questions

0/10 correct

1.C_d for a sharp orifice is typically about

2.If head on a rectangular weir doubles, Q multiplies by

3.A 90° V-notch weir Q is proportional to

4.Free discharge orifice assumes downstream

5.Cipoletti weir is a trapezoidal weir designed so that

6.Time to empty a tank through an orifice uses

7.Broad-crested weir discharge (critical) scales as

8.If C_d is neglected (set to 1), Q is

9.Head H on a weir is measured

10.A 80 mm orifice, Cd = 0.6, h = 2.0 m. Q is nearest