Normal Discharge At Given Stage Under Steady Uniform Flow Calculator

Formula Used:

\[ Q_n = \frac{Q_M}{\sqrt{1 + \frac{1}{v_W \cdot S_o} \cdot \frac{dh}{dt}}} \]

Measured Unsteady Flow (Q_M):

m³/s

Velocity of Flood Wave (v_W):

m/s

Channel Slope (S_o):

Rate of Change of Stage (dh/dt):

m/s

Normal Discharge (Q_n):

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1. What is Normal Discharge At Given Stage Under Steady Uniform Flow?

Normal Discharge at a given stage under steady uniform flow represents the discharge that would occur under normal, steady flow conditions. It is calculated from measured unsteady flow data considering the velocity of flood wave, channel slope, and rate of change of stage.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Q_n = \frac{Q_M}{\sqrt{1 + \frac{1}{v_W \cdot S_o} \cdot \frac{dh}{dt}}} \]

Where:

\( Q_n \) — Normal Discharge (m³/s)
\( Q_M \) — Measured Unsteady Flow (m³/s)
\( v_W \) — Velocity of Flood Wave (m/s)
\( S_o \) — Channel Slope
\( \frac{dh}{dt} \) — Rate of Change of Stage (m/s)

Explanation: This formula accounts for the dynamic effects in unsteady flow conditions to determine the equivalent steady uniform flow discharge.

3. Importance of Normal Discharge Calculation

Details: Calculating normal discharge is essential for hydraulic engineering, flood forecasting, and water resource management. It helps in understanding the relationship between stage and discharge under varying flow conditions.

4. Using the Calculator

Tips: Enter measured unsteady flow in m³/s, velocity of flood wave in m/s, channel slope (dimensionless), and rate of change of stage in m/s. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between normal discharge and measured unsteady flow?
A: Normal discharge represents the steady uniform flow equivalent, while measured unsteady flow is the actual flow measurement under dynamic conditions.

Q2: How is velocity of flood wave determined?
A: Velocity of flood wave can be estimated from field measurements or calculated using hydraulic models based on channel characteristics.

Q3: What factors affect channel slope?
A: Channel slope is influenced by topography, sediment transport, and channel morphology. It represents the gradient along which water flows.

Q4: Why is rate of change of stage important?
A: The rate of change of stage indicates how quickly water levels are rising or falling, which is crucial for understanding flood dynamics.

Q5: Are there limitations to this calculation?
A: This calculation assumes certain simplifications and may not account for all complex hydraulic phenomena in natural channels.