Coefficient Of Discharge Given Discharge If Velocity Considered Calculator

Coefficient of Discharge Formula:

\[ Cd = \frac{QFr \times 3}{2 \times \sqrt{2 \times g} \times (Lw - 0.1 \times n \times HStillwater) \times (HStillwater^{3/2} - HV^{3/2})} \]

Francis Discharge (QFr):

m³/s

Acceleration due to Gravity (g):

m/s²

Length of Weir Crest (Lw):

Number of End Contraction (n):

Still Water Head (HStillwater):

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 to differ from the ideal theoretical flow.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Cd = \frac{QFr \times 3}{2 \times \sqrt{2 \times g} \times (Lw - 0.1 \times n \times HStillwater) \times (HStillwater^{3/2} - HV^{3/2})} \]

Where:

\( Cd \) — Coefficient of Discharge
\( QFr \) — Francis Discharge (m³/s)
\( g \) — Acceleration due to Gravity (m/s²)
\( Lw \) — Length of Weir Crest (m)
\( n \) — Number of End Contraction
\( HStillwater \) — Still Water Head (m)
\( HV \) — Velocity Head (m)

Explanation: This formula calculates the discharge coefficient considering velocity head effects, which provides a more accurate measurement of flow over weirs.

3. Importance of Coefficient of Discharge Calculation

Details: Accurate calculation of the coefficient of discharge is crucial for hydraulic engineering applications, including flow measurement in open channels, weir design, and water resource management.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Coefficient of Discharge?
A: For most weirs, the coefficient of discharge typically ranges between 0.6 and 0.9, depending on the weir type and flow conditions.

Q2: Why is velocity head considered in this calculation?
A: Velocity head accounts for the kinetic energy of the approaching flow, which affects the discharge measurement accuracy.

Q3: What are end contractions?
A: End contractions occur when the weir width is less than the channel width, causing the nappe to contract at the ends.

Q4: When should this formula be used?
A: This formula is specifically designed for calculating discharge coefficient when velocity effects are significant and cannot be neglected.

Q5: What factors affect the coefficient of discharge?
A: The coefficient is affected by weir geometry, approach velocity, viscosity, surface tension, and measurement accuracy.