Discharge Over Broad-Crested Weir For Head Of Liquid At Middle Calculator

Discharge Over Broad-Crested Weir Formula:

\[ Q = C_d \times L_w \times \sqrt{2 \times g \times (h^2 \times H - h^3)} \]

Coefficient of Discharge (Cd):

(unitless)

Length of Weir (Lw):

meters

Head of Liquid Middle (h):

meters

Head of Liquid (H):

meters

Discharge Weir (Q):

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1. What is the Discharge Over Broad-Crested Weir Formula?

The Discharge Over Broad-Crested Weir formula calculates the flow rate of liquid over a broad-crested weir. This type of weir has a horizontal crest that is sufficiently broad in the direction of flow to support the fluid pressure.

2. How Does the Calculator Work?

The calculator uses the discharge formula:

\[ Q = C_d \times L_w \times \sqrt{2 \times g \times (h^2 \times H - h^3)} \]

Where:

\( Q \) — Discharge Weir (m³/s)
\( C_d \) — Coefficient of Discharge (unitless)
\( L_w \) — Length of Weir (meters)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( h \) — Head of Liquid Middle (meters)
\( H \) — Head of Liquid (meters)

Explanation: The formula calculates the volumetric flow rate over a broad-crested weir based on the physical dimensions and hydraulic characteristics.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for hydraulic engineering, water resource management, irrigation system design, and flood control infrastructure planning.

4. Using the Calculator

Tips: Enter all values in appropriate units. The coefficient of discharge typically ranges from 0.6 to 0.9 depending on weir geometry. Ensure the head of liquid middle (h) is less than the total head of liquid (H).

5. Frequently Asked Questions (FAQ)

Q1: What is a broad-crested weir?
A: A broad-crested weir is a hydraulic structure with a horizontal crest that is sufficiently long in the direction of flow to support the fluid pressure and create critical flow conditions.

Q2: How is the coefficient of discharge determined?
A: The coefficient of discharge is typically determined experimentally and depends on the weir geometry, approach conditions, and Reynolds number.

Q3: What are typical values for the coefficient of discharge?
A: For broad-crested weirs, the coefficient of discharge typically ranges from 0.6 to 0.9, with common values around 0.8 for well-designed weirs.

Q4: What are the limitations of this formula?
A: The formula assumes ideal flow conditions, a horizontal weir crest, and negligible velocity of approach. It may not be accurate for very low or very high flow rates.

Q5: How does this differ from other weir formulas?
A: Broad-crested weir formulas account for the extended crest length that supports hydrostatic pressure distribution, unlike sharp-crested weirs which have different flow characteristics.