Discharge over Trapezoidal Notch or Weir Solution

STEP 0: Pre-Calculation Summary
Formula Used
Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)
Qth = 2/3*Cd1*Lweir*sqrt(2*[g])*H^(3/2)+8/15*Cd2*tan(∠A/2)*sqrt(2*[g])*H^(5/2)
This formula uses 1 Constants, 2 Functions, 6 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
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
Theoretical Discharge - (Measured in Cubic Meter per Second) - The Theoretical Discharge is given by the theoretical area and velocity.
Coefficient of Discharge Rectangular - The Coefficient of Discharge Rectangular portion is considered in discharge through the trapezoidal notch.
Length of Weir - (Measured in Meter) - The Length of Weir is the of the base of weir through which discharge is taking place.
Head of Liquid - (Measured in Meter) - The Head of Liquid is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column from the base of its container.
Coefficient of Discharge Triangular - The Coefficient of Discharge Triangular portion is considered in discharge through the trapezoidal notch.
Angle A - (Measured in Radian) - The angle A the space between two intersecting lines or surfaces at or close to the point where they meet.
STEP 1: Convert Input(s) to Base Unit
Coefficient of Discharge Rectangular: 0.63 --> No Conversion Required
Length of Weir: 1.21 Meter --> 1.21 Meter No Conversion Required
Head of Liquid: 10 Meter --> 10 Meter No Conversion Required
Coefficient of Discharge Triangular: 0.65 --> No Conversion Required
Angle A: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Qth = 2/3*Cd1*Lweir*sqrt(2*[g])*H^(3/2)+8/15*Cd2*tan(∠A/2)*sqrt(2*[g])*H^(5/2) --> 2/3*0.63*1.21*sqrt(2*[g])*10^(3/2)+8/15*0.65*tan(0.5235987755982/2)*sqrt(2*[g])*10^(5/2)
Evaluating ... ...
Qth = 201.2609249507
STEP 3: Convert Result to Output's Unit
201.2609249507 Cubic Meter per Second --> No Conversion Required
FINAL ANSWER
201.2609249507 201.2609 Cubic Meter per Second <-- Theoretical Discharge
(Calculation completed in 00.004 seconds)

Credits

Created by Maiarutselvan V
PSG College of Technology (PSGCT), Coimbatore
Maiarutselvan V has created this Calculator and 300+ more calculators!
Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad
Sai Venkata Phanindra Chary Arendra has verified this Calculator and 300+ more calculators!

17 Discharge Calculators

Discharge over Trapezoidal Notch or Weir
Go Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)
Time Required to Empty Reservoir
Go Total Time Taken = ((3*Area of Weir)/(Coefficient of Discharge*Length of Weir*sqrt(2*[g])))*(1/sqrt(Final Height of Liquid)-1/sqrt(Initial Height of Liquid))
Coefficient of Discharge for Time Required to Empty Reservoir
Go Coefficient of Discharge = (3*Area of Weir)/(Total Time Taken*Length of Weir*sqrt(2*[g]))*(1/sqrt(Final Height of Liquid)-1/sqrt(Initial Height of Liquid))
Time Required to Empty Tank with Triangular Weir or Notch
Go Total Time Taken = ((5*Area of Weir)/(4*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])))*(1/(Final Height of Liquid^(3/2))-1/(Initial Height of Liquid^(3/2)))
Discharge over Rectangle Weir for Bazin's formula with Velocity of Approach
Go Discharge Weir = (0.405+0.003/(Head of Liquid+Head Due to Velocity of Approach))*Length of Weir*sqrt(2*[g])*(Head of Liquid+Head Due to Velocity of Approach)^(3/2)
Discharge with Velocity of Approach
Go Discharge = 2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2))
Discharge over Broad-Crested Weir for Head of Liquid at Middle
Go Discharge Weir = Coefficient of Discharge*Length of Weir*sqrt(2*[g]*(Head of Liquid Middle^2*Head of Liquid-Head of Liquid Middle^3))
Discharge over Broad-Crested Weir with Velocity of Approach
Go Discharge Weir = 1.705*Coefficient of Discharge*Length of Weir*((Head of Liquid+Head Due to Velocity of Approach)^(3/2)-Head Due to Velocity of Approach^(3/2))
Discharge over Rectangle Weir with Two End Contractions
Go Discharge Weir = 2/3*Coefficient of Discharge*(Length of Weir-0.2*Head of Liquid)*sqrt(2*[g])*Head of Liquid^(3/2)
Head of Liquid above V-notch
Go Head of Liquid = (Theoretical Discharge/(8/15*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])))^0.4
Discharge over Triangular Notch or Weir
Go Theoretical Discharge = 8/15*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)
Head of Liquid at Crest
Go Head of Liquid = (Theoretical Discharge/(2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])))^(2/3)
Discharge over Rectangle Notch or Weir
Go Theoretical Discharge = 2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)
Discharge without Velocity of Approach
Go Discharge = 2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])*Initial Height of Liquid^(3/2)
Discharge over Rectangle Weir Considering Bazin's formula
Go Discharge Weir = (0.405+0.003/Head of Liquid)*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)
Discharge over Rectangle Weir Considering Francis's formula
Go Discharge = 1.84*Length of Weir*((Initial Height of Liquid+Final Height of Liquid)^(3/2)-Final Height of Liquid^(3/2))
Discharge over Broad-Crested Weir
Go Discharge Weir = 1.705*Coefficient of Discharge*Length of Weir*Head of Liquid^(3/2)

Discharge over Trapezoidal Notch or Weir Formula

Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)
Qth = 2/3*Cd1*Lweir*sqrt(2*[g])*H^(3/2)+8/15*Cd2*tan(∠A/2)*sqrt(2*[g])*H^(5/2)

What is a notch?

A Notch is a device used for measuring the rate of flow of a liquid through a small channel or a tank. It may be defined as an opening in the side of a tank or vessel such as liquid surface in the tank is below the level of opening.

What is a trapezoidal notch or weir?

A trapezoidal notch is a combination of a rectangular notch and two triangular notches. It is, thus obvious that the discharge over such a notch will be the sum of the discharge over the rectangular and triangular notches.

How to Calculate Discharge over Trapezoidal Notch or Weir?

Discharge over Trapezoidal Notch or Weir calculator uses Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2) to calculate the Theoretical Discharge, The Discharge over trapezoidal notch or weir formula is known by considering or combination of both the discharges through the rectangular and triangular notch or weir. Theoretical Discharge is denoted by Qth symbol.

How to calculate Discharge over Trapezoidal Notch or Weir using this online calculator? To use this online calculator for Discharge over Trapezoidal Notch or Weir, enter Coefficient of Discharge Rectangular (Cd1), Length of Weir (Lweir), Head of Liquid (H), Coefficient of Discharge Triangular (Cd2) & Angle A (∠A) and hit the calculate button. Here is how the Discharge over Trapezoidal Notch or Weir calculation can be explained with given input values -> 201.2609 = 2/3*0.63*1.21*sqrt(2*[g])*10^(3/2)+8/15*0.65*tan(0.5235987755982/2)*sqrt(2*[g])*10^(5/2).

FAQ

What is Discharge over Trapezoidal Notch or Weir?
The Discharge over trapezoidal notch or weir formula is known by considering or combination of both the discharges through the rectangular and triangular notch or weir and is represented as Qth = 2/3*Cd1*Lweir*sqrt(2*[g])*H^(3/2)+8/15*Cd2*tan(∠A/2)*sqrt(2*[g])*H^(5/2) or Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2). The Coefficient of Discharge Rectangular portion is considered in discharge through the trapezoidal notch, The Length of Weir is the of the base of weir through which discharge is taking place, The Head of Liquid is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column from the base of its container, The Coefficient of Discharge Triangular portion is considered in discharge through the trapezoidal notch & The angle A the space between two intersecting lines or surfaces at or close to the point where they meet.
How to calculate Discharge over Trapezoidal Notch or Weir?
The Discharge over trapezoidal notch or weir formula is known by considering or combination of both the discharges through the rectangular and triangular notch or weir is calculated using Theoretical Discharge = 2/3*Coefficient of Discharge Rectangular*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)+8/15*Coefficient of Discharge Triangular*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2). To calculate Discharge over Trapezoidal Notch or Weir, you need Coefficient of Discharge Rectangular (Cd1), Length of Weir (Lweir), Head of Liquid (H), Coefficient of Discharge Triangular (Cd2) & Angle A (∠A). With our tool, you need to enter the respective value for Coefficient of Discharge Rectangular, Length of Weir, Head of Liquid, Coefficient of Discharge Triangular & Angle A 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 Theoretical Discharge?
In this formula, Theoretical Discharge uses Coefficient of Discharge Rectangular, Length of Weir, Head of Liquid, Coefficient of Discharge Triangular & Angle A. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Theoretical Discharge = 2/3*Coefficient of Discharge*Length of Weir*sqrt(2*[g])*Head of Liquid^(3/2)
  • Theoretical Discharge = 8/15*Coefficient of Discharge*tan(Angle A/2)*sqrt(2*[g])*Head of Liquid^(5/2)
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