Duration of Inflow given Inlet Channel Velocity Calculator

Duration of Inflow Formula:

\[ t = \frac{\arcsin\left(\frac{c_1}{V_m}\right) \times T}{2\pi} \]

Inlet Velocity (c₁):

m/s

Maximum Cross Sectional Average Velocity (Vₘ):

m/s

Tidal Period (T):

hours

Duration of Inflow (t):

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1. What is the Duration of Inflow Calculation?

The Duration of Inflow calculation determines the period over which a stream or river carries a consistent flow of water into a system, based on inlet velocity, maximum cross-sectional average velocity, and tidal period.

2. How Does the Calculator Work?

The calculator uses the Duration of Inflow formula:

\[ t = \frac{\arcsin\left(\frac{c_1}{V_m}\right) \times T}{2\pi} \]

Where:

\( t \) — Duration of Inflow (hours)
\( c_1 \) — Inlet Velocity (m/s)
\( V_m \) — Maximum Cross Sectional Average Velocity (m/s)
\( T \) — Tidal Period (hours)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula calculates the inflow duration using trigonometric relationships between velocity components and tidal period.

3. Importance of Duration of Inflow

Details: Accurate calculation of inflow duration is crucial for tidal flow analysis, coastal engineering, sediment transport studies, and environmental impact assessments in estuarine and coastal systems.

4. Using the Calculator

Tips: Enter inlet velocity and maximum cross-sectional average velocity in m/s, tidal period in hours. All values must be positive, and inlet velocity must not exceed maximum cross-sectional average velocity.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this calculation?
A: It helps determine how long water flows into a system during each tidal cycle, which is essential for understanding sediment transport and nutrient distribution.

Q2: Why must inlet velocity be less than maximum velocity?
A: The arcsin function requires an input between -1 and 1, so the ratio c₁/Vₘ must be within this range for valid mathematical operation.

Q3: What is a typical tidal period value?
A: A tidal period is approximately 12.42 hours for semi-diurnal tides or 24.84 hours for diurnal tides.

Q4: Can this formula be used for river systems without tides?
A: This specific formula is designed for tidal systems. For non-tidal rivers, different hydraulic formulas would be more appropriate.

Q5: What are the limitations of this calculation?
A: The formula assumes idealized conditions and may not account for complex bathymetry, wind effects, or non-uniform velocity distributions.