Effective Length of Spillway Crest When Outflow Is Considered Calculator

Formula Used:

\[ L_e = \frac{Q_h}{\frac{2}{3} \times C_d \times \sqrt{2 \times g} \times H^{3/2}} \]

Reservoir Discharge (Qh):

m³/s

Coefficient of Discharge (Cd):

Acceleration due to Gravity (g):

m/s²

Head over Weir (H):

Effective Length of the Spillway Crest (Le):

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1. What is the Effective Length of Spillway Crest?

The Effective Length of the Spillway Crest is the length used for the discharge passing over a spillway. It is a critical parameter in hydraulic engineering for designing spillways that can safely handle reservoir outflows during flood conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_e = \frac{Q_h}{\frac{2}{3} \times C_d \times \sqrt{2 \times g} \times H^{3/2}} \]

Where:

\( L_e \) — Effective Length of the Spillway Crest (m)
\( Q_h \) — Reservoir Discharge (m³/s)
\( C_d \) — Coefficient of Discharge
\( g \) — Acceleration due to Gravity (m/s²)
\( H \) — Head over Weir (m)

Explanation: This formula calculates the effective length required for a spillway crest to handle a specific reservoir discharge, taking into account the discharge coefficient and head over the weir.

3. Importance of Spillway Crest Length Calculation

Details: Accurate calculation of spillway crest length is essential for designing safe and efficient spillway systems. It ensures that the spillway can handle maximum expected flows without causing reservoir overtopping or structural failure.

4. Using the Calculator

Tips: Enter reservoir discharge in m³/s, coefficient of discharge, acceleration due to gravity in m/s² (default is 9.8), and head over weir in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for coefficient of discharge (Cd)?
A: The coefficient of discharge typically ranges from 0.6 to 0.8 for most spillway designs, depending on the shape and approach conditions.

Q2: Why is the head over weir raised to the power of 3/2?
A: The 3/2 power relationship comes from the fundamental hydraulic principles of weir flow, where discharge is proportional to the head raised to the 3/2 power.

Q3: How does spillway crest length affect reservoir safety?
A: Proper crest length ensures the spillway can safely pass flood waters, preventing overtopping of the dam and potential catastrophic failure.

Q4: What factors influence the coefficient of discharge?
A: The coefficient is influenced by spillway shape, approach velocity, upstream head, and the ratio of actual head to design head.

Q5: Can this formula be used for all types of spillways?
A: This formula is primarily for ogee crest spillways. Other spillway types may require different calculation methods.