Coefficient of Discharge given Discharge if Velocity considered Calculator

✖Francis Discharge is calculated from the empirical formula given by Francis.ⓘ Francis Discharge [Q_Fr]			+10% -10%
✖The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Length of Weir Crest is the measurement or extent of Weir Crest from end to end.ⓘ Length of Weir Crest [L_w]			+10% -10%
✖Number of End Contraction 1 can be described as the end contractions acting on a channel.ⓘ Number of End Contraction [n]			+10% -10%
✖Still Water Head is the head of water which is still over weir.ⓘ Still Water Head [H_Stillwater]			+10% -10%
✖Velocity Head is represented in the term of length unit, also referred to as kinetic head represents the kinetic energy of the fluid.ⓘ Velocity Head [H_V]			+10% -10%

✖The Coefficient of Discharge is ratio of actual discharge to theoretical discharge.ⓘ Coefficient of Discharge given Discharge if Velocity considered [C_d]

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Coefficient of Discharge given Discharge if Velocity considered Solution

STEP 0: Pre-Calculation Summary

Formula Used

Coefficient of Discharge = (Francis Discharge*3)/(2*(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)))
C_d = (Q_Fr*3)/(2*(sqrt(2*g))*(L_w-0.1*n*H_Stillwater)*(H_Stillwater^(3/2)-H_V^(3/2)))
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

Coefficient of Discharge - The Coefficient of Discharge is ratio of actual discharge to theoretical discharge.
Francis Discharge - (Measured in Cubic Meter per Second) - Francis Discharge is calculated from the empirical formula given by Francis.
Acceleration due to Gravity - (Measured in Meter per Square Second) - The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
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.
Still Water Head - (Measured in Meter) - Still Water Head is the head of water which is still over weir.
Velocity Head - (Measured in Meter) - Velocity Head is represented in the term of length unit, also referred to as kinetic head represents the kinetic energy of the fluid.

STEP 1: Convert Input(s) to Base Unit

Francis Discharge: 8 Cubic Meter per Second --> 8 Cubic Meter per Second No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Length of Weir Crest: 3 Meter --> 3 Meter No Conversion Required
Number of End Contraction: 4 --> No Conversion Required
Still Water Head: 6.6 Meter --> 6.6 Meter No Conversion Required
Velocity Head: 4.6 Meter --> 4.6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C_d = (Q_Fr*3)/(2*(sqrt(2*g))*(L_w-0.1*n*H_Stillwater)*(H_Stillwater^(3/2)-H_V^(3/2))) --> (8*3)/(2*(sqrt(2*9.8))*(3-0.1*4*6.6)*(6.6^(3/2)-4.6^(3/2)))

Evaluating ... ...

C_d = 1.06198002926074

STEP 3: Convert Result to Output's Unit

1.06198002926074 --> No Conversion Required

FINAL ANSWER

1.06198002926074 ≈ 1.06198 <-- Coefficient of Discharge

(Calculation completed in 00.020 seconds)

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National Institute of Technology (NIT), Warangal

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< Flow Over Rectangular Sharp Crested Weir or Notch Calculators

Coefficient of Discharge given Discharge if Velocity considered

LaTeX Go Coefficient of Discharge = (Francis Discharge*3)/(2*(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)))

Coefficient of Discharge given Discharge if Velocity not considered

LaTeX Go Coefficient of Discharge = (Francis Discharge*3)/(2*(sqrt(2*Acceleration due to Gravity))*(Length of Weir Crest-0.1*Number of End Contraction*Height of Water above Crest of Weir)*Height of Water above Crest of Weir^(3/2))

Coefficient of Discharge given Discharge Passing over Weir considering Velocity

LaTeX Go Coefficient of Discharge = (Francis Discharge with Suppressed End*3)/(2*(sqrt(2*Acceleration due to Gravity))*Length of Weir Crest*((Height of Water above Crest of Weir+Velocity Head)^(3/2)-Velocity Head^(3/2)))

Coefficient of Discharge given Discharge over Weir without considering Velocity

LaTeX Go Coefficient of Discharge = (Francis Discharge with Suppressed End*3)/(2*(sqrt(2*Acceleration due to Gravity))*Length of Weir Crest*Height of Water above Crest of Weir^(3/2))

Coefficient of Discharge given Discharge if Velocity considered Formula

LaTeX Go

What is Discharge?

The Discharge Over the Weir is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass. A commonly applied methodology for measuring, and estimating, the discharge of a river is based on a simplified form of the continuity equation. The equation implies that for any incompressible fluid, such as liquid water, the discharge (Q) is equal to the product of the stream's cross-sectional area (A) and its mean velocity.

What is a weir?

A weir or low head dam is a barrier across the width of a river that alters the flow characteristics of water and usually results in a change in the height of the river level. They are also used to control the flow of water for outlets of lakes, ponds, and reservoirs. Weirs are fixed barriers across a river or stream that force water to flow over their tops, where the height of the water above the weir can be used to calculate flow.
A weir, as defined in the USBR measurement manual, is simply an overflow structure built perpendicular to an open channel axis to measure the rate of flow of water. In other words, a weir is essentially a partial dam. It works by raising the water level upstream of the weir, and then forcing the water to spill over.

How to Calculate Coefficient of Discharge given Discharge if Velocity considered?

Coefficient of Discharge given Discharge if Velocity considered calculator uses Coefficient of Discharge = (Francis Discharge*3)/(2*(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 calculate the Coefficient of Discharge, Coefficient of Discharge given Discharge if Velocity considered is ratio of actual discharge through nozzle or orifice to theoretical discharge. Coefficient of Discharge is denoted by C_d symbol.

How to calculate Coefficient of Discharge given Discharge if Velocity considered using this online calculator? To use this online calculator for Coefficient of Discharge given Discharge if Velocity considered, enter Francis Discharge (Q_Fr), 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. Here is how the Coefficient of Discharge given Discharge if Velocity considered calculation can be explained with given input values -> 1.06198 = (8*3)/(2*(sqrt(2*9.8))*(3-0.1*4*6.6)*(6.6^(3/2)-4.6^(3/2))).

FAQ

What is Coefficient of Discharge given Discharge if Velocity considered?

Coefficient of Discharge given Discharge if Velocity considered is ratio of actual discharge through nozzle or orifice to theoretical discharge and is represented as C_d = (Q_Fr*3)/(2*(sqrt(2*g))*(L_w-0.1*n*H_Stillwater)*(H_Stillwater^(3/2)-H_V^(3/2))) or Coefficient of Discharge = (Francis Discharge*3)/(2*(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))). Francis Discharge is calculated from the empirical formula given by Francis, The Acceleration due to Gravity is acceleration gained by an object because of gravitational force, 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, Still Water Head is the head of water which is still over weir & Velocity Head is represented in the term of length unit, also referred to as kinetic head represents the kinetic energy of the fluid.

How to calculate Coefficient of Discharge given Discharge if Velocity considered?

Coefficient of Discharge given Discharge if Velocity considered is ratio of actual discharge through nozzle or orifice to theoretical discharge is calculated using Coefficient of Discharge = (Francis Discharge*3)/(2*(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 calculate Coefficient of Discharge given Discharge if Velocity considered, you need Francis Discharge (Q_Fr), 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). With our tool, you need to enter the respective value for Francis Discharge, Acceleration due to Gravity, Length of Weir Crest, Number of End Contraction, Still Water Head & Velocity Head 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 Coefficient of Discharge?

In this formula, Coefficient of Discharge uses Francis Discharge, Acceleration due to Gravity, Length of Weir Crest, Number of End Contraction, Still Water Head & Velocity Head. We can use 3 other way(s) to calculate the same, which is/are as follows -

Coefficient of Discharge = (Francis Discharge with Suppressed End*3)/(2*(sqrt(2*Acceleration due to Gravity))*Length of Weir Crest*Height of Water above Crest of Weir^(3/2))
Coefficient of Discharge = (Francis Discharge with Suppressed End*3)/(2*(sqrt(2*Acceleration due to Gravity))*Length of Weir Crest*((Height of Water above Crest of Weir+Velocity Head)^(3/2)-Velocity Head^(3/2)))
Coefficient of Discharge = (Francis Discharge*3)/(2*(sqrt(2*Acceleration due to Gravity))*(Length of Weir Crest-0.1*Number of End Contraction*Height of Water above Crest of Weir)*Height of Water above Crest of Weir^(3/2))

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