## Fluid Dynamics Flow Calculators - Prof. S. A. E. Miller

See notes and instructions at the bottom of the page. Copyright Steven A. E. Miller 2021 - Present. All rights reserved. Version 1.03. May 12, 2022. Return to my homepage. Visit me on my University of Florida research group page.

p [Pa]
ρ [kg/m3]
T [K]
R [J/kg K]

Altitude [m]
p [Pa]
ρ [kg/m3]
T [K]

## Isentropic Flow Calculator

A/A*
M
po/p
To/T
ρo
γ
Mach angle [deg.]
Prandtl-Meyer [deg.]

M1
M2
p2/p1
po,2/po,1
T2/T1
u2/u1
γ
ρ21
po,2/p1

## Oblique Shock (Wedge)

 M1 Mn,1 M2 Mn,2 p2/p1 po,2/po,1 T2/T1 u2/u1 v2/v1 β [deg.] γ ρ2/ρ1 θ [deg.] Weak Shock Strong Shock

## Oblique Shock (Cone)

 M1 Mc β [deg.] γ θ [deg.]

M
p/p *
p o/po*
T/T *
T o/To*
u/u *
γ
ρ/ρ *

4fL*/D
M
p/p*
po/po*
T/T*
u/u*
γ
ρ/ρ*

## Instructions and Notes

General use. Almost every calculator can be used by clearing them (clear button) and then typing in a single value. The calculator will automatically seek all other values. When there is a pull-down menu available, it will either denote the flow being supersonic or subsonic. Or, it might denote which variable is being used for the calculation.

These calculators are meant for someone with a working knowledge in the field. There are very few if no checks on input. The user may provide under-determined or over-determined information in the calculators. They are generally designed to give answers. However, certain values provide mathematiclaly impossible situations. These often return NaN or alter the original input value. Users should always be skeptical of all calculations, which is good practice in any event.

Each calculator solves analytical equations of fluid dynamics for specific problems. Closed form solutions are evaluated if possible. Numerical solutions using various techniques are employed when analytical approaches are not available. Below are descriptions or notes for each calculator

• Ideal Gas Calculator. Input all variables except the single unknown. The pull-down menu denotes which value is unknown. Push calculate to predict the unknown value. Based on the equation $p = \rho R T$. The upper buttons denote default values for STP and NTP atmosphere standards.
• Approximate Fast Standard Atmosphere Calculator. Type in an altitude in meters and click calculate. Thermodynamic values are reported in the other boxes at that altitude. Note that this calculator is approximate and does not exactly follow the standard atmosphere standard. It is good enough for engineering work up to 47 km on Earth.
• Isentropic Flow Calculator. Enter only one value. For area ratio input, indicate if the flow is supersonic or subsonic at location A. All other values will be returned. If no value of gamma is entered, the default value will be 1.40.
• Normal shock calculator. Enter only one value. All other values will be calculated automatically. If no value of gamma is entered, the default value will be 1.40.
• Oblique Shock (Wedge). Enter at least one or more known values. Use the pull-down menu to select if the shock wave is strong or weak then push calculator. Note that depending on which values are entered, the system of equations might be over-determiend or under-determined. Familirity with two-dimensional oblique shock wave theory is very useful here. If the calculator returns NaN, it is likely that the values entered were ill-determined, in conflict, resulted in a detached shock, or had some other non-physical issue. If no value of gamma is entered then 1.40 will be used. The calculator will do its best to find a solution, and even over-write poorly formed input values. A fully successful solution occurs when your input values remain unchanged and all values are not NaN. Most common problems are when detached shocks occur (no solution of these equations) or when the user provides unphysical values (e.g. M_1 = 0.50 as an obvious example).
• Oblique shock calculator (Cone). Enter only two values. All other values calculated automatically. If no value of gamma is entered, the default value will be 1.40. The value of M_1 represents the free-stream Mach number and must be entered. The second value should either be the cone half-angle, theta, or the weak shock angle, beta. There is no error detection or shock detachment checks. Error of the solver is shown in the debug text at bottom of page. The solver can take sometime on modern hardware as it is seeking single precision solutions using a bi-section method. Currently, I believe it is the highest accuracy solver available on the Internet. Based upon my students' solvers - Arman Ghannadian and Christian King.
• Rayleigh Flow. Rayleigh flow solver. The pull-down menu indicates if the flow is supersonic or subsonic. Generally, enter only one value and push calculate. All other values will be solved for automatically. Make sure unknown values are blank. Note that some input values will yield impossible solutions or cause numerical solutions to diverge.
• Fanno Flow. Solves the Fanno flow equations. The pull-down menu indicates if the flow is supersonic or subsonic. Generally, enter only one value and push calculate. All other values will be solved for automatically. Make sure unknown values are blank. Note that some input values will yield impossible solutions or cause numerical solutions to diverge.