Velocity at Section 1 from Bernoulli Equation Calculator

✖Pressure at Section 2 is pressure at a section of the pipe.ⓘ Pressure at Section 2 [P₂]			+10% -10%
✖Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.ⓘ Specific Weight of Liquid [γ_f]			+10% -10%
✖Velocity at Point 2 defines the direction of the movement of the body or the object.ⓘ Velocity at Point 2 [V_p2]			+10% -10%
✖Datum Height at Section 2 is height of flow at a particular section.ⓘ Datum Height at Section 2 [Z₂]			+10% -10%
✖Datum Height at Section 1 is height of flow at a particular section.ⓘ Datum Height at Section 1 [Z₁]			+10% -10%
✖Pressure at Section 1 is pressure at a section of the pipe.ⓘ Pressure at Section 1 [P₁]			+10% -10%

✖Velocity at Point 1 is the velocity of fluid passing through point 1 in flow.ⓘ Velocity at Section 1 from Bernoulli Equation [V₁]

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Formula

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Velocity at Section 1 from Bernoulli Equation

Formula

`"V"_{"1"} = sqrt(2*"[g]"*(("P"_{"2"}/"γ"_{"f"})+(0.5*(("V"_{"p2"}^2)/"[g]"))+"Z"_{"2"}-"Z"_{"1"}-"P"_{"1"}/"γ"_{"f"}))`

Example

`"58.09356m/s"=sqrt(2*"[g]"*(("10N/mm²"/"9.81kN/m³")+(0.5*((("34m/s")^2)/"[g]"))+"12.1m"-"11.1m"-"8.9N/mm²"/"9.81kN/m³"))`

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Velocity at Section 1 from Bernoulli Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
V₁ = sqrt(2*[g]*((P₂/γ_f)+(0.5*((V_p2^2)/[g]))+Z₂-Z₁-P₁/γ_f))
This formula uses 1 Constants, 1 Functions, 7 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

Velocity at Point 1 - (Measured in Meter per Second) - Velocity at Point 1 is the velocity of fluid passing through point 1 in flow.
Pressure at Section 2 - (Measured in Pascal) - Pressure at Section 2 is pressure at a section of the pipe.
Specific Weight of Liquid - (Measured in Newton per Cubic Meter) - Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid.
Velocity at Point 2 - (Measured in Meter per Second) - Velocity at Point 2 defines the direction of the movement of the body or the object.
Datum Height at Section 2 - (Measured in Meter) - Datum Height at Section 2 is height of flow at a particular section.
Datum Height at Section 1 - (Measured in Meter) - Datum Height at Section 1 is height of flow at a particular section.
Pressure at Section 1 - (Measured in Pascal) - Pressure at Section 1 is pressure at a section of the pipe.

STEP 1: Convert Input(s) to Base Unit

Pressure at Section 2: 10 Newton per Square Millimeter --> 10000000 Pascal (Check conversion here)
Specific Weight of Liquid: 9.81 Kilonewton per Cubic Meter --> 9810 Newton per Cubic Meter (Check conversion here)
Velocity at Point 2: 34 Meter per Second --> 34 Meter per Second No Conversion Required
Datum Height at Section 2: 12.1 Meter --> 12.1 Meter No Conversion Required
Datum Height at Section 1: 11.1 Meter --> 11.1 Meter No Conversion Required
Pressure at Section 1: 8.9 Newton per Square Millimeter --> 8900000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V₁ = sqrt(2*[g]*((P₂/γ_f)+(0.5*((V_p2^2)/[g]))+Z₂-Z₁-P₁/γ_f)) --> sqrt(2*[g]*((10000000/9810)+(0.5*((34^2)/[g]))+12.1-11.1-8900000/9810))

Evaluating ... ...

V₁ = 58.0935626880467

STEP 3: Convert Result to Output's Unit

58.0935626880467 Meter per Second --> No Conversion Required

FINAL ANSWER

58.0935626880467 ≈ 58.09356 Meter per Second <-- Velocity at Point 1

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Equations of Motion and Energy Equation » Euler's Equation of Motion » Velocity at Section 1 from Bernoulli Equation

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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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Velocity at Section 1 from Bernoulli Equation

Go 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))

Pressure at Section 1 from Bernoulli Equation

Go Pressure at Section 1 = Specific Weight of Liquid*((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-(0.5*((Velocity at Point 1^2)/[g])))

Datum Height at Section 1 from Bernoulli Equation

Go Datum Height at Section 1 = Pressure at Section 2/Specific Weight of Liquid+0.5*Velocity at Point 2^2/[g]+Datum Height at Section 2-Pressure at Section 1/Specific Weight of Liquid-0.5*Velocity at Point 1^2/[g]

Datum Height using Piezometric Head for Steady Non-Viscous Flow

Go Datum Height at Section 1 = Piezometric Head-Pressure of Fluid/Specific Weight of Liquid

Piezometric Head for Steady Non Viscous Flow

Go Piezometric Head = (Pressure of Fluid/Specific Weight of Liquid)+Height of Section

Velocity of Flow given Velocity Head for Steady Non Viscous Flow

Go Velocity of Fluid = sqrt(Velocity Head*2*[g])

Pressure using Pressure Head for Steady Non Viscous Flow

Go Pressure of Fluid = Specific Weight of Liquid*Pressure Head

Pressure Head for Steady Non Viscous Flow

Go Pressure Head = Pressure of Fluid/Specific Weight of Liquid

Velocity Head for Steady Non Viscous Flow

Go Velocity Head = (Velocity of Fluid^2)/2*[g]

Velocity at Section 1 from Bernoulli Equation Formula

What is Bernoulli Equation of Fluid?

Bernoulli's principle is an idea of fluid dynamics. It says that as speed of the fluid increases, pressure decreases. A higher pressure pushes (accelerates) fluid toward lower pressure. So any change in a fluid's speed must be matched by a change in pressure (force).

How to Calculate Velocity at Section 1 from Bernoulli Equation?

Velocity at Section 1 from Bernoulli Equation calculator 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 calculate 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 calculate Velocity at Section 1 from Bernoulli Equation using this online calculator? To use this online calculator 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. Here is how the Velocity at Section 1 from Bernoulli Equation calculation can be explained with given input values -> 58.09356 = sqrt(2*[g]*((10000000/9810)+(0.5*((34^2)/[g]))+12.1-11.1-8900000/9810)).

FAQ

What is Velocity at Section 1 from Bernoulli Equation?

The Velocity at Section 1 from Bernoulli Equation is defined as velocity at a particular section of the pipe and is represented as V₁ = sqrt(2*[g]*((P₂/γ_f)+(0.5*((V_p2^2)/[g]))+Z₂-Z₁-P₁/γ_f)) or 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)). Pressure at Section 2 is pressure at a section of the pipe, Specific Weight of Liquid represents the force exerted by gravity on a unit volume of a fluid, Velocity at Point 2 defines the direction of the movement of the body or the object, Datum Height at Section 2 is height of flow at a particular section, Datum Height at Section 1 is height of flow at a particular section & Pressure at Section 1 is pressure at a section of the pipe.

How to calculate Velocity at Section 1 from Bernoulli Equation?

The Velocity at Section 1 from Bernoulli Equation is defined as velocity at a particular section of the pipe is calculated using 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 calculate Velocity at Section 1 from Bernoulli Equation, you need 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). With our tool, you need to enter the respective value for Pressure at Section 2, Specific Weight of Liquid, Velocity at Point 2, Datum Height at Section 2, Datum Height at Section 1 & Pressure at Section 1 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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