Length Of Crest For Time Required To Lower Liquid Surface Calculator

Formula Used:

\[ L_w = \frac{2 \times A_R}{\frac{2}{3} \times C_d \times \sqrt{2 \times g} \times \Delta t} \times \left( \frac{1}{\sqrt{h_2}} - \frac{1}{\sqrt{H_{Upstream}}} \right) \]

Cross-Sectional Area of Reservoir (A_R):

m²

Coefficient of Discharge (C_d):

Acceleration due to Gravity (g):

m/s²

Time Interval (Δt):

Head on Downstream of Weir (h₂):

Head on Upstream of Weir (H_Upstream):

Length of Weir Crest (L_w):

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1. What is the Length of Crest Formula?

The formula calculates the required length of a weir crest to lower the liquid surface by a specified amount over a given time interval. It's derived from the fundamental principles of fluid mechanics and weir flow equations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_w = \frac{2 \times A_R}{\frac{2}{3} \times C_d \times \sqrt{2 \times g} \times \Delta t} \times \left( \frac{1}{\sqrt{h_2}} - \frac{1}{\sqrt{H_{Upstream}}} \right) \]

Where:

\( L_w \) — Length of Weir Crest (m)
\( A_R \) — Cross-Sectional Area of Reservoir (m²)
\( C_d \) — Coefficient of Discharge
\( g \) — Acceleration due to Gravity (m/s²)
\( \Delta t \) — Time Interval (s)
\( h_2 \) — Head on Downstream of Weir (m)
\( H_{Upstream} \) — Head on Upstream of Weir (m)

Explanation: The formula accounts for the relationship between reservoir geometry, flow characteristics, and time required to achieve the desired liquid level change.

3. Importance of Weir Crest Length Calculation

Details: Accurate calculation of weir crest length is crucial for designing efficient hydraulic structures, controlling water flow in reservoirs, and managing water resources effectively in irrigation and drainage systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Cross-sectional area should be in square meters, heads in meters, time in seconds, and acceleration due to gravity in m/s² (typically 9.8 m/s²). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Coefficient of Discharge?
A: The coefficient of discharge typically ranges from 0.6 to 0.8 for sharp-crested weirs, depending on the weir geometry and flow conditions.

Q2: How does weir crest length affect flow rate?
A: Longer weir crest lengths allow for greater discharge capacity, as the flow rate is directly proportional to the crest length for a given head.

Q3: When is this formula most applicable?
A: This formula is particularly useful for designing weirs in reservoir systems where controlled lowering of water levels is required over specific time periods.

Q4: What are the limitations of this calculation?
A: The formula assumes ideal flow conditions and may need adjustment for very large heads, rapidly changing flows, or non-standard weir configurations.

Q5: How accurate is this calculation for practical applications?
A: For well-designed weirs under normal operating conditions, this calculation provides good engineering accuracy, though field measurements may be needed for critical applications.