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Broad-Crested Weir Calculator

Broad-Crested Weir Formula

1. What is Broad-Crested Weir Calculator?

Definition: This calculator uses the broad-crested weir equation to compute the discharge (Q) over a broad-crested weir and the weir coefficient (C).

Purpose: It is used in hydraulics and civil engineering to measure and predict the flow rate of water over a weir, which is essential for designing spillways, dams, and irrigation systems.

2. How Does the Calculator Work?

The calculator uses the following equations:

  • Q=C×L×H3/2
  • C=(23)3/2g0.5

Where:

  • Q: Discharge (m³/s);
  • C: Weir coefficient (dimensionless);
  • L: Length of the weir (m);
  • H: Upstream head (m);
  • g: Acceleration due to gravity (m/s²).

Steps:

  • Enter the upstream head (H) with its unit.
  • Enter the length of the weir (L) with its unit.
  • Enter the acceleration due to gravity (g) with its unit (default is 9.80665 m/s²).
  • Convert all inputs to base units (m for length, m/s² for gravity).
  • Calculate the weir coefficient: C=(23)3/2g0.5.
  • Calculate the discharge: Q=C×L×H3/2.
  • Convert the discharge to the selected output unit and display both C and Q, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of Broad-Crested Weir Calculation

Calculating the discharge over a broad-crested weir is crucial for:

  • Water Management: Measuring flow rates in rivers, canals, and irrigation systems to manage water resources effectively.
  • Dam and Spillway Design: Ensuring safe and efficient design of spillways to handle flood flows.
  • Environmental Engineering: Monitoring and controlling water flow to maintain ecological balance in aquatic systems.

4. Using the Calculator

Example 1: Calculate C and Q for a broad-crested weir with the following properties:

  • Upstream Head: H=0.5m;
  • Length of Weir: L=2m;
  • Acceleration due to Gravity: g=9.80665m/s2;
  • Weir Coefficient: C=(23)3/2×9.806650.51.7048;
  • Discharge: Q=1.7048×2×0.53/21.2047m3/s;
  • Result: C=1.7048, Q=1.2047m3/s.

Example 2 (Different Units): Calculate C and Q with the following properties:

  • Upstream Head: H=1.5ft;
  • Length of Weir: L=10ft;
  • Acceleration due to Gravity: g=32.174ft/s2;
  • Convert units: H=1.5×0.3048=0.4572m, L=10×0.3048=3.048m, g=32.174×0.3048=9.8066m/s2;
  • Weir Coefficient: C=(23)3/2×9.80660.51.7048;
  • Discharge: Q=1.7048×3.048×0.45723/21.6042m3/s;
  • Result (in selected units, e.g., ft³/s): C=1.7048, Q=56.6319ft3/s.

5. Frequently Asked Questions (FAQ)

Q: What is the significance of the weir coefficient C?
A: The weir coefficient C accounts for the weir's geometry and the effects of gravity on the flow. It adjusts the theoretical flow rate to match real-world conditions.

Q: Why does the discharge depend on H3/2?
A: The H3/2 term arises from the physics of open-channel flow over a weir, reflecting the relationship between the head and the velocity of the water as it passes over the weir.

Q: Can this calculator be used for other types of weirs?
A: This calculator is specific to broad-crested weirs. Other types of weirs (e.g., sharp-crested weirs) use different equations and coefficients, which this calculator does not account for.

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