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Slope of Streamline Formula

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Slope of Streamline is angle of inclination of streamline with horizontal. Check FAQs

θ = \arctan (\frac{v}{u}) \cdot (\frac{180}{π})

θ - Slope of Streamline?v - Component of Velocity in Y Direction?u - Component of Velocity in X Direction?π - Archimedes' constant?

Slope of Streamline Example

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Here is how the Slope of Streamline equation looks like with Values.

Here is how the Slope of Streamline equation looks like with Units.

Here is how the Slope of Streamline equation looks like.

51.3402 = \arctan (\frac{10}{8}) \cdot (\frac{180}{3.1416})

51.3402 = \arctan (\frac{10m/s}{8m/s}) \cdot (\frac{180}{3.1416})

51.3402 = \arctan (\frac{10}{8}) \cdot (\frac{180}{3.1416})

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Slope of Streamline Solution

Follow our step by step solution on how to calculate Slope of Streamline?

FIRST Step Consider the formula

θ = \arctan (\frac{v}{u}) \cdot (\frac{180}{π})

Next Step Substitute values of Variables

∴

θ = \arctan (\frac{10m/s}{8m/s}) \cdot (\frac{180}{π})

Next Step Substitute values of Constants

∴

θ = \arctan (\frac{10m/s}{8m/s}) \cdot (\frac{180}{3.1416})

Next Step Prepare to Evaluate

∴

θ = \arctan (\frac{10}{8}) \cdot (\frac{180}{3.1416})

Next Step Evaluate

∴

θ = 51.3401917459099

LAST Step Rounding Answer

∴

θ = 51.3402

Slope of Streamline Formula Elements

Variables

Constants

Functions

Slope of Streamline

Slope of Streamline is angle of inclination of streamline with horizontal.

Symbol: θ

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Slope of Streamline

Component of Velocity in Y Direction

Component of Velocity in Y Direction is velocity in Vertical direction.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Component of Velocity in Y Direction

Component of Velocity in X Direction

Component of Velocity in X Direction is velocity in horizontal direction.

Symbol: u

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Component of Velocity in X Direction

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

ctan

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: ctan(Angle)

arctan

Inverse trigonometric functions are usually accompanied by the prefix - arc. Mathematically, we represent arctan or the inverse tangent function as tan-1 x or arctan(x).

Syntax: arctan(Number)

Other formulas in Description of the Flow Pattern category

Go Slope of Equipotential Line

Φ = \frac{u}{v}

Go Component of Velocity in Y Direction given Slope of Equipotential Line

v = \frac{u}{Φ}

Go Component of Velocity in X Direction given Slope of Equipotential Line

u = v \cdot Φ

Go Component of Velocity in X Direction using Slope of Streamline

u = \frac{v}{\tan (\frac{π}{180} \cdot θ)}

How to Evaluate Slope of Streamline?

Slope of Streamline evaluator uses Slope of Streamline = arctan(Component of Velocity in Y Direction/Component of Velocity in X Direction)*(180/pi) to evaluate the Slope of Streamline, The Slope of Streamline is defined as inclination of streamline with respect to horizontal with velocity component. Slope of Streamline is denoted by θ symbol.

How to evaluate Slope of Streamline using this online evaluator? To use this online evaluator for Slope of Streamline, enter Component of Velocity in Y Direction (v) & Component of Velocity in X Direction (u) and hit the calculate button.

FAQs on Slope of Streamline

What is the formula to find Slope of Streamline?

The formula of Slope of Streamline is expressed as Slope of Streamline = arctan(Component of Velocity in Y Direction/Component of Velocity in X Direction)*(180/pi). Here is an example- 51.34019 = arctan(10/8)*(180/pi).

How to calculate Slope of Streamline?

With Component of Velocity in Y Direction (v) & Component of Velocity in X Direction (u) we can find Slope of Streamline using the formula - Slope of Streamline = arctan(Component of Velocity in Y Direction/Component of Velocity in X Direction)*(180/pi). This formula also uses Archimedes' constant and , Tangent (tan), Cotangent (ctan), Inverse Tangent (arctan) function(s).

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