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Weir is defined as a barrier over which the water flows in an open channel. The edge or surface over which the water flows is called the crest. The overflowing sheet of water is the nappe.
If the nappe discharges into the air, the weir has free discharge. If the discharge is partly under water, the weir is submerged or drowned.

Types of Weirs.

A weir with a sharp upstream corner or edge such that the water springs clear of the crest is a sharp-crested weir.
All other weirs are classed as weirs not sharp crested. Sharp-crested weirs are classified according to the shape of the weir opening, such as rectangular weirs, triangular or V-notch weirs, trapezoidal weirs, and parabolic weirs. Weirs not sharp crested are classified according to the shape of their cross section, such as broad-crested weirs, triangular weirs, and trapezoidal weirs.

The channel leading up to a weir is the channel of approach. The mean velocity in this channel is the velocity of approach. The depth of water producing the discharge is the head.
Sharp-crested weirs are useful only as a means of meas- uring flowing water. In contrast, weirs not sharp crested are commonly incorporated into hydraulic structures as control or regulation devices, with measurement of flow as their secondary function.

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1) Rectangular Weir

The Francis formula for the discharge of a sharp-crested rectangular weir having a length b greater than 3h is

Q=3.33*(b -nh)/10*[(h+h0)(3/2)-h0(3/2)]

Q= discharge over weir, ft3/s (m3/s)
b= length of weir, ft (m)
h= vertical distance from level of crest of weir to water surface at point unaffected by weir drawdown (head on weir), ft (m)
n= number of end contractions (0, 1, or 2)
h0= head of velocity of approach

If the sides of the weir are coincident with the sides of the approach channel, the weir is considered to be suppressed, and n=0. If both sides of the weir are far enough removed from the sides of the approach channel to permit free lateral approach of water, the weir is considered to be contracted, and n= 2. If one side is suppressed and one is contracted, n=1.

2) Triangular Weir

The discharge of triangular weirs with notch angles of 30°,
60°, and 90° is given by the formulas as

Discharge of Triangular Weirs

Notch (vertex) angle Discharge formula
90° Q 0.685h2.45
60° Q 1.45h2.47
30° Q 2.49h2.48

h is as defined above in the Francis formula.

3) Trapezoidal (Cipolletti) Weir

The Cipolletti weir, extensively used for irrigation work, is trapezoidal in shape. The sides slope outward from the crest at an inclination of 1:4, (horizontal/vertical). The discharge is


where b, h, and Q are as defined earlier. The advantage of this type of weir is that no correction needs to be made for contractions.

4) Broad-Crested Weir

The discharge of a broad-crested weir is


Variations in Head Ratio and
Coefficient of Discharge for Broad-Crested Weirs

Ratio of actual head

to design head
Coefficient of discharge
0.20 3.30
0.40 3.50
0.60 3.70
0.80 3.85
1.00 3.98
1.20 4.10
1.40 4.22

Q, b, and h are as defined for rectangular weirs.
Values of C for broad-crested weirs with rounded upstream corners generally range from 2.6 to 2.9. For sharp upstream corners, C generally ranges from 2.4 to 2.6.

More Entries :
  • Ron Johnson July 11, 2008 at 7:44 pm

    We are looking for the formula for a broad crested parabolic weir. Can you please direct us. Thanks, Ron

  • Hasnan Ishak September 10, 2008 at 1:18 am

    I have a rectangular weir to measure water flow in the water treatment plant. With
    b is 1005mm. Thicknes of the plate is 5mm
    –| |——-
    | |
    | |

    What si the correct formula can be used and what is the C value. I hope u can reply quickly

  • OTEGBADE ADENIYI March 28, 2009 at 11:10 am

    I WISH I COULD BE PART OF YOU,BUT I AM FINANCIALLY LACK..My experience during when the experiment was conducting is very low,pls what can you do to help me

  • Qamar July 5, 2010 at 7:29 am

    i want to know the values of C for broad crested weir and for all type of weirs with reference to some book or paper etc.

  • Nadia August 6, 2010 at 8:59 am

    I require the general floe rate value for a rectangular weir as well as a v-notch weir

  • jason January 19, 2011 at 10:36 pm

    i wish to have more sample problems about trapezoidal weis and unsteady flow

  • Promise ukay March 13, 2011 at 3:27 pm

    Does flow net in dams has any thing 2 do with weirs?

  • anam May 9, 2012 at 12:23 pm

    can you simplify these fomulas of weires nd plz explain the H……..

  • kb September 30, 2012 at 5:59 pm

    The coefficient of 3.33 for a sharp crested weir is appropriate only for US Customary Units (ie, ft and sec),
    if u are using meters and s, use a coeficient of 1.8

  • Rob May 19, 2013 at 9:31 pm

    For metric units the broad crested weir C is 1.6 or 1.7. Best to consult a text book until this site is repaired.

    • Rick October 9, 2017 at 3:34 am

      For metric units it will be 0.886 for broad crested weir, and 1.6 for US (imperial) units.

  • Michael September 5, 2013 at 10:12 am

    What is the purpose of the discharge coefficient in weir flow?

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