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Weir Flow Calculator

Calculate flow over weirs, spillways, and open channel structures

Parameters

mⓘ
mⓘ
mⓘ
ⓘ
Show Trail

Controls

xⓘ

Calculated Values

Flow Rate:
1.94;m3/s1.94;m³/s
Head:
0.50;m0.50;m
Velocity:
3.13;m/s3.13;m/s
Power:
9525.00;W9525.00;W

Examples

Example 1: Rectangular Weir

Water flowing over a rectangular weir.

  • Flow Rate: 2.192.19
  • Head: 0.500.50
  • Velocity: 3.133.13
  • Power: 10750.0010750.00

Example 2: Spillway

High flow over a dam spillway.

  • Flow Rate: 87.6087.60
  • Head: 2.002.00
  • Velocity: 6.266.26
  • Power: 1720000.001720000.00

Example 3: Small Weir

Low flow over a small weir.

  • Flow Rate: 0.250.25
  • Head: 0.300.30
  • Velocity: 2.432.43
  • Power: 735.00735.00

Visualization

Weir Flow

A weir is a barrier across a river or stream that alters the flow characteristics and usually results in a change in the height of the water level. Weirs are commonly used to measure flow rate, control water levels, and provide energy dissipation in hydraulic structures.

The basic weir flow equation is: Q = C_d L H^(3/2) √(2g), where Q is flow rate, C_d is discharge coefficient, L is weir width, H is head over the weir, and g is gravitational acceleration. This equation applies to rectangular weirs with free flow conditions.

The discharge coefficient (C_d) depends on the weir geometry, approach velocity, and flow conditions. For sharp-crested rectangular weirs, C_d typically ranges from 0.6 to 0.7. The coefficient accounts for energy losses and flow contraction.

Different types of weirs include: rectangular weirs, triangular (V-notch) weirs, trapezoidal weirs, and broad-crested weirs. Each type has specific applications and discharge coefficients.

Weir flow is used in: flow measurement in rivers and canals, dam spillways, water treatment plants, irrigation systems, and hydraulic modeling. The principle is fundamental to hydraulic engineering and water resource management.

Key Concepts

  • Flow Rate: Q = C_d L H^(3/2) √(2g)
  • Head: H = water depth - weir height
  • Discharge Coefficient: C_d (accounts for losses)
  • Froude Number: Fr = v/√(gh)
  • Submerged Flow: When downstream affects upstream
  • Broad-Crested Weir: When crest length > 3H

Real-World Applications

  • Flow Measurement: River and canal discharge
  • Dam Spillways: Flood control and energy dissipation
  • Water Treatment: Flow control and measurement
  • Irrigation: Water level control
  • Hydraulic Modeling: Laboratory studies

Explore Further

More fluid mechanics tools

Physics Equations

Flow Rate:
Q=CdLH3/22gQ = C_d L H^{3/2} \sqrt{2g}
Head:
H=h−PH = h - P
Velocity:
v=2gHv = \sqrt{2gH}
Froude Number:
Fr=vghFr = \frac{v}{\sqrt{gh}}
Power:
P=ρgQHP = \rho g Q H

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Identify Parameters

First, we identify the parameters needed for weir flow calculation:

Equation:

Q=CdLH3/22gQ = C_d L H^{3/2} \sqrt{2g}

Calculation:

P=1 m,h=1.5 m,L=2 m,Cd=0.62P = 1 \text{ m}, h = 1.5 \text{ m}, L = 2 \text{ m}, C_d = 0.62

Explanation:

These are the weir height, water depth, weir width, and discharge coefficient.

2

Step 2: Calculate Head

Calculate the head over the weir:

Equation:

H=h−PH = h - P

Calculation:

H=1.5−1=0.5 mH = 1.5 - 1 = 0.5 \text{ m}

Explanation:

Head is the difference between water depth and weir height.

3

Step 3: Calculate Flow Rate

Using the weir flow equation:

Equation:

Q=CdLH3/22gQ = C_d L H^{3/2} \sqrt{2g}

Calculation:

Q=0.62×2×(0.5)3/2×2×9.81=1.94 m3/sQ = 0.62 \times 2 \times (0.5)^{3/2} \times \sqrt{2 \times 9.81} = 1.94 \text{ m}^3/\text{s}

Explanation:

This gives the volumetric flow rate over the weir.

4

Step 4: Calculate Velocity

Calculate the theoretical velocity:

Equation:

v=2gHv = \sqrt{2gH}

Calculation:

v=2×9.81×0.5=3.13 m/sv = \sqrt{2 \times 9.81 \times 0.5} = 3.13 \text{ m/s}

Explanation:

This is the velocity based on the head over the weir.

5

Step 5: Calculate Power

Calculate the power associated with the flow:

Equation:

P=ρgQHP = \rho g Q H

Calculation:

P=1000×9.81×1.94×0.5=9525 WP = 1000 \times 9.81 \times 1.94 \times 0.5 = 9525 \text{ W}

Explanation:

This represents the power available from the flow over the weir.

Frequently Asked Questions (FAQ)

What is a weir?

A weir is a barrier across a river or stream that alters flow characteristics and usually results in a change in water level. It's used for flow measurement and water level control.

What is the weir flow equation?

The basic weir flow equation is Q = C_d L H^(3/2) √(2g), where Q is flow rate, C_d is discharge coefficient, L is weir width, H is head over the weir, and g is gravitational acceleration.

What is the discharge coefficient?

The discharge coefficient (C_d) accounts for energy losses and flow contraction. For sharp-crested rectangular weirs, it typically ranges from 0.6 to 0.7.

What is head over a weir?

Head (H) is the difference between water depth and weir height (H = h - P). It represents the energy available to drive flow over the weir.

What are the types of weirs?

Common types include rectangular weirs, triangular (V-notch) weirs, trapezoidal weirs, and broad-crested weirs. Each has specific applications and discharge coefficients.

Practice MCQs

  1. The weir flow equation is:
  2. Head over a weir is:
  3. For sharp-crested rectangular weirs, C_d is typically:
  4. Flow rate is proportional to:
  5. A broad-crested weir occurs when:

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