Length of Crest Considering Velocity Calculator

Formula Used:

\[ L_w = \frac{3Q_{Fr'}}{2C_d\sqrt{2g}(H_{Stillwater}^{3/2} - H_V^{3/2})} + 0.1nH_{Stillwater} \]

Francis Discharge with Suppressed End (Q_Fr'):

m³/s

Coefficient of Discharge (C_d):

Acceleration due to Gravity (g):

m/s²

Still Water Head (H_Stillwater):

Velocity Head (H_V):

Number of End Contraction (n):

Length of Weir Crest (L_w):

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1. What is the Length of Crest Considering Velocity Formula?

The Length of Crest Considering Velocity formula calculates the required length of a weir crest while accounting for velocity effects. It's derived from Francis formula with modifications for end contractions and velocity head considerations in hydraulic engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L_w = \frac{3Q_{Fr'}}{2C_d\sqrt{2g}(H_{Stillwater}^{3/2} - H_V^{3/2})} + 0.1nH_{Stillwater} \]

Where:

\( L_w \) — Length of Weir Crest (m)
\( Q_{Fr'} \) — Francis Discharge with Suppressed End (m³/s)
\( C_d \) — Coefficient of Discharge
\( g \) — Acceleration due to Gravity (m/s²)
\( H_{Stillwater} \) — Still Water Head (m)
\( H_V \) — Velocity Head (m)
\( n \) — Number of End Contraction

Explanation: The formula accounts for both the discharge characteristics and the end contraction effects on weir performance.

3. Importance of Weir Crest Length Calculation

Details: Accurate weir crest length calculation is crucial for proper hydraulic structure design, ensuring efficient water flow measurement and control in channels and rivers.

4. Using the Calculator

Tips: Enter all values in appropriate units. Francis discharge and coefficient of discharge should be positive values. Still water head and velocity head must be positive, with velocity head typically less than still water head.

5. Frequently Asked Questions (FAQ)

Q1: What is Francis Discharge with Suppressed End?
A: It's the discharge calculation method developed by James B. Francis for weirs without end contractions, providing more accurate flow measurements.

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: What is Velocity Head in this context?
A: Velocity head represents the kinetic energy of the approaching flow, converted to an equivalent head of water.

Q4: When are end contractions considered?
A: End contractions are considered when the weir width is less than the channel width, causing the flow to contract at the ends.

Q5: What are typical values for these parameters?
A: Coefficient of discharge typically ranges from 0.6-0.8, acceleration due to gravity is 9.8 m/s², and number of end contractions depends on weir installation.