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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.

**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+h_{0})^{(3/2)}-h_{0}^{(3/2)}]

where

Q= discharge over weir, ft^{3}/s (m^{3}/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)

h_{0}= 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 | 0.685h^{2.45} |

60° | Q | 1.45h^{2.47} |

30° | Q | 2.49h^{2.48} |

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

Q=3.367bh^{3/2}

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

Q=Cbh3/2

**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.

If you have a query, you can **ask a question here**.

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

I have a rectangular weir to measure water flow in the water treatment plant. With

b is 1005mm. Thicknes of the plate is 5mm

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b=1005mm

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

TQ

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

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.

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

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

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

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

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

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.

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

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

is there a source for these formulas?