Measured Unsteady Flow Calculator

Measured Unsteady Flow Formula:

\[ Q_M = Q_n \times \sqrt{1 + \left(\frac{1}{v_W \times S_o}\right) \times \frac{dh}{dt}} \]

Normal Discharge (Qn):

m³/s

Velocity of Flood Wave (vW):

m/s

Channel Slope (So):

Rate of Change of Stage (dh/dt):

m/s

Measured Unsteady Flow (QM):

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1. What is the Measured Unsteady Flow Equation?

The Measured Unsteady Flow equation calculates the flow rate in a channel under unsteady flow conditions, accounting for the effects of flood wave velocity, channel slope, and rate of change of water stage.

2. How Does the Calculator Work?

The calculator uses the Measured Unsteady Flow equation:

\[ Q_M = Q_n \times \sqrt{1 + \left(\frac{1}{v_W \times S_o}\right) \times \frac{dh}{dt}} \]

Where:

\( Q_M \) — Measured Unsteady Flow (m³/s)
\( Q_n \) — Normal Discharge (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: The equation accounts for the dynamic effects of unsteady flow conditions in open channels, particularly during flood events.

3. Importance of Measured Unsteady Flow Calculation

Details: Accurate calculation of unsteady flow is crucial for flood forecasting, hydraulic engineering design, and water resource management during transient flow conditions.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between steady and unsteady flow?
A: Steady flow has constant discharge over time, while unsteady flow has discharge that varies with time, typically during flood events.

Q2: How is flood wave velocity determined?
A: Flood wave velocity can be measured using stream gauges or calculated based on channel characteristics and flow conditions.

Q3: What factors affect channel slope?
A: Channel slope is determined by the topography and geometry of the channel and remains relatively constant for a given channel section.

Q4: When is this equation most applicable?
A: This equation is particularly useful for analyzing flood wave propagation in rivers and channels during storm events.

Q5: What are the limitations of this equation?
A: The equation assumes certain simplifications and may not account for all complex hydraulic interactions in extreme flood conditions.