Head Over Crest Given Discharge Passing Over Weir With Velocity Calculator

Formula Used:

\[ Height\ of\ Water\ above\ Crest\ of\ Weir = \left(\left(\frac{Francis\ Discharge\ with\ Suppressed\ End \times 3}{2 \times Coefficient\ of\ Discharge \times \sqrt{2 \times Acceleration\ due\ to\ Gravity} \times Length\ of\ Weir\ Crest}\right) + Velocity\ Head^{3/2}\right)^{2/3} - Velocity\ Head \]

Francis Discharge with Suppressed End:

m³/s

Coefficient of Discharge:

Acceleration due to Gravity:

m/s²

Length of Weir Crest:

Velocity Head:

Height of Water above Crest of Weir:

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1. What is the Head Over Crest Calculation?

The Head Over Crest calculation determines the height of water above the crest of a weir, considering the discharge passing over the weir with velocity. This is essential in hydraulic engineering for designing and analyzing weir structures.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

Francis Discharge with Suppressed End — Discharge of flow without end contraction (m³/s)
Coefficient of Discharge — Ratio of actual discharge to theoretical discharge
Acceleration due to Gravity — Gravitational acceleration (m/s²)
Length of Weir Crest — Measurement of weir crest from end to end (m)
Velocity Head — Kinetic energy of the fluid represented as head (m)

Explanation: The formula accounts for the relationship between discharge, weir characteristics, and velocity head to determine the water height above the weir crest.

3. Importance of Weir Flow Calculation

Details: Accurate calculation of head over crest is crucial for proper weir design, flow measurement, flood control, and hydraulic structure analysis in water resource engineering.

4. Using the Calculator

Tips: Enter all required values with appropriate units. Ensure Francis Discharge, Coefficient of Discharge, Acceleration due to Gravity, Length of Weir Crest, and Velocity Head are positive values.

5. Frequently Asked Questions (FAQ)

Q1: What is Francis Discharge with Suppressed End?
A: It is the discharge over a weir without end contractions, where the weir spans the full width of the channel.

Q2: How is Coefficient of Discharge determined?
A: The coefficient of discharge is typically determined experimentally and varies based on weir shape, approach conditions, and flow characteristics.

Q3: Why is velocity head important in weir calculations?
A: Velocity head accounts for the kinetic energy of the approaching flow, which affects the discharge characteristics over the weir.

Q4: What are typical values for Coefficient of Discharge?
A: For sharp-crested weirs, the coefficient typically ranges from 0.60 to 0.75, depending on specific weir geometry and flow conditions.

Q5: When is this calculation most applicable?
A: This calculation is most applicable for sharp-crested weirs with suppressed ends under free flow conditions where the nappe is properly ventilated.