Professor Tang's Interactive Tools

Explore core equations through interactive plots & schematics. Adjust inputs → see the math respond.

How to use ↓

Finite Control Volume Analysis

Linear momentum: change in flow direction

Linear Momentum – Change in Flow Direction

Coming soon

Linear momentum: moving control volume

Linear Momentum – Moving Control Volume

Coming soon

Conservation of mass: relative velocity

Conservation of Mass – Relative Velocity

Coming soon

Moment-of-momentum: torque

Moment-of-Momentum – Torque

Coming soon

Differential Analysis

Uniform flow

Uniform Flow

Coming soon

Source and sink

Source and Sink

Coming soon

Source in a uniform stream

Source in a Uniform Stream – Half-Body

Coming soon

Viscous Flow in Pipes

Circular tubes

Steady, Laminar, Viscous, Incompressible Flow in Circular Tubes

Coming soon

Entrance length

Entrance Length

Coming soon

Inclined circular tubes

Steady, Laminar, Viscous, Incompressible Flow in Inclined Circular Tubes

Coming soon

Darcy Friction Factor (Moody Chart)
Major and minor losses

Example of Major and Minor Losses

Coming soon

Flow over Immersed Bodies

Blasius boundary layer

Blasius Boundary Layer Thickness and Wall Shear Stress of Steady, Laminar, Viscous, Incompressible Flow over Flat Plates

Coming soon

Terminal velocity

Terminal Velocity of Small Spherical Particles

Coming soon

Open-Channel Flow

Wave speed

Wave Speed

Coming soon

Ramp with a bump

Water Flows Up a Ramp with a Bump

Coming soon

Manning equation

Manning Equation

Coming soon

Hydraulic jump

Hydraulic Jump

Coming soon

Compressible Flow

Sound speed

Sound Speed of the Isentropic Flow of an Ideal Gas with Constant cp and cv

Coming soon

Mach number

Mach Number of the Isentropic Flow of an Ideal Gas with Constant cp and cv

Coming soon

Ratio of Static Properties / Stagnation Properties of the Isentropic Flow of an Ideal Gas with Constant cp and cv
Area ratio

A/A*, Where Ma = 1 at A*

Coming soon

Converging nozzle

Performance of a Converging Nozzle at Various Pressure Ratios

Coming soon

Converging-diverging nozzle

Performance of a Converging-Diverging Nozzle at Various Pressure Ratios

Coming soon

How to use

Pick a course tab, use the left outline to jump to a topic, then click a card to open a simulation. Change one control at a time and watch the plots & equations update together.

Feedback & Ideas

Have an idea to add or something to fix? I’d love to hear it.

Give feedback

About this project

Built by Aarav Shah (UIUC ME ’26) under the guidance of Prof. Tang. Ongoing effort to create interactive teaching tools for fluids & thermal sciences. Tech: JavaScript/D3, HTML, CSS. Questions or ideas? Email me.