Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment Calculator

✖Constant n is for the catchment to be determined by the effective rainfall of the catchment.ⓘ Constant n [n]			+10% -10%
✖Constant K is for the catchment to be determined by flood hydrograph characteristics of the catchment.ⓘ Constant K [K]			+10% -10%
✖Time Interval is the amount of time required for the change from the initial to the final state.ⓘ Time Interval [Δt]			+10% -10%

✖Ordinates of Unit Hydrograph with respect to time 't'.ⓘ Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment [U_t]

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Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment

Formula

`"U"_{"t"} = (1/((("n"-1)!)*("K"^"n")))*("Δt"^("n"-1))*exp(-"Δt"/"n")`

Example

`"0.03689cm/h"=(1/((("3"-1)!)*(("4")^"3")))*(("5s")^("3"-1))*exp(-"5s"/"3")`

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Download Clark's Method and Nash Model for IUH (Instantaneous Unit Hydrograph) Formulas PDF

Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ordinates of Unit Hydrograph = (1/(((Constant n-1)!)*(Constant K^Constant n)))*(Time Interval^(Constant n-1))*exp(-Time Interval/Constant n)
U_t = (1/(((n-1)!)*(K^n)))*(Δt^(n-1))*exp(-Δt/n)
This formula uses 1 Functions, 4 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Ordinates of Unit Hydrograph - (Measured in Centimeter per Hour) - Ordinates of Unit Hydrograph with respect to time 't'.
Constant n - Constant n is for the catchment to be determined by the effective rainfall of the catchment.
Constant K - Constant K is for the catchment to be determined by flood hydrograph characteristics of the catchment.
Time Interval - (Measured in Second) - Time Interval is the amount of time required for the change from the initial to the final state.

STEP 1: Convert Input(s) to Base Unit

Constant n: 3 --> No Conversion Required
Constant K: 4 --> No Conversion Required
Time Interval: 5 Second --> 5 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

U_t = (1/(((n-1)!)*(K^n)))*(Δt^(n-1))*exp(-Δt/n) --> (1/(((3-1)!)*(4^3)))*(5^(3-1))*exp(-5/3)

Evaluating ... ...

U_t = 0.0368897661792113

STEP 3: Convert Result to Output's Unit

1.02471572720031E-07 Meter per Second -->0.0368897661792113 Centimeter per Hour (Check conversion here)

FINAL ANSWER

0.0368897661792113 ≈ 0.03689 Centimeter per Hour <-- Ordinates of Unit Hydrograph

(Calculation completed in 00.004 seconds)

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< 6 Nash's Conceptual Model Calculators

Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment

Go Ordinates of Unit Hydrograph = (1/(((Constant n-1)!)*(Constant K^Constant n)))*(Time Interval^(Constant n-1))*exp(-Time Interval/Constant n)

Outflow in nth Reservoir

Go Outflow in the Reservoir = (1/(((Constant n-1)!)*(Constant K^Constant n)))*(Time Interval^(Constant n-1))*exp(-Time Interval/Constant n)

Outflow in Third Reservoir

Go Outflow in the Reservoir = (1/2)*(1/Constant K^3)*(Time Interval^2)*exp(-Time Interval/Constant K)

Outflow in Second Reservoir

Go Outflow in the Reservoir = (1/Constant K^2)*Time Interval*exp(-Time Interval/Constant K)

Outflow in First Reservoir

Go Outflow in the Reservoir = (1/Constant K)*exp(-Time Interval/Constant K)

Equation for Inflow from Continuity Equation

Go Inflow Rate = Constant K*Rate of Change of Discharge+Outflow Rate

Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment Formula

Ordinates of Unit Hydrograph = (1/(((Constant n-1)!)*(Constant K^Constant n)))*(Time Interval^(Constant n-1))*exp(-Time Interval/Constant n)
U_t = (1/(((n-1)!)*(K^n)))*(Δt^(n-1))*exp(-Δt/n)

What is meant by Unit Hydrograph?

The Unit Hydrograph is the hydrograph that results from unit (e.g. 1 inch) excess rainfall uniformly over the watershed at a uniform rate during a given period of time.

What is a catchment?

Catchments are areas of land where runoff collects to a specific zone. This movement is caused by water moving from areas of high energy to low energy due to the influence of gravity.

How to Calculate Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment?

Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment calculator uses Ordinates of Unit Hydrograph = (1/(((Constant n-1)!)*(Constant K^Constant n)))*(Time Interval^(Constant n-1))*exp(-Time Interval/Constant n) to calculate the Ordinates of Unit Hydrograph, The Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment formula is defined as the hydrograph of direct runoff resulting from a unit depth of effective rainfall generated uniformly over watershed in an infinitesimally small period. Ordinates of Unit Hydrograph is denoted by U_t symbol.

How to calculate Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment using this online calculator? To use this online calculator for Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment, enter Constant n (n), Constant K (K) & Time Interval (Δt) and hit the calculate button. Here is how the Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment calculation can be explained with given input values -> 13280.32 = (1/(((3-1)!)*(4^3)))*(5^(3-1))*exp(-5/3).

FAQ

What is Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment?

The Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment formula is defined as the hydrograph of direct runoff resulting from a unit depth of effective rainfall generated uniformly over watershed in an infinitesimally small period and is represented as U_t = (1/(((n-1)!)*(K^n)))*(Δt^(n-1))*exp(-Δt/n) or Ordinates of Unit Hydrograph = (1/(((Constant n-1)!)*(Constant K^Constant n)))*(Time Interval^(Constant n-1))*exp(-Time Interval/Constant n). Constant n is for the catchment to be determined by the effective rainfall of the catchment, Constant K is for the catchment to be determined by flood hydrograph characteristics of the catchment & Time Interval is the amount of time required for the change from the initial to the final state.

How to calculate Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment?

The Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment formula is defined as the hydrograph of direct runoff resulting from a unit depth of effective rainfall generated uniformly over watershed in an infinitesimally small period is calculated using Ordinates of Unit Hydrograph = (1/(((Constant n-1)!)*(Constant K^Constant n)))*(Time Interval^(Constant n-1))*exp(-Time Interval/Constant n). To calculate Ordinates of Instantaneous Unit Hydrograph representing IUH of Catchment, you need Constant n (n), Constant K (K) & Time Interval (Δt). With our tool, you need to enter the respective value for Constant n, Constant K & Time Interval and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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