Location of stagnation point on x-axis Calculator

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Incompressible Flow Characteristics

Assorted Characteristics

✖Distance from end A is the distance of the concentrated load from end A.ⓘ Distance from End A [a']			+10% -10%
✖The Strength of source, q is defined as the volume flow rate per unit depth of the fluid.ⓘ Strength of Source [q]			+10% -10%
✖The Uniform flow velocity is considered in flow past a half body.ⓘ Uniform Flow Velocity [U]			+10% -10%

✖The Distance of stagnation point is from the origin O along the x-axis.ⓘ Location of stagnation point on x-axis [x_s]

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Formula

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Location of stagnation point on x-axis

Formula

`"x"_{"s"} = "a'"*sqrt((1+("q"/(pi*"a'"*"U"))))`

Example

`"0.525857m"="0.5m"*sqrt((1+("1.5m²/s"/(pi*"0.5m"*"9m/s"))))`

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Location of stagnation point on x-axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distance of Stagnation Point = Distance from End A*sqrt((1+(Strength of Source/(pi*Distance from End A*Uniform Flow Velocity))))
x_s = a'*sqrt((1+(q/(pi*a'*U))))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Distance of Stagnation Point - (Measured in Meter) - The Distance of stagnation point is from the origin O along the x-axis.
Distance from End A - (Measured in Meter) - Distance from end A is the distance of the concentrated load from end A.
Strength of Source - (Measured in Square Meter per Second) - The Strength of source, q is defined as the volume flow rate per unit depth of the fluid.
Uniform Flow Velocity - (Measured in Meter per Second) - The Uniform flow velocity is considered in flow past a half body.

STEP 1: Convert Input(s) to Base Unit

Distance from End A: 0.5 Meter --> 0.5 Meter No Conversion Required
Strength of Source: 1.5 Square Meter per Second --> 1.5 Square Meter per Second No Conversion Required
Uniform Flow Velocity: 9 Meter per Second --> 9 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x_s = a'*sqrt((1+(q/(pi*a'*U)))) --> 0.5*sqrt((1+(1.5/(pi*0.5*9))))

Evaluating ... ...

x_s = 0.525857227628041

STEP 3: Convert Result to Output's Unit

0.525857227628041 Meter --> No Conversion Required

FINAL ANSWER

0.525857227628041 ≈ 0.525857 Meter <-- Distance of Stagnation Point

(Calculation completed in 00.004 seconds)

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< 23 Incompressible Flow Characteristics Calculators

Uniform flow velocity for stream function at point in combined flow

Go Uniform Flow Velocity = (Stream Function-(Strength of Source/(2*pi*Angle A)))/(Distance from End A*sin(Angle A))

Stream Function at Point in Combined Flow

Go Stream Function = (Uniform Flow Velocity*Distance from End A*sin(Angle A))+((Strength of Source/(2*pi))*Angle A)

Location of stagnation point on x-axis

Go Distance of Stagnation Point = Distance from End A*sqrt((1+(Strength of Source/(pi*Distance from End A*Uniform Flow Velocity))))

Temperature Lapse Rate given Gas Constant

Go Temperature Lapse Rate = (-Acceleration Due to Gravity/Universal Gas Constant)*((Specific constant-1)/(Specific constant))

Stream function at point

Go Stream Function = -(Strength of Doublet/(2*pi))*(Length y/((Length X^2)+(Length y^2)))

Strength of doublet for stream function

Go Strength of Doublet = -(Stream Function*2*pi*((Length X^2)+(Length y^2)))/Length y

Uniform flow velocity for Rankine half body

Go Uniform Flow Velocity = (Strength of Source/(2*Length y))*(1-(Angle A/pi))

Dimensions of Rankine half-body

Go Length y = (Strength of Source/(2*Uniform Flow Velocity))*(1-(Angle A/pi))

Strength of source for Rankine half body

Go Strength of Source = (Length y*2*Uniform Flow Velocity)/(1-(Angle A/pi))

Pressure Head given Density

Go Pressure Head = Pressure above Atmospheric Pressure/(Density of Fluid*Acceleration Due to Gravity)

Radius of Rankine circle

Go Radius = sqrt(Strength of Doublet/(2*pi*Uniform Flow Velocity))

Pressure at point in piezometer given Mass and Volume

Go Pressure = (Mass of water*Acceleration Due to Gravity*Height of Water above Bottom of Wall)

Height of liquid in piezometer

Go Height of Liquid = Water Pressure/(Water Density*Acceleration Due to Gravity)

Distance of stagnation point S from source in flow past half body

Go Radial Distance = Strength of Source/(2*pi*Uniform Flow Velocity)

Pressure at any point in liquid

Go Pressure = Density*Acceleration Due to Gravity*Pressure Head

Stream function in sink flow for angle

Go Stream Function = (Strength of Source/(2*pi))*(Angle A)

Radius at any point considering radial velocity

Go Radius 1 = Strength of Source/(2*pi*Radial Velocity)

Radial velocity at any radius

Go Radial Velocity = Strength of Source/(2*pi*Radius 1)

Strength of source for radial velocity and at any radius

Go Strength of Source = Radial Velocity*2*pi*Radius 1

Hydrostatic law

Go Weight density = Density of Fluid*Acceleration Due to Gravity

Force on Plunger given Intensity

Go Force Acting on Plunger = Pressure Intensity*Area of plunger

Area of plunger

Go Area of plunger = Force Acting on Plunger/Pressure Intensity

Absolute Pressure given Gauge Pressure

Go Absolute Pressure = Gauge Pressure+Atmospheric Pressure

Location of stagnation point on x-axis Formula

Distance of Stagnation Point = Distance from End A*sqrt((1+(Strength of Source/(pi*Distance from End A*Uniform Flow Velocity))))
x_s = a'*sqrt((1+(q/(pi*a'*U))))

What is Rankine Oval body?

A Rankine oval is created by superimposing a uniform flow with a source and a sink. As the distance between the source and sink decreases to zero, the Rankine oval will become more blunt. Eventually, the shape of the Rankine oval will become a circle.

What is the characteristic of stagnation point?

At stagnation, point velocity is zero, as the fluid comes at rest. This characteristic at the stagnation point. There are two stagnation points are present in a source and sink pair in a uniform flow.

How to Calculate Location of stagnation point on x-axis?

Location of stagnation point on x-axis calculator uses Distance of Stagnation Point = Distance from End A*sqrt((1+(Strength of Source/(pi*Distance from End A*Uniform Flow Velocity)))) to calculate the Distance of Stagnation Point, The Location of stagnation point on x-axis formula is defined from the relation of flow past a Rankine Oval body considering the distance of the stagnation point from origin O along the x-axis, the distance between source and sink. Distance of Stagnation Point is denoted by x_s symbol.

How to calculate Location of stagnation point on x-axis using this online calculator? To use this online calculator for Location of stagnation point on x-axis, enter Distance from End A (a'), Strength of Source (q) & Uniform Flow Velocity (U) and hit the calculate button. Here is how the Location of stagnation point on x-axis calculation can be explained with given input values -> 0.525857 = 0.5*sqrt((1+(1.5/(pi*0.5*9)))).

FAQ

What is Location of stagnation point on x-axis?

The Location of stagnation point on x-axis formula is defined from the relation of flow past a Rankine Oval body considering the distance of the stagnation point from origin O along the x-axis, the distance between source and sink and is represented as x_s = a'*sqrt((1+(q/(pi*a'*U)))) or Distance of Stagnation Point = Distance from End A*sqrt((1+(Strength of Source/(pi*Distance from End A*Uniform Flow Velocity)))). Distance from end A is the distance of the concentrated load from end A, The Strength of source, q is defined as the volume flow rate per unit depth of the fluid & The Uniform flow velocity is considered in flow past a half body.

How to calculate Location of stagnation point on x-axis?

The Location of stagnation point on x-axis formula is defined from the relation of flow past a Rankine Oval body considering the distance of the stagnation point from origin O along the x-axis, the distance between source and sink is calculated using Distance of Stagnation Point = Distance from End A*sqrt((1+(Strength of Source/(pi*Distance from End A*Uniform Flow Velocity)))). To calculate Location of stagnation point on x-axis, you need Distance from End A (a'), Strength of Source (q) & Uniform Flow Velocity (U). With our tool, you need to enter the respective value for Distance from End A, Strength of Source & Uniform Flow Velocity 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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