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Velocity at Section 1 from Bernoulli Equation Formula

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The Velocity at Point 1 refers to the velocity of fluid passing through point 1 in flow. Check FAQs

V 1 = \sqrt{2 \cdot [g] \cdot ((\frac{P 2}{γ f}) + (0.5 \cdot (\frac{{V p2}^{2}}{[g]})) + Z 2 - Z 1 - \frac{P 1}{γ f})}

V₁ - Velocity at Point 1?P₂ - Pressure at Section 2?γ_f - Specific Weight of Liquid?V_p2 - Velocity at Point 2?Z₂ - Datum Height at Section 2?Z₁ - Datum Height at Section 1?P₁ - Pressure at Section 1?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?

Velocity at Section 1 from Bernoulli Equation Example

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Here is how the Velocity at Section 1 from Bernoulli Equation equation looks like with Values.

Here is how the Velocity at Section 1 from Bernoulli Equation equation looks like with Units.

Here is how the Velocity at Section 1 from Bernoulli Equation equation looks like.

58.0936 = \sqrt{2 \cdot 9.8066 \cdot ((\frac{10}{9.81}) + (0.5 \cdot (\frac{34^{2}}{9.8066})) + 12.1 - 11.1 - \frac{8.9}{9.81})}

58.0936m/s = \sqrt{2 \cdot 9.8066m/s² \cdot ((\frac{10N/mm²}{9.81kN/m³}) + (0.5 \cdot (\frac{{34m/s}^{2}}{9.8066m/s²})) + 12.1m - 11.1m - \frac{8.9N/mm²}{9.81kN/m³})}

58.0936 = \sqrt{2 \cdot 9.8066 \cdot ((\frac{10}{9.81}) + (0.5 \cdot (\frac{34^{2}}{9.8066})) + 12.1 - 11.1 - \frac{8.9}{9.81})}

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Velocity at Section 1 from Bernoulli Equation Solution

Follow our step by step solution on how to calculate Velocity at Section 1 from Bernoulli Equation?

FIRST Step Consider the formula

V 1 = \sqrt{2 \cdot [g] \cdot ((\frac{P 2}{γ f}) + (0.5 \cdot (\frac{{V p2}^{2}}{[g]})) + Z 2 - Z 1 - \frac{P 1}{γ f})}

Next Step Substitute values of Variables

∴

V 1 = \sqrt{2 \cdot [g] \cdot ((\frac{10N/mm²}{9.81kN/m³}) + (0.5 \cdot (\frac{{34m/s}^{2}}{[g]})) + 12.1m - 11.1m - \frac{8.9N/mm²}{9.81kN/m³})}

Next Step Substitute values of Constants

∴

V 1 = \sqrt{2 \cdot 9.8066m/s² \cdot ((\frac{10N/mm²}{9.81kN/m³}) + (0.5 \cdot (\frac{{34m/s}^{2}}{9.8066m/s²})) + 12.1m - 11.1m - \frac{8.9N/mm²}{9.81kN/m³})}

Next Step Convert Units

∴

V 1 = \sqrt{2 \cdot 9.8066m/s² \cdot ((\frac{1E+7Pa}{9810N/m³}) + (0.5 \cdot (\frac{{34m/s}^{2}}{9.8066m/s²})) + 12.1m - 11.1m - \frac{8.9E+6Pa}{9810N/m³})}

Next Step Prepare to Evaluate

∴

V 1 = \sqrt{2 \cdot 9.8066 \cdot ((\frac{1E+7}{9810}) + (0.5 \cdot (\frac{34^{2}}{9.8066})) + 12.1 - 11.1 - \frac{8.9E+6}{9810})}

Next Step Evaluate

∴

V 1 = 58.0935626880467m/s

LAST Step Rounding Answer

∴

V 1 = 58.0936m/s

Velocity at Section 1 from Bernoulli Equation Formula Elements

Variables

Constants

Functions

Velocity at Point 1

The Velocity at Point 1 refers to the velocity of fluid passing through point 1 in flow.

Symbol: V₁

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity at Point 1

Pressure at Section 2

The Pressure at Section 2 refers to the pressure at a section of the pipe.

Symbol: P₂

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Pressure at Section 2

Specific Weight of Liquid

The Specific Weight of Liquid refers to the weight per unit volume of that substance.

Symbol: γ_f

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Specific Weight of Liquid

Velocity at Point 2

The Velocity at Point 2 refers to the direction of the movement of the body or the object.

Symbol: V_p2

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Velocity at Point 2

Datum Height at Section 2

The Datum Height at Section 2 refers to the height of flow at a particular section.

Symbol: Z₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Datum Height at Section 2

Datum Height at Section 1

The Datum Height at Section 1 refers to the height of flow at a particular section.

Symbol: Z₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Datum Height at Section 1

Pressure at Section 1

The Pressure at Section 1 refers to the pressure at a section of the pipe.

Symbol: P₁

Measurement: PressureUnit: N/mm²

Note: Value can be positive or negative.

Formulas to find Pressure at Section 1

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

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 Euler's Equation of Motion category

Go Piezometric Head for Steady Non Viscous Flow

P = (\frac{P h}{γ f}) + h

Go Datum Height using Piezometric Head for Steady Non-Viscous Flow

Z 1 = P - \frac{P h}{γ f}

How to Evaluate Velocity at Section 1 from Bernoulli Equation?

Velocity at Section 1 from Bernoulli Equation evaluator uses Velocity at Point 1 = sqrt(2*[g]*((Pressure at Section 2/Specific Weight of Liquid)+(0.5*((Velocity at Point 2^2)/[g]))+Datum Height at Section 2-Datum Height at Section 1-Pressure at Section 1/Specific Weight of Liquid)) to evaluate the Velocity at Point 1, The Velocity at Section 1 from Bernoulli Equation is defined as velocity at a particular section of the pipe. Velocity at Point 1 is denoted by V₁ symbol.

How to evaluate Velocity at Section 1 from Bernoulli Equation using this online evaluator? To use this online evaluator for Velocity at Section 1 from Bernoulli Equation, enter Pressure at Section 2 (P₂), Specific Weight of Liquid (γ_f), Velocity at Point 2 (V_p2), Datum Height at Section 2 (Z₂), Datum Height at Section 1 (Z₁) & Pressure at Section 1 (P₁) and hit the calculate button.

FAQs on Velocity at Section 1 from Bernoulli Equation

What is the formula to find Velocity at Section 1 from Bernoulli Equation?

The formula of Velocity at Section 1 from Bernoulli Equation is expressed as Velocity at Point 1 = sqrt(2*[g]*((Pressure at Section 2/Specific Weight of Liquid)+(0.5*((Velocity at Point 2^2)/[g]))+Datum Height at Section 2-Datum Height at Section 1-Pressure at Section 1/Specific Weight of Liquid)). Here is an example- 58.09356 = sqrt(2*[g]*((10000000/9810)+(0.5*((34^2)/[g]))+12.1-11.1-8900000/9810)).

How to calculate Velocity at Section 1 from Bernoulli Equation?

With Pressure at Section 2 (P₂), Specific Weight of Liquid (γ_f), Velocity at Point 2 (V_p2), Datum Height at Section 2 (Z₂), Datum Height at Section 1 (Z₁) & Pressure at Section 1 (P₁) we can find Velocity at Section 1 from Bernoulli Equation using the formula - Velocity at Point 1 = sqrt(2*[g]*((Pressure at Section 2/Specific Weight of Liquid)+(0.5*((Velocity at Point 2^2)/[g]))+Datum Height at Section 2-Datum Height at Section 1-Pressure at Section 1/Specific Weight of Liquid)). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth constant(s) and Square Root (sqrt) function(s).

Can the Velocity at Section 1 from Bernoulli Equation be negative?

Yes, the Velocity at Section 1 from Bernoulli Equation, measured in Speed can be negative.

Which unit is used to measure Velocity at Section 1 from Bernoulli Equation?

Velocity at Section 1 from Bernoulli Equation is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Velocity at Section 1 from Bernoulli Equation can be measured.

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Velocity at Section 1 from Bernoulli Equation Formula

Velocity at Section 1 from Bernoulli Equation Example

Velocity at Section 1 from Bernoulli Equation Solution

Velocity at Section 1 from Bernoulli Equation Formula Elements

Other formulas in Euler's Equation of Motion category

How to Evaluate Velocity at Section 1 from Bernoulli Equation?

FAQs on Velocity at Section 1 from Bernoulli Equation

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