Time Required to Lower Liquid Surface using Francis Formula Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time Interval for Francis = ((2*Cross-Sectional Area of Reservoir)/(1.84*(Length of Weir Crest-(0.1*Number of End Contraction*Average Height of Downstream and Upstream))))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
tF = ((2*AR)/(1.84*(Lw-(0.1*n*HAvg))))*(1/sqrt(h2)-1/sqrt(HUpstream))
This formula uses 1 Functions, 7 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Time Interval for Francis - (Measured in Second) - Time Interval for Francis is calculated with the help of francis formula.
Cross-Sectional Area of Reservoir - (Measured in Square Meter) - Cross-Sectional Area of Reservoir is the area of a reservoir that is obtained when a three-dimensional reservoir shape is sliced perpendicular to some specified axis at a point.
Length of Weir Crest - (Measured in Meter) - Length of Weir Crest is the measurement or extent of Weir Crest from end to end.
Number of End Contraction - Number of End Contraction 1 can be described as the end contractions acting on a channel.
Average Height of Downstream and Upstream - (Measured in Meter) - Average Height of Downstream and Upstream is the height of downstream and upstream.
Head on Downstream of Weir - (Measured in Meter) - Head on Downstream of Weir pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.
Head on Upstream of Weir - (Measured in Meter) - Head on Upstream of Weirr pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.
STEP 1: Convert Input(s) to Base Unit
Cross-Sectional Area of Reservoir: 13 Square Meter --> 13 Square Meter No Conversion Required
Length of Weir Crest: 3 Meter --> 3 Meter No Conversion Required
Number of End Contraction: 4 --> No Conversion Required
Average Height of Downstream and Upstream: 5.5 Meter --> 5.5 Meter No Conversion Required
Head on Downstream of Weir: 5.1 Meter --> 5.1 Meter No Conversion Required
Head on Upstream of Weir: 10.1 Meter --> 10.1 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tF = ((2*AR)/(1.84*(Lw-(0.1*n*HAvg))))*(1/sqrt(h2)-1/sqrt(HUpstream)) --> ((2*13)/(1.84*(3-(0.1*4*5.5))))*(1/sqrt(5.1)-1/sqrt(10.1))
Evaluating ... ...
tF = 2.26350233027382
STEP 3: Convert Result to Output's Unit
2.26350233027382 Second --> No Conversion Required
FINAL ANSWER
2.26350233027382 2.263502 Second <-- Time Interval for Francis
(Calculation completed in 00.020 seconds)

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National Institute of Technology (NIT), Warangal
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19 Time Required to Empty a Reservoir with Rectangular Weir Calculators

Coefficient of Discharge for Time Required to Lower Liquid Surface
Go Coefficient of Discharge = ((2*Cross-Sectional Area of Reservoir)/((2/3)*Time Interval*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
Cross Sectional Area given Time required to Lower Liquid Surface
Go Cross-Sectional Area of Reservoir = (Time Interval*(2/3)*Coefficient of Discharge* sqrt(2*Acceleration due to Gravity)*Length of Weir Crest)/(2*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir)))
Length of Crest for time required to Lower Liquid Surface
Go Length of Weir Crest = ((2*Cross-Sectional Area of Reservoir)/((2/3)*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*Time Interval))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
Time Required to Lower Liquid Surface
Go Time Interval = ((2*Cross-Sectional Area of Reservoir)/((2/3)*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*Length of Weir Crest))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
Head given Time Required to Lower Liquid Surface using Francis Formula
Go Average Height of Downstream and Upstream = (((2*Cross-Sectional Area of Reservoir)/(1.84*Time Interval for Francis))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))-Length of Weir Crest)/(-0.1*Number of End Contraction)
Length of Crest given Time Required to Lower Liquid Surface using Francis Formula
Go Length of Weir Crest = (((2*Cross-Sectional Area of Reservoir)/(1.84*Time Interval for Francis))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir)))+(0.1*Number of End Contraction*Average Height of Downstream and Upstream)
Time Required to Lower Liquid Surface using Francis Formula
Go Time Interval for Francis = ((2*Cross-Sectional Area of Reservoir)/(1.84*(Length of Weir Crest-(0.1*Number of End Contraction*Average Height of Downstream and Upstream))))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
Head1 given Time Required to Lower Liquid for Triangular Notch
Go Head on Upstream of Weir = (1/((1/Head on Downstream of Weir^(3/2))-((Time Interval*(8/15)*Coefficient of Discharge* sqrt(2*Acceleration due to Gravity)*tan(Theta/2))/((2/3)*Cross-Sectional Area of Reservoir))))^(2/3)
Head1 given Time Required to Lower Liquid Surface
Go Head on Upstream of Weir = ((1/((1/sqrt(Head on Downstream of Weir))-(Time Interval*(2/3)*Coefficient of Discharge* sqrt(2*Acceleration due to Gravity)*Length of Weir Crest)/(2*Cross-Sectional Area of Reservoir)))^2)
Coefficient of Discharge given Time required to Lower Liquid for Triangular Notch
Go Coefficient of Discharge = (((2/3)*Cross-Sectional Area of Reservoir)/((8/15)*Time Interval*sqrt(2*Acceleration due to Gravity)*tan(Theta/2)))*((1/Head on Downstream of Weir^(3/2))-(1/Head on Upstream of Weir^(3/2)))
Cross Sectional Area given Time required to Lower Liquid for Triangular Notch
Go Cross-Sectional Area of Reservoir = (Time Interval*(8/15)*Coefficient of Discharge* sqrt(2*Acceleration due to Gravity)*tan(Theta/2))/((2/3)*((1/Head on Downstream of Weir^(3/2))-(1/Head on Upstream of Weir^(3/2))))
Head2 given Time Required to Lower Liquid for Triangular Notch
Go Head on Downstream of Weir = (1/(((Time Interval*(8/15)*Coefficient of Discharge* sqrt(2*Acceleration due to Gravity)*tan(Theta/2))/((2/3)*Cross-Sectional Area of Reservoir))+(1/Head on Upstream of Weir^(3/2))))^(2/3)
Time Required to Lower Liquid Surface for Triangular Notch
Go Time Interval = (((2/3)*Cross-Sectional Area of Reservoir)/((8/15)*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*tan(Theta/2)))*((1/Head on Downstream of Weir^(3/2))-(1/Head on Upstream of Weir^(3/2)))
Head2 given Time Required to Lower Liquid Surface
Go Head on Downstream of Weir = (1/((Time Interval*(2/3)*Coefficient of Discharge* sqrt(2*Acceleration due to Gravity)*Length of Weir Crest)/(2*Cross-Sectional Area of Reservoir)+(1/sqrt(Head on Upstream of Weir))))^2
Cross Sectional Area given time required to Lower Liquid Surface using Bazins Formula
Go Cross-Sectional Area of Reservoir = (Time Interval*Bazins Coefficient*sqrt(2*Acceleration due to Gravity))/((1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))*2)
Bazins Constant given Time Required to Lower Liquid Surface
Go Bazins Coefficient = ((2*Cross-Sectional Area of Reservoir)/(Time Interval*sqrt(2*Acceleration due to Gravity)))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
Time Required to Lower Liquid Surface using Bazins Formula
Go Time Interval = ((2*Cross-Sectional Area of Reservoir)/(Bazins Coefficient*sqrt(2*Acceleration due to Gravity)))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
Head1 given Time Required to Lower Liquid Surface using Bazins Formula
Go Head on Upstream of Weir = ((1/((Time Interval*Bazins Coefficient*sqrt(2*Acceleration due to Gravity))/(2*Cross-Sectional Area of Reservoir)-(1/sqrt(Head on Downstream of Weir))))^2)
Head2 given Time Required to Lower Liquid Surface using Bazins Formula
Go Head on Downstream of Weir = (1/((Time Interval*Bazins Coefficient*sqrt(2*Acceleration due to Gravity))/(2*Cross-Sectional Area of Reservoir)+(1/sqrt(Head on Upstream of Weir))))^2

Time Required to Lower Liquid Surface using Francis Formula Formula

Time Interval for Francis = ((2*Cross-Sectional Area of Reservoir)/(1.84*(Length of Weir Crest-(0.1*Number of End Contraction*Average Height of Downstream and Upstream))))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir))
tF = ((2*AR)/(1.84*(Lw-(0.1*n*HAvg))))*(1/sqrt(h2)-1/sqrt(HUpstream))

What is meant by Head?

Hydraulic head is a specific measurement of liquid pressure above a vertical datum. It is usually measured as a liquid surface elevation.

How to Calculate Time Required to Lower Liquid Surface using Francis Formula?

Time Required to Lower Liquid Surface using Francis Formula calculator uses Time Interval for Francis = ((2*Cross-Sectional Area of Reservoir)/(1.84*(Length of Weir Crest-(0.1*Number of End Contraction*Average Height of Downstream and Upstream))))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir)) to calculate the Time Interval for Francis, The Time Required to Lower Liquid Surface using Francis Formula as amount of time taken by lowering water surface from Head1 to Head2. Time Interval for Francis is denoted by tF symbol.

How to calculate Time Required to Lower Liquid Surface using Francis Formula using this online calculator? To use this online calculator for Time Required to Lower Liquid Surface using Francis Formula, enter Cross-Sectional Area of Reservoir (AR), Length of Weir Crest (Lw), Number of End Contraction (n), Average Height of Downstream and Upstream (HAvg), Head on Downstream of Weir (h2) & Head on Upstream of Weir (HUpstream) and hit the calculate button. Here is how the Time Required to Lower Liquid Surface using Francis Formula calculation can be explained with given input values -> 2.263502 = ((2*13)/(1.84*(3-(0.1*4*5.5))))*(1/sqrt(5.1)-1/sqrt(10.1)).

FAQ

What is Time Required to Lower Liquid Surface using Francis Formula?
The Time Required to Lower Liquid Surface using Francis Formula as amount of time taken by lowering water surface from Head1 to Head2 and is represented as tF = ((2*AR)/(1.84*(Lw-(0.1*n*HAvg))))*(1/sqrt(h2)-1/sqrt(HUpstream)) or Time Interval for Francis = ((2*Cross-Sectional Area of Reservoir)/(1.84*(Length of Weir Crest-(0.1*Number of End Contraction*Average Height of Downstream and Upstream))))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir)). Cross-Sectional Area of Reservoir is the area of a reservoir that is obtained when a three-dimensional reservoir shape is sliced perpendicular to some specified axis at a point, Length of Weir Crest is the measurement or extent of Weir Crest from end to end, Number of End Contraction 1 can be described as the end contractions acting on a channel, Average Height of Downstream and Upstream is the height of downstream and upstream, Head on Downstream of Weir pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures & Head on Upstream of Weirr pertains to the energy status of water in water flow systems and is useful for describing flow in hydraulic structures.
How to calculate Time Required to Lower Liquid Surface using Francis Formula?
The Time Required to Lower Liquid Surface using Francis Formula as amount of time taken by lowering water surface from Head1 to Head2 is calculated using Time Interval for Francis = ((2*Cross-Sectional Area of Reservoir)/(1.84*(Length of Weir Crest-(0.1*Number of End Contraction*Average Height of Downstream and Upstream))))*(1/sqrt(Head on Downstream of Weir)-1/sqrt(Head on Upstream of Weir)). To calculate Time Required to Lower Liquid Surface using Francis Formula, you need Cross-Sectional Area of Reservoir (AR), Length of Weir Crest (Lw), Number of End Contraction (n), Average Height of Downstream and Upstream (HAvg), Head on Downstream of Weir (h2) & Head on Upstream of Weir (HUpstream). With our tool, you need to enter the respective value for Cross-Sectional Area of Reservoir, Length of Weir Crest, Number of End Contraction, Average Height of Downstream and Upstream, Head on Downstream of Weir & Head on Upstream of Weir 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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