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Flow Deflection Angle using Prandtl Meyer Function Formula

GoFlow Deflection Angle due to Expansion Wave Formula

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Flow Deflection Angle is defined as the angle by which the flow turns through the expansion wave. Check FAQs

θ e = v M2 - v M1

θ_e - Flow Deflection Angle?v_M2 - Prandtl Meyer Function at Downstream Mach no.?v_M1 - Prandtl Meyer Function at Upstream Mach no.?

Flow Deflection Angle using Prandtl Meyer Function Example

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Here is how the Flow Deflection Angle using Prandtl Meyer Function equation looks like with Values.

Here is how the Flow Deflection Angle using Prandtl Meyer Function equation looks like with Units.

Here is how the Flow Deflection Angle using Prandtl Meyer Function equation looks like.

6 = 83 - 77

6° = 83° - 77°

6 = 83 - 77

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Flow Deflection Angle using Prandtl Meyer Function Solution

Follow our step by step solution on how to calculate Flow Deflection Angle using Prandtl Meyer Function?

FIRST Step Consider the formula

θ e = v M2 - v M1

Next Step Substitute values of Variables

∴

θ e = 83° - 77°

Next Step Convert Units

∴

θ e = 1.4486rad - 1.3439rad

Next Step Prepare to Evaluate

∴

θ e = 1.4486 - 1.3439

Next Step Evaluate

∴

θ e = 0.10471975511964rad

Next Step Convert to Output's Unit

∴

θ e = 5.99999999999999°

LAST Step Rounding Answer

∴

θ e = 6°

Flow Deflection Angle using Prandtl Meyer Function Formula Elements

Variables

Flow Deflection Angle

Flow Deflection Angle is defined as the angle by which the flow turns through the expansion wave.

Symbol: θ_e

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Flow Deflection Angle

Prandtl Meyer Function at Downstream Mach no.

Prandtl Meyer Function at Downstream Mach no. is the Prandtl Meyer Functional value at downstream of expansion wave.

Symbol: v_M2

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Prandtl Meyer Function at Downstream Mach no.

Prandtl Meyer Function at Upstream Mach no.

Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.

Symbol: v_M1

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Prandtl Meyer Function at Upstream Mach no.

Other Formulas to find Flow Deflection Angle

Go Flow Deflection Angle due to Expansion Wave

θ e = (\sqrt{\frac{γ e + 1}{γ e - 1}} \cdot a \tan (\sqrt{\frac{(γ e - 1) \cdot ({M e2}^{2} - 1)}{γ e + 1}}) - a \tan (\sqrt{{M e2}^{2} - 1})) - (\sqrt{\frac{γ e + 1}{γ e - 1}} \cdot a \tan (\sqrt{\frac{(γ e - 1) \cdot ({M e1}^{2} - 1)}{γ e + 1}}) - a \tan (\sqrt{{M e1}^{2} - 1}))

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 Flow Deflection Angle using Prandtl Meyer Function?

Flow Deflection Angle using Prandtl Meyer Function evaluator uses Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no. to evaluate the Flow Deflection Angle, The Flow deflection angle using Prandtl Meyer function formula relates the Mach number to the maximum deflection angle achievable through an isentropic (constant entropy) expansion process. It is obtained as the difference of the Prandtl Meyer function calculated at downstream and upstream Mach number. Flow Deflection Angle is denoted by θ_e symbol.

How to evaluate Flow Deflection Angle using Prandtl Meyer Function using this online evaluator? To use this online evaluator for Flow Deflection Angle using Prandtl Meyer Function, enter Prandtl Meyer Function at Downstream Mach no. (v_M2) & Prandtl Meyer Function at Upstream Mach no. (v_M1) and hit the calculate button.

FAQs on Flow Deflection Angle using Prandtl Meyer Function

What is the formula to find Flow Deflection Angle using Prandtl Meyer Function?

The formula of Flow Deflection Angle using Prandtl Meyer Function is expressed as Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.. Here is an example- 343.7747 = 1.44862327915502-1.34390352403538.

How to calculate Flow Deflection Angle using Prandtl Meyer Function?

With Prandtl Meyer Function at Downstream Mach no. (v_M2) & Prandtl Meyer Function at Upstream Mach no. (v_M1) we can find Flow Deflection Angle using Prandtl Meyer Function using the formula - Flow Deflection Angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no..

What are the other ways to Calculate Flow Deflection Angle?

Here are the different ways to Calculate Flow Deflection Angle-

Flow Deflection Angle=(sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Behind Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Behind Expansion Fan^2-1)))-(sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number Ahead of Expansion Fan^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number Ahead of Expansion Fan^2-1)))

Can the Flow Deflection Angle using Prandtl Meyer Function be negative?

Yes, the Flow Deflection Angle using Prandtl Meyer Function, measured in Angle can be negative.

Which unit is used to measure Flow Deflection Angle using Prandtl Meyer Function?

Flow Deflection Angle using Prandtl Meyer Function is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Flow Deflection Angle using Prandtl Meyer Function can be measured.

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Flow Deflection Angle using Prandtl Meyer Function Formula

​GoFlow Deflection Angle due to Expansion Wave Formula

Flow Deflection Angle using Prandtl Meyer Function Example

Flow Deflection Angle using Prandtl Meyer Function Solution

Flow Deflection Angle using Prandtl Meyer Function Formula Elements

Other Formulas to find Flow Deflection Angle

Other formulas in Expansion Waves category

How to Evaluate Flow Deflection Angle using Prandtl Meyer Function?

FAQs on Flow Deflection Angle using Prandtl Meyer Function

Variable Name

GoFlow Deflection Angle due to Expansion Wave Formula