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Theoretical Discharge through Pipe Formula

GoTheoretical Discharge given Coefficient of Discharge Formula

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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. Check FAQs

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

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

Theoretical Discharge through Pipe Example

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Here is how the Theoretical Discharge through Pipe equation looks like with Values.

Here is how the Theoretical Discharge through Pipe equation looks like with Units.

Here is how the Theoretical Discharge through Pipe equation looks like.

1.2767 = \frac{7.1 \cdot 1.8 \cdot (\sqrt{2 \cdot 9.8066 \cdot 24})}{\sqrt{{(7.1)}^{2} - {(1.8)}^{2}}}

1.2767m³/s = \frac{7.1m² \cdot 1.8m² \cdot (\sqrt{2 \cdot 9.8066m/s² \cdot 24mm})}{\sqrt{{(7.1m²)}^{2} - {(1.8m²)}^{2}}}

1.2767 = \frac{7.1 \cdot 1.8 \cdot (\sqrt{2 \cdot 9.8066 \cdot 24})}{\sqrt{{(7.1)}^{2} - {(1.8)}^{2}}}

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Theoretical Discharge through Pipe Solution

Follow our step by step solution on how to calculate Theoretical Discharge through Pipe?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

Q th = \frac{7.1m² \cdot 1.8m² \cdot (\sqrt{2 \cdot [g] \cdot 24mm})}{\sqrt{{(7.1m²)}^{2} - {(1.8m²)}^{2}}}

Next Step Substitute values of Constants

∴

Q th = \frac{7.1m² \cdot 1.8m² \cdot (\sqrt{2 \cdot 9.8066m/s² \cdot 24mm})}{\sqrt{{(7.1m²)}^{2} - {(1.8m²)}^{2}}}

Next Step Convert Units

∴

Q th = \frac{7.1m² \cdot 1.8m² \cdot (\sqrt{2 \cdot 9.8066m/s² \cdot 0.024m})}{\sqrt{{(7.1m²)}^{2} - {(1.8m²)}^{2}}}

Next Step Prepare to Evaluate

∴

Q th = \frac{7.1 \cdot 1.8 \cdot (\sqrt{2 \cdot 9.8066 \cdot 0.024})}{\sqrt{{(7.1)}^{2} - {(1.8)}^{2}}}

Next Step Evaluate

∴

Q th = 1.27667064378257m³/s

LAST Step Rounding Answer

∴

Q th = 1.2767m³/s

Theoretical Discharge through Pipe Formula Elements

Variables

Constants

Functions

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 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

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 to find Theoretical Discharge

Go Theoretical Discharge given Coefficient of Discharge

Q th = \frac{Q actual}{C d}

Other formulas in Venturi Meter category

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 Inlet Area given Theoretical Discharge

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

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 Theoretical Discharge through Pipe?

Theoretical Discharge through Pipe evaluator 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 evaluate 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 evaluate Theoretical Discharge through Pipe using this online evaluator? To use this online evaluator 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.

FAQs on Theoretical Discharge through Pipe

What is the formula to find Theoretical Discharge through Pipe?

The formula of Theoretical Discharge through Pipe is expressed as 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))). Here is an example- 1.276671 = (7.1*1.8*(sqrt(2*[g]*0.024)))/(sqrt((7.1)^(2)-(1.8)^(2))).

How to calculate Theoretical Discharge through Pipe?

With Cross Section Area 1 (A_i), Cross Section Area 2 (A_f) & Venturi Head (h_venturi) we can find Theoretical Discharge through Pipe using the formula - 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))). This formula also uses Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

What are the other ways to Calculate Theoretical Discharge?

Here are the different ways to Calculate Theoretical Discharge-

Theoretical Discharge=Actual Discharge/Coefficient of Discharge

Can the Theoretical Discharge through Pipe be negative?

No, the Theoretical Discharge through Pipe, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Theoretical Discharge through Pipe?

Theoretical Discharge through Pipe is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Theoretical Discharge through Pipe can be measured.

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Theoretical Discharge through Pipe Formula

​GoTheoretical Discharge given Coefficient of Discharge Formula

Theoretical Discharge through Pipe Example

Theoretical Discharge through Pipe Solution

Theoretical Discharge through Pipe Formula Elements

Other Formulas to find Theoretical Discharge

Other formulas in Venturi Meter category

How to Evaluate Theoretical Discharge through Pipe?

FAQs on Theoretical Discharge through Pipe

Variable Name

GoTheoretical Discharge given Coefficient of Discharge Formula