Ordinates Of Instantaneous Unit Hydrograph Representing IUH Of Catchment Calculator

Formula Used:

\[ U_t = \frac{1}{(n-1)! \cdot K^n} \cdot \Delta t^{n-1} \cdot e^{-\Delta t / K} \]

Ordinates of Unit Hydrograph:

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1. What is the Ordinates of Instantaneous Unit Hydrograph?

The Ordinates of Instantaneous Unit Hydrograph (IUH) represents the catchment's response to an instantaneous unit rainfall excess. It provides the theoretical basis for deriving unit hydrographs of different durations and is fundamental in hydrological modeling and flood forecasting.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ U_t = \frac{1}{(n-1)! \cdot K^n} \cdot \Delta t^{n-1} \cdot e^{-\Delta t / K} \]

Where:

\( U_t \) — Ordinates of Unit Hydrograph (cm/hr)
\( n \) — Constant for the catchment determined by effective rainfall
\( K \) — Constant for the catchment determined by flood hydrograph characteristics
\( \Delta t \) — Time interval (seconds)
\( e \) — Base of natural logarithm (approximately 2.71828)

Explanation: The formula calculates the ordinates of the instantaneous unit hydrograph based on catchment characteristics and time interval, using factorial and exponential functions.

3. Importance of IUH Calculation

Details: Accurate IUH calculation is crucial for flood prediction, watershed management, hydraulic structure design, and understanding catchment response to rainfall events.

4. Using the Calculator

Tips: Enter constant n (must be greater than 0), constant K (must be greater than 0), and time interval in seconds (must be greater than 0). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of constants n and K?
A: Constant n represents the catchment's storage characteristics, while constant K relates to the time characteristics of the flood hydrograph.

Q2: How are n and K determined for a specific catchment?
A: These constants are typically determined through analysis of historical rainfall-runoff data and calibration against observed hydrographs.

Q3: What is the range of typical values for n and K?
A: n typically ranges from 1 to 5, while K values depend on catchment size and characteristics, usually ranging from hours to days.

Q4: Can this formula be used for all catchment types?
A: While widely applicable, the formula may need adjustment for highly urbanized catchments or those with significant anthropogenic influences.

Q5: How does time interval affect the计算结果?
A: Smaller time intervals provide more detailed hydrograph ordinates, while larger intervals give a smoother but less detailed representation.