Discharge Passing Over Weir Considering Velocity Calculator

Francis Discharge with Suppressed End Formula:

\[ QFr' = \frac{2}{3} \times Cd \times \sqrt{2 \times g} \times Lw \times ((Sw + HV)^{\frac{3}{2}} - HV^{\frac{3}{2}}) \]

Coefficient of Discharge (Cd):

Acceleration due to Gravity (g):

m/s²

Length of Weir Crest (Lw):

Height of Water above Crest of Weir (Sw):

Velocity Head (HV):

Francis Discharge with Suppressed End (QFr'):

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1. What is Francis Discharge with Suppressed End?

Francis Discharge with Suppressed End is the discharge of flow over a weir without end contraction. It provides a more accurate measurement of fluid flow by considering the velocity head in the calculation.

2. How Does the Calculator Work?

The calculator uses the Francis Discharge formula:

\[ QFr' = \frac{2}{3} \times Cd \times \sqrt{2 \times g} \times Lw \times ((Sw + HV)^{\frac{3}{2}} - HV^{\frac{3}{2}}) \]

Where:

\( Cd \) — Coefficient of Discharge
\( g \) — Acceleration due to Gravity (m/s²)
\( Lw \) — Length of Weir Crest (m)
\( Sw \) — Height of Water above Crest of Weir (m)
\( HV \) — Velocity Head (m)

Explanation: The formula accounts for the kinetic energy of the fluid through the velocity head term, providing a more accurate discharge calculation.

3. Importance of Discharge Calculation

Details: Accurate discharge calculation is crucial for hydraulic engineering, water resource management, irrigation systems, and flood control measures.

4. Using the Calculator

Tips: Enter all values in appropriate units. Coefficient of Discharge typically ranges from 0.6 to 0.8. Acceleration due to gravity is approximately 9.8 m/s².

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between suppressed and contracted weir?
A: Suppressed weir has no end contraction (width equals channel width), while contracted weir has end contractions that reduce the effective crest length.

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

Q3: What are typical values for Coefficient of Discharge?
A: For sharp-crested weirs, Cd typically ranges from 0.60 to 0.80, depending on the weir geometry and flow conditions.

Q4: When should this formula be used?
A: This formula is appropriate for rectangular sharp-crested weirs with suppressed ends where velocity of approach is significant.

Q5: What are the limitations of this formula?
A: The formula assumes ideal flow conditions and may require adjustments for viscous effects, surface tension, and non-uniform velocity distribution.