Inlet Area given Theoretical Discharge Calculator

✖The Theoretical Discharge refers to the ideal flow rate of a fluid through a system, calculated under perfect conditions without considering any real-world losses like friction or turbulence.ⓘ Theoretical Discharge [Q_th]			+10% -10%
✖The Cross Section Area 2 refers to the area of cross-section at the throat (venturi meter) of the structure.ⓘ Cross Section Area 2 [A_f]			+10% -10%
✖The Venturi head refers to the difference between pressure head at inlet and pressure head at the throat.ⓘ Venturi Head [h_venturi]			+10% -10%

✖The Cross Section Area 1 refers to the area of cross section at the inlet of the structure (venturi meter or pipe).ⓘ Inlet Area given Theoretical Discharge [A_i]

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Formula

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Inlet Area given Theoretical Discharge

Formula

A i = \sqrt{\frac{{(Q th \cdot A f)}^{2}}{{(Q th)}^{2} - ({A f}^{2} \cdot 2 \cdot [g] \cdot h venturi)}}

Example

7.073493 m² = \sqrt{\frac{{(1.277 m³/s \cdot 1.8 m²)}^{2}}{{(1.277 m³/s)}^{2} - ({1.8 m²}^{2} \cdot 2 \cdot [g] \cdot 24 mm)}}

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Inlet Area given Theoretical Discharge Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Cross Section Area 1 - (Measured in Square Meter) - The Cross Section Area 1 refers to the area of cross section at the inlet of the structure (venturi meter or pipe).
Theoretical Discharge - (Measured in Cubic Meter per Second) - The Theoretical Discharge refers to the ideal flow rate of a fluid through a system, calculated under perfect conditions without considering any real-world losses like friction or turbulence.
Cross Section Area 2 - (Measured in Square Meter) - The Cross Section Area 2 refers to the area of cross-section at the throat (venturi meter) of the structure.
Venturi Head - (Measured in Meter) - The Venturi head refers to the difference between pressure head at inlet and pressure head at the throat.

STEP 1: Convert Input(s) to Base Unit

Theoretical Discharge: 1.277 Cubic Meter per Second --> 1.277 Cubic Meter per Second 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

A_i = sqrt(((Q_th*A_f)^2)/((Q_th)^2-(A_f^2*2*[g]*h_venturi))) --> sqrt(((1.277*1.8)^2)/((1.277)^2-(1.8^2*2*[g]*0.024)))

Evaluating ... ...

A_i = 7.07349298747947

STEP 3: Convert Result to Output's Unit

7.07349298747947 Square Meter --> No Conversion Required

FINAL ANSWER

7.07349298747947 ≈ 7.073493 Square Meter <-- Cross Section Area 1

(Calculation completed in 00.020 seconds)

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Created by Rithik Agrawal

National Institute of Technology Karnataka (NITK), Surathkal

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National Institute of Technology (NIT), Warangal

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< Venturi Meter 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))

Inlet Area given Theoretical Discharge Formula

What is Conservation of Energy?

Conservation of energy, principle of physics according to which the energy of interacting bodies or particles in a closed system remains constant. When the pendulum swings back down, the potential energy is converted back into kinetic energy. At all times, the sum of potential and kinetic energy is constant.

How to Calculate Inlet Area given Theoretical Discharge?

Inlet Area given Theoretical Discharge calculator uses Cross Section Area 1 = sqrt(((Theoretical Discharge*Cross Section Area 2)^2)/((Theoretical Discharge)^2-(Cross Section Area 2^2*2*[g]*Venturi Head))) to calculate the Cross Section Area 1, The Inlet Area given Theoretical Discharge formula is defined as the area at a particular section of pipe. Cross Section Area 1 is denoted by A_i symbol.

How to calculate Inlet Area given Theoretical Discharge using this online calculator? To use this online calculator for Inlet Area given Theoretical Discharge, enter Theoretical Discharge (Q_th), Cross Section Area 2 (A_f) & Venturi Head (h_venturi) and hit the calculate button. Here is how the Inlet Area given Theoretical Discharge calculation can be explained with given input values -> 7.073493 = sqrt(((1.277*1.8)^2)/((1.277)^2-(1.8^2*2*[g]*0.024))).

FAQ

What is Inlet Area given Theoretical Discharge?

The Inlet Area given Theoretical Discharge formula is defined as the area at a particular section of pipe and is represented as A_i = sqrt(((Q_th*A_f)^2)/((Q_th)^2-(A_f^2*2*[g]*h_venturi))) or Cross Section Area 1 = sqrt(((Theoretical Discharge*Cross Section Area 2)^2)/((Theoretical Discharge)^2-(Cross Section Area 2^2*2*[g]*Venturi Head))). The Theoretical Discharge refers to the ideal flow rate of a fluid through a system, calculated under perfect conditions without considering any real-world losses like friction or turbulence, The Cross Section Area 2 refers to the area of cross-section at the throat (venturi meter) of the structure & The Venturi head refers to the difference between pressure head at inlet and pressure head at the throat.

How to calculate Inlet Area given Theoretical Discharge?

The Inlet Area given Theoretical Discharge formula is defined as the area at a particular section of pipe is calculated using Cross Section Area 1 = sqrt(((Theoretical Discharge*Cross Section Area 2)^2)/((Theoretical Discharge)^2-(Cross Section Area 2^2*2*[g]*Venturi Head))). To calculate Inlet Area given Theoretical Discharge, you need Theoretical Discharge (Q_th), Cross Section Area 2 (A_f) & Venturi Head (h_venturi). With our tool, you need to enter the respective value for Theoretical Discharge, 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.

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