Storage in Beginning of Time Interval Calculator

✖Storage at the End of Time Interval is the amount of water stored in reservoirs within the system of hydrological cycle at the end of the time.ⓘ Storage at the End of Time Interval [S₂]			+10% -10%
✖Constant K is for the catchment to be determined by flood hydrograph characteristics of the catchment.ⓘ Constant K [K]			+10% -10%
✖Coefficient x in the Equation of maximum intensity of rainfall in general form in the Muskingum Equation is known as the weighing factor.ⓘ Coefficient x in the Equation [x]			+10% -10%
✖Inflow at the End of Time Interval is the amount of water entering a body of water at the end of the time.ⓘ Inflow at the End of Time Interval [I₂]			+10% -10%
✖Inflow at the Beginning of Time Interval is the amount of water entering a body of water at the start of the time.ⓘ Inflow at the Beginning of Time Interval [I₁]			+10% -10%
✖Outflow at the End of Time Interval is the removal of water from the hydrological cycle at the end of the time.ⓘ Outflow at the End of Time Interval [Q₂]			+10% -10%
✖Outflow at the Beginning of Time Interval is the removal of water from the hydrological cycle at the start of the time.ⓘ Outflow at the Beginning of Time Interval [Q₁]			+10% -10%

✖Storage at the Beginning of Time Interval is the amount of water stored in reservoirs within the system of the hydrological cycle at the start of the time. Make Validation type greater than zero.ⓘ Storage in Beginning of Time Interval [S₁]

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Formula

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Storage in Beginning of Time Interval

Formula

`"S"_{"1"} = "S"_{"2"}-("K"*("x"*("I"_{"2"}-"I"_{"1"})+(1-"x")*("Q"_{"2"}-"Q"_{"1"})))`

Example

`"14.2"="35"-("4"*("1.8"*("65m³/s"-"55m³/s")+(1-"1.8")*("64m³/s"-"48m³/s")))`

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Storage in Beginning of Time Interval Solution

STEP 0: Pre-Calculation Summary

Formula Used

Storage at the Beginning of Time Interval = Storage at the End of Time Interval-(Constant K*(Coefficient x in the Equation*(Inflow at the End of Time Interval-Inflow at the Beginning of Time Interval)+(1-Coefficient x in the Equation)*(Outflow at the End of Time Interval-Outflow at the Beginning of Time Interval)))
S₁ = S₂-(K*(x*(I₂-I₁)+(1-x)*(Q₂-Q₁)))
This formula uses 8 Variables

Variables Used

Storage at the Beginning of Time Interval - Storage at the Beginning of Time Interval is the amount of water stored in reservoirs within the system of the hydrological cycle at the start of the time. Make Validation type greater than zero.
Storage at the End of Time Interval - Storage at the End of Time Interval is the amount of water stored in reservoirs within the system of hydrological cycle at the end of the time.
Constant K - Constant K is for the catchment to be determined by flood hydrograph characteristics of the catchment.
Coefficient x in the Equation - Coefficient x in the Equation of maximum intensity of rainfall in general form in the Muskingum Equation is known as the weighing factor.
Inflow at the End of Time Interval - (Measured in Cubic Meter per Second) - Inflow at the End of Time Interval is the amount of water entering a body of water at the end of the time.
Inflow at the Beginning of Time Interval - (Measured in Cubic Meter per Second) - Inflow at the Beginning of Time Interval is the amount of water entering a body of water at the start of the time.
Outflow at the End of Time Interval - (Measured in Cubic Meter per Second) - Outflow at the End of Time Interval is the removal of water from the hydrological cycle at the end of the time.
Outflow at the Beginning of Time Interval - (Measured in Cubic Meter per Second) - Outflow at the Beginning of Time Interval is the removal of water from the hydrological cycle at the start of the time.

STEP 1: Convert Input(s) to Base Unit

Storage at the End of Time Interval: 35 --> No Conversion Required
Constant K: 4 --> No Conversion Required
Coefficient x in the Equation: 1.8 --> No Conversion Required
Inflow at the End of Time Interval: 65 Cubic Meter per Second --> 65 Cubic Meter per Second No Conversion Required
Inflow at the Beginning of Time Interval: 55 Cubic Meter per Second --> 55 Cubic Meter per Second No Conversion Required
Outflow at the End of Time Interval: 64 Cubic Meter per Second --> 64 Cubic Meter per Second No Conversion Required
Outflow at the Beginning of Time Interval: 48 Cubic Meter per Second --> 48 Cubic Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S₁ = S₂-(K*(x*(I₂-I₁)+(1-x)*(Q₂-Q₁))) --> 35-(4*(1.8*(65-55)+(1-1.8)*(64-48)))

Evaluating ... ...

S₁ = 14.2

STEP 3: Convert Result to Output's Unit

14.2 --> No Conversion Required

FINAL ANSWER

14.2 <-- Storage at the Beginning of Time Interval

(Calculation completed in 00.004 seconds)

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Storage in Beginning of Time Interval

Go Storage at the Beginning of Time Interval = Storage at the End of Time Interval-(Constant K*(Coefficient x in the Equation*(Inflow at the End of Time Interval-Inflow at the Beginning of Time Interval)+(1-Coefficient x in the Equation)*(Outflow at the End of Time Interval-Outflow at the Beginning of Time Interval)))

Storage during end of time interval in Muskingum method of Routing

Go Storage at the End of Time Interval = Constant K*(Coefficient x in the Equation*(Inflow at the End of Time Interval-Inflow at the Beginning of Time Interval)+(1-Coefficient x in the Equation)*(Outflow at the End of Time Interval-Outflow at the Beginning of Time Interval))+Storage at the Beginning of Time Interval

Storage during Beginning of Time Interval for Continuity Equation of Reach

Go Storage at the Beginning of Time Interval = Storage at the End of Time Interval+((Outflow at the End of Time Interval+Outflow at the Beginning of Time Interval)/2)*Time Interval-((Inflow at the End of Time Interval+Inflow at the Beginning of Time Interval)/2)*Time Interval

Storage during End of Time Interval in Continuity Equation for Reach

Go Storage at the End of Time Interval = ((Inflow at the End of Time Interval+Inflow at the Beginning of Time Interval)/2)*Time Interval-((Outflow at the End of Time Interval+Outflow at the Beginning of Time Interval)/2)*Time Interval+Storage at the Beginning of Time Interval

Total Wedge Storage in Channel Reach

Go Total Storage in Channel Reach = Constant K*(Coefficient x in the Equation*Inflow Rate^A Constant Exponent+(1-Coefficient x in the Equation)*Outflow Rate^A Constant Exponent)

Equation for Linear Storage or Linear Reservoir

Go Total Storage in Channel Reach = Constant K*Outflow Rate

Outflow given Linear Storage

Go Outflow Rate = Total Storage in Channel Reach/Constant K

Storage in Beginning of Time Interval Formula

What is Routing in Civil Engineering?

In Hydrology, Routing is a technique used to predict the changes in the shape of a hydrograph as water moves through a river channel or a reservoir. If the water flow at a particular point, A, in a stream is measured over time with a flow gauge, this information can be used to create a hydrograph.

What is Muskingum Routing?

The Muskingum routing procedure is used for systems that have Storage - Discharge relationships that are hysteretic. That is, for systems for which the outflow is not a unique function of storage.

How to Calculate Storage in Beginning of Time Interval?

Storage in Beginning of Time Interval calculator uses Storage at the Beginning of Time Interval = Storage at the End of Time Interval-(Constant K*(Coefficient x in the Equation*(Inflow at the End of Time Interval-Inflow at the Beginning of Time Interval)+(1-Coefficient x in the Equation)*(Outflow at the End of Time Interval-Outflow at the Beginning of Time Interval))) to calculate the Storage at the Beginning of Time Interval, The Storage in Beginning of Time Interval formula is defined as the water in the system resides or "rests" as it moves from one water reservoir to another. Storage at the Beginning of Time Interval is denoted by S₁ symbol.

How to calculate Storage in Beginning of Time Interval using this online calculator? To use this online calculator for Storage in Beginning of Time Interval, enter Storage at the End of Time Interval (S₂), Constant K (K), Coefficient x in the Equation (x), Inflow at the End of Time Interval (I₂), Inflow at the Beginning of Time Interval (I₁), Outflow at the End of Time Interval (Q₂) & Outflow at the Beginning of Time Interval (Q₁) and hit the calculate button. Here is how the Storage in Beginning of Time Interval calculation can be explained with given input values -> -17 = 35-(4*(1.8*(65-55)+(1-1.8)*(64-48))).

FAQ

What is Storage in Beginning of Time Interval?

The Storage in Beginning of Time Interval formula is defined as the water in the system resides or "rests" as it moves from one water reservoir to another and is represented as S₁ = S₂-(K*(x*(I₂-I₁)+(1-x)*(Q₂-Q₁))) or Storage at the Beginning of Time Interval = Storage at the End of Time Interval-(Constant K*(Coefficient x in the Equation*(Inflow at the End of Time Interval-Inflow at the Beginning of Time Interval)+(1-Coefficient x in the Equation)*(Outflow at the End of Time Interval-Outflow at the Beginning of Time Interval))). Storage at the End of Time Interval is the amount of water stored in reservoirs within the system of hydrological cycle at the end of the time, Constant K is for the catchment to be determined by flood hydrograph characteristics of the catchment, Coefficient x in the Equation of maximum intensity of rainfall in general form in the Muskingum Equation is known as the weighing factor, Inflow at the End of Time Interval is the amount of water entering a body of water at the end of the time, Inflow at the Beginning of Time Interval is the amount of water entering a body of water at the start of the time, Outflow at the End of Time Interval is the removal of water from the hydrological cycle at the end of the time & Outflow at the Beginning of Time Interval is the removal of water from the hydrological cycle at the start of the time.

How to calculate Storage in Beginning of Time Interval?

The Storage in Beginning of Time Interval formula is defined as the water in the system resides or "rests" as it moves from one water reservoir to another is calculated using Storage at the Beginning of Time Interval = Storage at the End of Time Interval-(Constant K*(Coefficient x in the Equation*(Inflow at the End of Time Interval-Inflow at the Beginning of Time Interval)+(1-Coefficient x in the Equation)*(Outflow at the End of Time Interval-Outflow at the Beginning of Time Interval))). To calculate Storage in Beginning of Time Interval, you need Storage at the End of Time Interval (S₂), Constant K (K), Coefficient x in the Equation (x), Inflow at the End of Time Interval (I₂), Inflow at the Beginning of Time Interval (I₁), Outflow at the End of Time Interval (Q₂) & Outflow at the Beginning of Time Interval (Q₁). With our tool, you need to enter the respective value for Storage at the End of Time Interval, Constant K, Coefficient x in the Equation, Inflow at the End of Time Interval, Inflow at the Beginning of Time Interval, Outflow at the End of Time Interval & Outflow at the Beginning of Time Interval and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Storage at the Beginning of Time Interval?

In this formula, Storage at the Beginning of Time Interval uses Storage at the End of Time Interval, Constant K, Coefficient x in the Equation, Inflow at the End of Time Interval, Inflow at the Beginning of Time Interval, Outflow at the End of Time Interval & Outflow at the Beginning of Time Interval. We can use 1 other way(s) to calculate the same, which is/are as follows -

Storage at the Beginning of Time Interval = Storage at the End of Time Interval+((Outflow at the End of Time Interval+Outflow at the Beginning of Time Interval)/2)*Time Interval-((Inflow at the End of Time Interval+Inflow at the Beginning of Time Interval)/2)*Time Interval

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