Stream Function for Flow over Rankine Oval Calculator

✖The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.ⓘ Freestream Velocity [V_∞]			+10% -10%
✖Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.ⓘ Radial Coordinate [r]			+10% -10%
✖Polar Angle is the angular position of a point from a reference direction.ⓘ Polar Angle [θ]			+10% -10%
✖Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.ⓘ Source Strength [Λ]			+10% -10%
✖Polar Angle from Source is the angular position of a point in polar coordinates where origin is at the source.ⓘ Polar Angle from Source [θ₁]			+10% -10%
✖Polar Angle from Sink is the angular position of a point in polar coordinates where origin is at the sink.ⓘ Polar Angle from Sink [θ₂]			+10% -10%

✖Rankine Oval Stream Function is a mathematical function used to describe the flow pattern around an oval-shaped object in potential flow theory.ⓘ Stream Function for Flow over Rankine Oval [ψ_r]

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Stream Function for Flow over Rankine Oval Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink)
ψ_r = V_∞*r*sin(θ)+(Λ/(2*pi))*(θ₁-θ₂)
This formula uses 1 Constants, 1 Functions, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Rankine Oval Stream Function - (Measured in Square Meter per Second) - Rankine Oval Stream Function is a mathematical function used to describe the flow pattern around an oval-shaped object in potential flow theory.
Freestream Velocity - (Measured in Meter per Second) - The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air.
Radial Coordinate - (Measured in Meter) - Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin.
Polar Angle - (Measured in Radian) - Polar Angle is the angular position of a point from a reference direction.
Source Strength - (Measured in Square Meter per Second) - Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point.
Polar Angle from Source - (Measured in Radian) - Polar Angle from Source is the angular position of a point in polar coordinates where origin is at the source.
Polar Angle from Sink - (Measured in Radian) - Polar Angle from Sink is the angular position of a point in polar coordinates where origin is at the sink.

STEP 1: Convert Input(s) to Base Unit

Freestream Velocity: 6.4 Meter per Second --> 6.4 Meter per Second No Conversion Required
Radial Coordinate: 9 Meter --> 9 Meter No Conversion Required
Polar Angle: 0.7 Radian --> 0.7 Radian No Conversion Required
Source Strength: 134 Square Meter per Second --> 134 Square Meter per Second No Conversion Required
Polar Angle from Source: 10 Radian --> 10 Radian No Conversion Required
Polar Angle from Sink: 14 Radian --> 14 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ψ_r = V_∞*r*sin(θ)+(Λ/(2*pi))*(θ₁-θ₂) --> 6.4*9*sin(0.7)+(134/(2*pi))*(10-14)

Evaluating ... ...

ψ_r = -48.2001107123649

STEP 3: Convert Result to Output's Unit

-48.2001107123649 Square Meter per Second --> No Conversion Required

FINAL ANSWER

-48.2001107123649 ≈ -48.200111 Square Meter per Second <-- Rankine Oval Stream Function

(Calculation completed in 00.004 seconds)

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Home » Physics » Aerodynamics » Two Dimensional Incompressible Flow » Elementary Flows » Aerospace » Source Flow » Stream Function for Flow over Rankine Oval

Credits

Created by Shikha Maurya

Indian Institute of Technology (IIT), Bombay

Shikha Maurya has created this Calculator and 100+ more calculators!

Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< Source Flow Calculators

Velocity Potential for 2-D Source Flow

LaTeX Go Velocity Potential = Source Strength/(2*pi)*ln(Radial Coordinate)

Radial Velocity for 2-D Incompressible Source Flow

LaTeX Go Radial Velocity = (Source Strength)/(2*pi*Radial Coordinate)

Stream Function for 2-D Incompressible Source Flow

LaTeX Go Source Stream Function = Source Strength/(2*pi)*Polar Angle

Source Strength for 2-D Incompressible Source Flow

LaTeX Go Source Strength = 2*pi*Radial Coordinate*Radial Velocity

Stream Function for Flow over Rankine Oval Formula

LaTeX Go

What does the region outside the oval interpreted?

The region outside the oval can be interpreted as the inviscid, potential, incompressible flow over the solid body. The flow from the source is consumed by the sink inside the oval, whereas the flow outside the oval has originated with the uniform stream only.

How to obtain the flow over rankine oval?

The flow over Rankine oval is obtained as the superposition of uniform flow and source-sink pair for two-dimensional flow.

How to Calculate Stream Function for Flow over Rankine Oval?

Stream Function for Flow over Rankine Oval calculator uses Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink) to calculate the Rankine Oval Stream Function, The Stream Function for Flow over Rankine Oval formula is obtained as the summation of stream functions for uniform flow and source-sink pair, this expression describes the flow pattern around a Rankine oval in potential flow theory, it accounts for the free stream flow, the presence of the oval, and any circulation around the oval. Rankine Oval Stream Function is denoted by ψ_r symbol.

How to calculate Stream Function for Flow over Rankine Oval using this online calculator? To use this online calculator for Stream Function for Flow over Rankine Oval, enter Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ), Source Strength (Λ), Polar Angle from Source (θ₁) & Polar Angle from Sink (θ₂) and hit the calculate button. Here is how the Stream Function for Flow over Rankine Oval calculation can be explained with given input values -> -48.200111 = 6.4*9*sin(0.7)+(134/(2*pi))*(10-14).

FAQ

What is Stream Function for Flow over Rankine Oval?

The Stream Function for Flow over Rankine Oval formula is obtained as the summation of stream functions for uniform flow and source-sink pair, this expression describes the flow pattern around a Rankine oval in potential flow theory, it accounts for the free stream flow, the presence of the oval, and any circulation around the oval and is represented as ψ_r = V_∞*r*sin(θ)+(Λ/(2*pi))*(θ₁-θ₂) or Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink). The Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air, Radial Coordinate for an object refers to the coordinate of the object that moves in radial direction from a point of origin, Polar Angle is the angular position of a point from a reference direction, Source Strength measures the magnitude or intensity of a source, which is a theoretical construct used to represent fluid flow emanating from a point, Polar Angle from Source is the angular position of a point in polar coordinates where origin is at the source & Polar Angle from Sink is the angular position of a point in polar coordinates where origin is at the sink.

How to calculate Stream Function for Flow over Rankine Oval?

The Stream Function for Flow over Rankine Oval formula is obtained as the summation of stream functions for uniform flow and source-sink pair, this expression describes the flow pattern around a Rankine oval in potential flow theory, it accounts for the free stream flow, the presence of the oval, and any circulation around the oval is calculated using Rankine Oval Stream Function = Freestream Velocity*Radial Coordinate*sin(Polar Angle)+(Source Strength/(2*pi))*(Polar Angle from Source-Polar Angle from Sink). To calculate Stream Function for Flow over Rankine Oval, you need Freestream Velocity (V_∞), Radial Coordinate (r), Polar Angle (θ), Source Strength (Λ), Polar Angle from Source (θ₁) & Polar Angle from Sink (θ₂). With our tool, you need to enter the respective value for Freestream Velocity, Radial Coordinate, Polar Angle, Source Strength, Polar Angle from Source & Polar Angle from Sink 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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