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Forward Mach Angle of Expansion Fan Formula

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Forward Mach Angle is the angle formed between the forward Mach line and upstream flow direction. Check FAQs

μ 1 = a r \sin (\frac{1}{M e1})

μ₁ - Forward Mach Angle?M_e1 - Mach Number Ahead of Expansion Fan?

Forward Mach Angle of Expansion Fan Example

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Here is how the Forward Mach Angle of Expansion Fan equation looks like with Values.

Here is how the Forward Mach Angle of Expansion Fan equation looks like with Units.

Here is how the Forward Mach Angle of Expansion Fan equation looks like.

11.537 = a r \sin (\frac{1}{5})

11.537° = a r \sin (\frac{1}{5})

11.537 = a r \sin (\frac{1}{5})

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Forward Mach Angle of Expansion Fan Solution

Follow our step by step solution on how to calculate Forward Mach Angle of Expansion Fan?

FIRST Step Consider the formula

μ 1 = a r \sin (\frac{1}{M e1})

Next Step Substitute values of Variables

∴

μ 1 = a r \sin (\frac{1}{5})

Next Step Prepare to Evaluate

∴

μ 1 = a r \sin (\frac{1}{5})

Next Step Evaluate

∴

μ 1 = 0.201357920790331rad

Next Step Convert to Output's Unit

∴

μ 1 = 11.5369590328177°

LAST Step Rounding Answer

∴

μ 1 = 11.537°

Forward Mach Angle of Expansion Fan Formula Elements

Variables

Functions

Forward Mach Angle

Forward Mach Angle is the angle formed between the forward Mach line and upstream flow direction.

Symbol: μ₁

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Forward Mach Angle

Mach Number Ahead of Expansion Fan

Mach Number Ahead of Expansion Fan is the Mach number of the upstream flow.

Symbol: M_e1

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Mach Number Ahead of Expansion Fan

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.

Syntax: sin(Angle)

arsin

Arcsine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: arsin(Number)

Other formulas in Expansion Waves category

Go Pressure Ratio across Expansion Fan

P e,r = {(\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})}^{\frac{γ e}{γ e - 1}}

Go Temperature Ratio across Expansion Fan

T e,r = \frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}}

Go Pressure behind Expansion Fan

P 2 = P 1 \cdot {(\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})}^{\frac{γ e}{γ e - 1}}

Go Temperature behind Expansion Fan

T 2 = T 1 \cdot (\frac{1 + 0.5 \cdot (γ e - 1) \cdot {M e1}^{2}}{1 + 0.5 \cdot (γ e - 1) \cdot {M e2}^{2}})

How to Evaluate Forward Mach Angle of Expansion Fan?

Forward Mach Angle of Expansion Fan evaluator uses Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan) to evaluate the Forward Mach Angle, The Forward Mach Angle of Expansion Fan refers to the angle between the direction of flow within the expansion fan and the Mach wave generated by the expansion process. Forward Mach Angle is denoted by μ₁ symbol.

How to evaluate Forward Mach Angle of Expansion Fan using this online evaluator? To use this online evaluator for Forward Mach Angle of Expansion Fan, enter Mach Number Ahead of Expansion Fan (M_e1) and hit the calculate button.

FAQs on Forward Mach Angle of Expansion Fan

What is the formula to find Forward Mach Angle of Expansion Fan?

The formula of Forward Mach Angle of Expansion Fan is expressed as Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan). Here is an example- 661.0191 = arsin(1/5).

How to calculate Forward Mach Angle of Expansion Fan?

With Mach Number Ahead of Expansion Fan (M_e1) we can find Forward Mach Angle of Expansion Fan using the formula - Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan). This formula also uses Sine (sin), Inverse Sine (arsin) function(s).

Can the Forward Mach Angle of Expansion Fan be negative?

Yes, the Forward Mach Angle of Expansion Fan, measured in Angle can be negative.

Which unit is used to measure Forward Mach Angle of Expansion Fan?

Forward Mach Angle of Expansion Fan is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Forward Mach Angle of Expansion Fan can be measured.

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