Flow Deflection Angle using Prandtl Meyer Function Solution

STEP 0: Pre-Calculation Summary
Formula Used
Flow Deflection angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.
θe = vM2-vM1
This formula uses 3 Variables
Variables Used
Flow Deflection angle - (Measured in Radian) - Flow Deflection angle is defined as the angle by which the flow turns towards the oblique shock.
Prandtl Meyer Function at Downstream Mach no. - (Measured in Radian) - Prandtl Meyer Function at Downstream Mach no. is the Prandtl Meyer Functional value at downstream of expansion wave.
Prandtl Meyer Function at Upstream Mach no. - (Measured in Radian) - Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.
STEP 1: Convert Input(s) to Base Unit
Prandtl Meyer Function at Downstream Mach no.: 83 Degree --> 1.44862327915502 Radian (Check conversion here)
Prandtl Meyer Function at Upstream Mach no.: 77 Degree --> 1.34390352403538 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θe = vM2-vM1 --> 1.44862327915502-1.34390352403538
Evaluating ... ...
θe = 0.10471975511964
STEP 3: Convert Result to Output's Unit
0.10471975511964 Radian -->5.99999999999999 Degree (Check conversion here)
FINAL ANSWER
5.99999999999999 6 Degree <-- Flow Deflection angle
(Calculation completed in 00.004 seconds)

Credits

Created by Shikha Maurya
Indian Institute of Technology (IIT), Bombay
Shikha Maurya has created this Calculator and 100+ more calculators!
Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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10+ Expansion Waves Calculators

Flow Deflection Angle due to Expansion Wave
Go 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)))
Prandtl Meyer Function at Upstream Mach Number
Go Prandtl Meyer Function at Upstream Mach no. = 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))
Prandtl Meyer Function
Go Prandtl Meyer Function = sqrt((Specific Heat Ratio Expansion Wave+1)/(Specific Heat Ratio Expansion Wave-1))*atan(sqrt(((Specific Heat Ratio Expansion Wave-1)*(Mach Number^2-1))/(Specific Heat Ratio Expansion Wave+1)))-atan(sqrt(Mach Number^2-1))
Pressure behind Expansion Fan
Go Pressure Behind Expansion Fan = Pressure Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))
Pressure Ratio across Expansion Fan
Go Pressure Ratio Across Expansion Fan = ((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))^((Specific Heat Ratio Expansion Wave)/(Specific Heat Ratio Expansion Wave-1))
Temperature behind Expansion Fan
Go Temperature Behind Expansion Fan = Temperature Ahead of Expansion Fan*((1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2))
Temperature Ratio across Expansion Fan
Go Temperature Ratio Across Expansion Fan = (1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Ahead of Expansion Fan^2)/(1+0.5*(Specific Heat Ratio Expansion Wave-1)*Mach Number Behind Expansion Fan^2)
Flow Deflection Angle using Prandtl Meyer Function
Go Flow Deflection angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.
Forward Mach Angle of Expansion Fan
Go Forward Mach Angle = arsin(1/Mach Number Ahead of Expansion Fan)
Rearward Mach Angle of Expansion Fan
Go Rearward Mach Angle = arsin(1/Mach Number Behind Expansion Fan)

Flow Deflection Angle using Prandtl Meyer Function Formula

Flow Deflection angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.
θe = vM2-vM1

What is expansion wave?

When a supersonic flow is turned away from itself an expansion wave is formed. The fan continuously opens in the direction away from the corner. The expansion wave is in the shape of a fan centered at the corner.

How to Calculate Flow Deflection Angle using Prandtl Meyer Function?

Flow Deflection Angle using Prandtl Meyer Function calculator uses Flow Deflection angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no. to calculate 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 θe symbol.

How to calculate Flow Deflection Angle using Prandtl Meyer Function using this online calculator? To use this online calculator for Flow Deflection Angle using Prandtl Meyer Function, enter Prandtl Meyer Function at Downstream Mach no. (vM2) & Prandtl Meyer Function at Upstream Mach no. (vM1) and hit the calculate button. Here is how the Flow Deflection Angle using Prandtl Meyer Function calculation can be explained with given input values -> 343.7747 = 1.44862327915502-1.34390352403538.

FAQ

What is Flow Deflection Angle using Prandtl Meyer Function?
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 and is represented as θe = vM2-vM1 or Flow Deflection angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.. Prandtl Meyer Function at Downstream Mach no. is the Prandtl Meyer Functional value at downstream of expansion wave & Prandtl Meyer Function at Upstream Mach no. is the Prandtl Meyer Functional value at upstream of expansion wave.
How to calculate Flow Deflection Angle using Prandtl Meyer Function?
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 is calculated using Flow Deflection angle = Prandtl Meyer Function at Downstream Mach no.-Prandtl Meyer Function at Upstream Mach no.. To calculate Flow Deflection Angle using Prandtl Meyer Function, you need Prandtl Meyer Function at Downstream Mach no. (vM2) & Prandtl Meyer Function at Upstream Mach no. (vM1). With our tool, you need to enter the respective value for Prandtl Meyer Function at Downstream Mach no & Prandtl Meyer Function at Upstream Mach no and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Flow Deflection angle?
In this formula, Flow Deflection angle uses Prandtl Meyer Function at Downstream Mach no & Prandtl Meyer Function at Upstream Mach no. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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)))
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