Coefficient Of Discharge Given Discharge Passing Over Weir Considering Velocity Calculator

Coefficient of Discharge Formula:

\[ C_d = \frac{Q_{Fr'} \times 3}{2 \times \sqrt{2 \times g} \times L_w \times ((S_w + H_v)^{3/2} - H_v^{3/2})} \]

Francis Discharge with Suppressed End (QFr'):

m³/s

Acceleration due to Gravity (g):

m/s²

Length of Weir Crest (Lw):

Height of Water above Crest of Weir (Sw):

Velocity Head (Hv):

Coefficient of Discharge (Cd):

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1. What is the Coefficient of Discharge?

The Coefficient of Discharge (Cd) is the ratio of actual discharge to theoretical discharge. It accounts for energy losses and other factors that cause the actual flow rate to differ from the ideal theoretical flow rate in hydraulic systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_d = \frac{Q_{Fr'} \times 3}{2 \times \sqrt{2 \times g} \times L_w \times ((S_w + H_v)^{3/2} - H_v^{3/2})} \]

Where:

\( C_d \) — Coefficient of Discharge
\( Q_{Fr'} \) — Francis Discharge with Suppressed End (m³/s)
\( g \) — Acceleration due to Gravity (m/s²)
\( L_w \) — Length of Weir Crest (m)
\( S_w \) — Height of Water above Crest of Weir (m)
\( H_v \) — Velocity Head (m)

Explanation: This formula calculates the discharge coefficient considering the velocity head for weirs with suppressed ends.

3. Importance of Coefficient of Discharge Calculation

Details: Accurate calculation of the coefficient of discharge is crucial for designing and analyzing hydraulic structures, flow measurement devices, and ensuring proper water management in irrigation and drainage systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Francis Discharge, Acceleration due to Gravity, Length of Weir Crest must be positive values. Height of Water and Velocity Head must be non-negative values.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the velocity head important in this calculation?
A: Velocity head accounts for the kinetic energy of the approaching flow, which affects the discharge characteristics over the weir.

Q3: What does "suppressed end" mean in Francis Discharge?
A: Suppressed end means the weir extends across the full width of the channel, eliminating end contractions that would otherwise affect the flow.

Q4: When should this formula be used?
A: This formula is specifically designed for calculating the discharge coefficient for weirs with suppressed ends when velocity head considerations are important.

Q5: What factors can affect the accuracy of this calculation?
A: Factors include weir geometry, approach velocity distribution, water surface conditions, and measurement accuracy of input parameters.