Theoretical Discharge through Pipe Calculator

✖Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe).ⓘ Cross Section Area 1 [A_i]			+10% -10%
✖Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.ⓘ Cross Section Area 2 [A_f]			+10% -10%
✖Venturi headt is the difference between pressure head at inlet and pressure head at the throat.ⓘ Venturi Head [h_venturi]			+10% -10%

✖The Theoretical Discharge is given by the theoretical area and velocity.ⓘ Theoretical Discharge through Pipe [Q_th]

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Formula

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Theoretical Discharge through Pipe

Formula

`"Q"_{"th"} = ("A"_{"i"}*"A"_{"f"}*(sqrt(2*"[g]"*"h"_{"venturi"})))/(sqrt(("A"_{"i"})^(2)-("A"_{"f"})^(2)))`

Example

`"1.276671m³/s"=("7.1m²"*"1.8m²"*(sqrt(2*"[g]"*"24mm")))/(sqrt(("7.1m²")^(2)-("1.8m²")^(2)))`

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Theoretical Discharge through Pipe Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theoretical Discharge = (Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]*Venturi Head)))/(sqrt((Cross Section Area 1)^(2)-(Cross Section Area 2)^(2)))
Q_th = (A_i*A_f*(sqrt(2*[g]*h_venturi)))/(sqrt((A_i)^(2)-(A_f)^(2)))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

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

Theoretical Discharge - (Measured in Cubic Meter per Second) - The Theoretical Discharge is given by the theoretical area and velocity.
Cross Section Area 1 - (Measured in Square Meter) - Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe).
Cross Section Area 2 - (Measured in Square Meter) - Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure.
Venturi Head - (Measured in Meter) - Venturi headt is the difference between pressure head at inlet and pressure head at the throat.

STEP 1: Convert Input(s) to Base Unit

Cross Section Area 1: 7.1 Square Meter --> 7.1 Square Meter No Conversion Required
Cross Section Area 2: 1.8 Square Meter --> 1.8 Square Meter No Conversion Required
Venturi Head: 24 Millimeter --> 0.024 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_th = (A_i*A_f*(sqrt(2*[g]*h_venturi)))/(sqrt((A_i)^(2)-(A_f)^(2))) --> (7.1*1.8*(sqrt(2*[g]*0.024)))/(sqrt((7.1)^(2)-(1.8)^(2)))

Evaluating ... ...

Q_th = 1.27667064378257

STEP 3: Convert Result to Output's Unit

1.27667064378257 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

1.27667064378257 ≈ 1.276671 Cubic Meter per Second <-- Theoretical Discharge

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Equations of Motion and Energy Equation » Venturimeter » Theoretical Discharge through Pipe

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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Bhilai Institute of Technology (BIT), Raipur

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< 10+ Venturimeter Calculators

Theoretical Discharge through Pipe

Go Theoretical Discharge = (Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]*Venturi Head)))/(sqrt((Cross Section Area 1)^(2)-(Cross Section Area 2)^(2)))

Venturi Head given Theoretical Discharge through Pipe

Go Venturi Head = ((Theoretical Discharge/(Cross Section Area 1*Cross Section Area 2))*(sqrt(((Cross Section Area 1)^2-(Cross Section Area 2)^2)/(2*[g]))))^2

Inlet Area given Theoretical Discharge

Go Cross Section Area 1 = sqrt(((Theoretical Discharge*Cross Section Area 2)^2)/((Theoretical Discharge)^2-(Cross Section Area 2^2*2*[g]*Venturi Head)))

Throat area given Theoretical Discharge

Go Cross Section Area 2 = sqrt((Cross Section Area 1*Theoretical Discharge)^2/((Cross Section Area 1^2*2*[g]*Venturi Head)+Theoretical Discharge^2))

Venturi Head given Difference in Levels of Manometric Liquid in Two Limbs

Go Venturi Head = Length of Venturimeter*(Weight per unit Volume of Manometer Fluid/Specific Weight of Liquid-1)

Density of Manometric Liquid given Venturi Head

Go Weight per unit Volume of Manometer Fluid = Specific Weight of Liquid*(Venturi Head/Length of Venturimeter+1)

Density of Liquid in Pipe given Venturi Head

Go Specific Weight of Liquid = Weight per unit Volume of Manometer Fluid/(Venturi Head/Length of Venturimeter+1)

Theoretical Discharge given Coefficient of Discharge

Go Theoretical Discharge = Actual Discharge/Coefficient of Discharge

Actual Discharge given Coefficient of Discharge

Go Actual Discharge = Theoretical Velocity*Coefficient of Discharge

Coefficient of Discharge given Discharges

Go Coefficient of Discharge = Actual Discharge/Theoretical Velocity

Theoretical Discharge through Pipe Formula

What is Venturi Meter?

Venturi Meter is flow measurement instruments which use a converging section of pipe to give an increase in the flow velocity and a corresponding pressure drop from which the flowrate can be deduced. They have been in common use for many years, especially in the water supply industry.

How to Calculate Theoretical Discharge through Pipe?

Theoretical Discharge through Pipe calculator uses Theoretical Discharge = (Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]*Venturi Head)))/(sqrt((Cross Section Area 1)^(2)-(Cross Section Area 2)^(2))) to calculate the Theoretical Discharge, The Theoretical Discharge through Pipe formula is defined as the rate of flow of a liquid through a venturi meter channel. Theoretical Discharge is denoted by Q_th symbol.

How to calculate Theoretical Discharge through Pipe using this online calculator? To use this online calculator for Theoretical Discharge through Pipe, enter Cross Section Area 1 (A_i), Cross Section Area 2 (A_f) & Venturi Head (h_venturi) and hit the calculate button. Here is how the Theoretical Discharge through Pipe calculation can be explained with given input values -> 1.276671 = (7.1*1.8*(sqrt(2*[g]*0.024)))/(sqrt((7.1)^(2)-(1.8)^(2))).

FAQ

What is Theoretical Discharge through Pipe?

The Theoretical Discharge through Pipe formula is defined as the rate of flow of a liquid through a venturi meter channel and is represented as Q_th = (A_i*A_f*(sqrt(2*[g]*h_venturi)))/(sqrt((A_i)^(2)-(A_f)^(2))) or Theoretical Discharge = (Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]*Venturi Head)))/(sqrt((Cross Section Area 1)^(2)-(Cross Section Area 2)^(2))). Cross Section Area 1 is the area of cross section at the inlet of the structure (venturimeter or pipe), Cross Section Area 2 is defined as the area of cross-section at the throat (venturimeter) of the structure & Venturi headt is the difference between pressure head at inlet and pressure head at the throat.

How to calculate Theoretical Discharge through Pipe?

The Theoretical Discharge through Pipe formula is defined as the rate of flow of a liquid through a venturi meter channel is calculated using Theoretical Discharge = (Cross Section Area 1*Cross Section Area 2*(sqrt(2*[g]*Venturi Head)))/(sqrt((Cross Section Area 1)^(2)-(Cross Section Area 2)^(2))). To calculate Theoretical Discharge through Pipe, you need Cross Section Area 1 (A_i), Cross Section Area 2 (A_f) & Venturi Head (h_venturi). With our tool, you need to enter the respective value for Cross Section Area 1, Cross Section Area 2 & Venturi 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 Theoretical Discharge?

In this formula, Theoretical Discharge uses Cross Section Area 1, Cross Section Area 2 & Venturi Head. We can use 1 other way(s) to calculate the same, which is/are as follows -

Theoretical Discharge = Actual Discharge/Coefficient of Discharge

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