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Discharge considering Approach Velocity Formula

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Francis Discharge is calculated from the empirical formula given by Francis. Check FAQs

Q Fr = (\frac{2}{3}) \cdot C d \cdot \sqrt{2 \cdot g} \cdot (L w - 0.1 \cdot n \cdot H Stillwater) \cdot ({H Stillwater}^{\frac{3}{2}} - {H V}^{\frac{3}{2}})

Q_Fr - Francis Discharge?C_d - Coefficient of Discharge?g - Acceleration due to Gravity?L_w - Length of Weir Crest?n - Number of End Contraction?H_Stillwater - Still Water Head?H_V - Velocity Head?

Discharge considering Approach Velocity Example

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Here is how the Discharge considering Approach Velocity equation looks like with Values.

Here is how the Discharge considering Approach Velocity equation looks like with Units.

Here is how the Discharge considering Approach Velocity equation looks like.

4.9718 = (\frac{2}{3}) \cdot 0.66 \cdot \sqrt{2 \cdot 9.8} \cdot (3 - 0.1 \cdot 4 \cdot 6.6) \cdot ({6.6}^{\frac{3}{2}} - {4.6}^{\frac{3}{2}})

4.9718m³/s = (\frac{2}{3}) \cdot 0.66 \cdot \sqrt{2 \cdot 9.8m/s²} \cdot (3m - 0.1 \cdot 4 \cdot 6.6m) \cdot ({6.6m}^{\frac{3}{2}} - {4.6m}^{\frac{3}{2}})

4.9718 = (\frac{2}{3}) \cdot 0.66 \cdot \sqrt{2 \cdot 9.8} \cdot (3 - 0.1 \cdot 4 \cdot 6.6) \cdot ({6.6}^{\frac{3}{2}} - {4.6}^{\frac{3}{2}})

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Discharge considering Approach Velocity Solution

Follow our step by step solution on how to calculate Discharge considering Approach Velocity?

FIRST Step Consider the formula

Q Fr = (\frac{2}{3}) \cdot C d \cdot \sqrt{2 \cdot g} \cdot (L w - 0.1 \cdot n \cdot H Stillwater) \cdot ({H Stillwater}^{\frac{3}{2}} - {H V}^{\frac{3}{2}})

Next Step Substitute values of Variables

∴

Q Fr = (\frac{2}{3}) \cdot 0.66 \cdot \sqrt{2 \cdot 9.8m/s²} \cdot (3m - 0.1 \cdot 4 \cdot 6.6m) \cdot ({6.6m}^{\frac{3}{2}} - {4.6m}^{\frac{3}{2}})

Next Step Prepare to Evaluate

∴

Q Fr = (\frac{2}{3}) \cdot 0.66 \cdot \sqrt{2 \cdot 9.8} \cdot (3 - 0.1 \cdot 4 \cdot 6.6) \cdot ({6.6}^{\frac{3}{2}} - {4.6}^{\frac{3}{2}})

Next Step Evaluate

∴

Q Fr = 4.97184490717351m³/s

LAST Step Rounding Answer

∴

Q Fr = 4.9718m³/s

Discharge considering Approach Velocity Formula Elements

Variables

Functions

Francis Discharge

Francis Discharge is calculated from the empirical formula given by Francis.

Symbol: Q_Fr

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Francis Discharge

Coefficient of Discharge

The Coefficient of Discharge is ratio of actual discharge to theoretical discharge.

Symbol: C_d

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.2.

Formulas to find Coefficient of Discharge

Acceleration due to Gravity

The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Length of Weir Crest

Length of Weir Crest is the measurement or extent of Weir Crest from end to end.

Symbol: L_w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Weir Crest

Number of End Contraction

Number of End Contraction 1 can be described as the end contractions acting on a channel.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of End Contraction

Still Water Head

Still Water Head is the head of water which is still over weir.

Symbol: H_Stillwater

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Still Water Head

Velocity Head

Velocity Head is represented in the term of length unit, also referred to as kinetic head represents the kinetic energy of the fluid.

Symbol: H_V

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Velocity Head

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.

Syntax: sqrt(Number)

Other formulas in Discharge category

Go Discharge over Weir without considering Velocity

Q Fr' = (\frac{2}{3}) \cdot C d \cdot \sqrt{2 \cdot g} \cdot L w \cdot {S w}^{\frac{3}{2}}

Go Discharge Passing over Weir considering Velocity

Q Fr' = (\frac{2}{3}) \cdot C d \cdot \sqrt{2 \cdot g} \cdot L w \cdot ({(S w + H V)}^{\frac{3}{2}} - {H V}^{\frac{3}{2}})

How to Evaluate Discharge considering Approach Velocity?

Discharge considering Approach Velocity evaluator uses Francis Discharge = (2/3)*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*(Length of Weir Crest-0.1*Number of End Contraction*Still Water Head)*(Still Water Head^(3/2)-Velocity Head^(3/2)) to evaluate the Francis Discharge, Discharge considering approach velocity is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass. Francis Discharge is denoted by Q_Fr symbol.

How to evaluate Discharge considering Approach Velocity using this online evaluator? To use this online evaluator for Discharge considering Approach Velocity, enter Coefficient of Discharge (C_d), Acceleration due to Gravity (g), Length of Weir Crest (L_w), Number of End Contraction (n), Still Water Head (H_Stillwater) & Velocity Head (H_V) and hit the calculate button.

FAQs on Discharge considering Approach Velocity

What is the formula to find Discharge considering Approach Velocity?

The formula of Discharge considering Approach Velocity is expressed as Francis Discharge = (2/3)*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*(Length of Weir Crest-0.1*Number of End Contraction*Still Water Head)*(Still Water Head^(3/2)-Velocity Head^(3/2)). Here is an example- 4.971845 = (2/3)*0.66*sqrt(2*9.8)*(3-0.1*4*6.6)*(6.6^(3/2)-4.6^(3/2)).

How to calculate Discharge considering Approach Velocity?

With Coefficient of Discharge (C_d), Acceleration due to Gravity (g), Length of Weir Crest (L_w), Number of End Contraction (n), Still Water Head (H_Stillwater) & Velocity Head (H_V) we can find Discharge considering Approach Velocity using the formula - Francis Discharge = (2/3)*Coefficient of Discharge*sqrt(2*Acceleration due to Gravity)*(Length of Weir Crest-0.1*Number of End Contraction*Still Water Head)*(Still Water Head^(3/2)-Velocity Head^(3/2)). This formula also uses Square Root (sqrt) function(s).

Can the Discharge considering Approach Velocity be negative?

No, the Discharge considering Approach Velocity, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Discharge considering Approach Velocity?

Discharge considering Approach Velocity is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Discharge considering Approach Velocity can be measured.

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Discharge considering Approach Velocity Formula

Discharge considering Approach Velocity Example

Discharge considering Approach Velocity Solution

Discharge considering Approach Velocity Formula Elements

Other formulas in Discharge category

How to Evaluate Discharge considering Approach Velocity?

FAQs on Discharge considering Approach Velocity

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