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Inlet Area given Theoretical Discharge Formula

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The Cross Section Area 1 refers to the area of cross section at the inlet of the structure (venturi meter or pipe). Check FAQs

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

A_i - Cross Section Area 1?Q_th - Theoretical Discharge?A_f - Cross Section Area 2?h_venturi - Venturi Head?[g] - Gravitational acceleration on Earth?

Inlet Area given Theoretical Discharge Example

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Here is how the Inlet Area given Theoretical Discharge equation looks like with Values.

Here is how the Inlet Area given Theoretical Discharge equation looks like with Units.

Here is how the Inlet Area given Theoretical Discharge equation looks like.

7.0735 = \sqrt{\frac{{(1.277 \cdot 1.8)}^{2}}{{(1.277)}^{2} - ({1.8}^{2} \cdot 2 \cdot 9.8066 \cdot 24)}}

7.0735m² = \sqrt{\frac{{(1.277m³/s \cdot 1.8m²)}^{2}}{{(1.277m³/s)}^{2} - ({1.8m²}^{2} \cdot 2 \cdot 9.8066m/s² \cdot 24mm)}}

7.0735 = \sqrt{\frac{{(1.277 \cdot 1.8)}^{2}}{{(1.277)}^{2} - ({1.8}^{2} \cdot 2 \cdot 9.8066 \cdot 24)}}

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Inlet Area given Theoretical Discharge Solution

Follow our step by step solution on how to calculate Inlet Area given Theoretical Discharge?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

A i = \sqrt{\frac{{(1.277m³/s \cdot 1.8m²)}^{2}}{{(1.277m³/s)}^{2} - ({1.8m²}^{2} \cdot 2 \cdot 9.8066m/s² \cdot 24mm)}}

Next Step Convert Units

∴

A i = \sqrt{\frac{{(1.277m³/s \cdot 1.8m²)}^{2}}{{(1.277m³/s)}^{2} - ({1.8m²}^{2} \cdot 2 \cdot 9.8066m/s² \cdot 0.024m)}}

Next Step Prepare to Evaluate

∴

A i = \sqrt{\frac{{(1.277 \cdot 1.8)}^{2}}{{(1.277)}^{2} - ({1.8}^{2} \cdot 2 \cdot 9.8066 \cdot 0.024)}}

Next Step Evaluate

∴

A i = 7.07349298747947m²

LAST Step Rounding Answer

∴

A i = 7.0735m²

Inlet Area given Theoretical Discharge Formula Elements

Variables

Constants

Functions

Cross Section Area 1

The Cross Section Area 1 refers to the area of cross section at the inlet of the structure (venturi meter or pipe).

Symbol: A_i

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Section Area 1

Theoretical Discharge

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.

Symbol: Q_th

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Theoretical Discharge

Cross Section Area 2

The Cross Section Area 2 refers to the area of cross-section at the throat (venturi meter) of the structure.

Symbol: A_f

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Cross Section Area 2

Venturi Head

The Venturi head refers to the difference between pressure head at inlet and pressure head at the throat.

Symbol: h_venturi

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Venturi Head

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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 Venturi Meter category

Go Theoretical Discharge through Pipe

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

Go Throat Area given Theoretical Discharge

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

Go Venturi Head given Theoretical Discharge through Pipe

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

Go Coefficient of Discharge given Discharges

C d = \frac{Q actual}{V theoritical}

How to Evaluate Inlet Area given Theoretical Discharge?

Inlet Area given Theoretical Discharge evaluator 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 evaluate 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 evaluate Inlet Area given Theoretical Discharge using this online evaluator? To use this online evaluator 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.

FAQs on Inlet Area given Theoretical Discharge

What is the formula to find Inlet Area given Theoretical Discharge?

The formula of Inlet Area given Theoretical Discharge is expressed as Cross Section Area 1 = sqrt(((Theoretical Discharge*Cross Section Area 2)^2)/((Theoretical Discharge)^2-(Cross Section Area 2^2*2*[g]*Venturi Head))). Here is an example- 7.073493 = sqrt(((1.277*1.8)^2)/((1.277)^2-(1.8^2*2*[g]*0.024))).

How to calculate Inlet Area given Theoretical Discharge?

With Theoretical Discharge (Q_th), Cross Section Area 2 (A_f) & Venturi Head (h_venturi) we can find Inlet Area given Theoretical Discharge using the formula - Cross Section Area 1 = sqrt(((Theoretical Discharge*Cross Section Area 2)^2)/((Theoretical Discharge)^2-(Cross Section Area 2^2*2*[g]*Venturi Head))). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

Can the Inlet Area given Theoretical Discharge be negative?

No, the Inlet Area given Theoretical Discharge, measured in Area cannot be negative.

Which unit is used to measure Inlet Area given Theoretical Discharge?

Inlet Area given Theoretical Discharge is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Inlet Area given Theoretical Discharge can be measured.

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Inlet Area given Theoretical Discharge Formula

Inlet Area given Theoretical Discharge Example

Inlet Area given Theoretical Discharge Solution

Inlet Area given Theoretical Discharge Formula Elements

Other formulas in Venturi Meter category

How to Evaluate Inlet Area given Theoretical Discharge?

FAQs on Inlet Area given Theoretical Discharge

Variable Name