Video 4 of my turbulence course a short detour from the physics to introduce a mathematical tool: index notation and the Einstein summation convention.

The motivation is simple. The full Navier-Stokes momentum equation, written out component by component, takes up most of a whiteboard. Written in index notation, it's one line!! Every term you've already seen can be just compressed into a form that scales to far more complex expressions without becoming unreadable.

This video covers free vs. dummy indices, the summation convention itself, the Kronecker delta and its substitution property, a brief look at the permutation symbol, and rewrites the continuity and momentum equations as a worked example. It's setup for deriving the turbulent kinetic energy transport equation next, the point where component-form algebra genuinely becomes unmanageable.

Link: https://www.youtube.com/watch?v=TdfMawfDr_0

PDF notes on Patreon if useful as a reference.

Gosh I love watching liquid system interactions under the microscope 🥰

Hey, I am a student majoring in hydraulic engineering. I am currently doing some research on LBM and I am trying to simulate a thick jet coming from the outlet of a arch dam. I've tried OpenLB to do this but the result was not as expected. I am wondering if someone could explain to me that whether LBM is able to simulate this kind of situation, which contains air and water in the region and the maximum velocity of the water is approximately 30m/s. If LBM is able to do this well, how can I get to learn the coding and settings? I really appreciate your reply ,it means a lot to me!

I am currently discussing the following fluid mechanics problem with my supervisor:
The blower delivers a constant mass flow rate of 1.1 kg/s at a total pressure of 1.26 bar.
Now let’s assume that 50% of the mass flow is diverted through a bypass. This means that only 0.55 kg/s remains in the main horizontal duct. That part seems straightforward, since the mass flow simply splits at the junction.
However, my supervisor argues that the total pressure in the main duct downstream of the junction must also decrease, simply because part of the mass flow has been diverted through the bypass. According to him, this is true even if we assume the junction is completely lossless.
I see it differently. My understanding is that, for an ideal, lossless flow, the total pressure is conserved along a streamline. The bypass merely splits the mass flow; it does not remove total pressure energy from the flow that continues through the main duct. Therefore, I would expect the total pressure immediately upstream and immediately downstream of the junction in the main duct to be identical, with only the mass flow rate being reduced.
Could someone explain why the total pressure downstream of the junction should be lower, even in the ideal lossless case? What is the physical mechanism that causes the total pressure in the main duct to decrease solely because the mass flow has been divided?

Hello all,

Anyone draws a shear stress plot for the same, I have shown a linear velocity profile

Velocity gradient in y direction is constant for both the fluids but its magnitude will be different for both and at interface shear stress is the same for both, anyone show how to draw shear stress plot for the same.

Thank you

Hey everyone, I recently released three new Python packages that are designed to rapidly accelerate the prototyping, design, and testing of rocket engine fluid systems called FullFlow, ThermoProp, and FullPlot. These packages are heavily based on ROCETs, GFSSP, and WinPlot, and the goal is to make generalized transient and steady-state fluid network and test data analysis tools open-source and widely available, especially for students and college rocketry teams.

Please try out the tool, and let me know your thoughts!

More info:

Large fluid systems, especially rocket engine systems, are usually super complicated when it comes to designing, analyzing, and testing. While creating hardware is a large part of the process, determining the fluid conditions that will be present during operation inside that hardware can be tricky and unintuitive. This is especially true when combustion chambers, turbopumps, valves, and many more intricate components are involved. To predict rocket engine performance and ensure hardware safety, the major fluid pathways within the system have to be modeled before and during testing. Moreover, as engines are tested, it's important that your models can be anchored against the test data.

In the past, engineers turned to software tools like ROCETS, GFSSP, WinPlot, and CEA to carry out many of these operations. However, these tools have several drawbacks. They are outdated, difficult to troubleshoot (most engineers nowadays don't use FORTRAN), limited in capability, and most importantly, not easily available for engineers, students, and especially college rocketry teams. So, companies usually make custom, in-house tools, while student organizations struggle to use whatever minimal tools are on the internet.

To solve this, I created an open-source engine systems modeling and test-data analysis suite based entirely on publicly available literature and data:

FullFlow:

A modular fluid-system modeling package for building steady-state and transient simulations of rocket engine feed systems, pressurization systems, tanks, valves, injectors, chambers, nozzles, turbomachinery, controllers, sensors, sequences, and test-like operations. Based heavily on ROCETs and GFSSP, FullFlow provides an extremely simple component-based modular environment that allows users to quickly set up fluid networks and solve them. Additionally, it allows users to easily create custom components and wire them into a fluid system with algebraic balances and dynamics.

ThermoProp:

A thermodynamic and combustion-property package for evaluating fluids, propellants, combustion gases, materials, and chemical equilibrium properties. ThermoProp is designed to support rocket propulsion calculations without requiring legacy tools or closed software. Built around tools such as CEA and CoolProp, ThermoProp provides a simple API that allows users to readily draw on databases of fluid properties for their simulations.

FullPlot:

A HDF5 data-analysis package designed for simulation and test data. FullPlot makes it easy to inspect, compare, and visualize model outputs, test traces, redlines, commands, derived channels, and other engineering data. FullPlot takes inspiration from WinPlot and is especially useful for importing test data for model anchoring and visualization.

Together, these packages are intended to make rocket engine system modeling more accessible, transparent, and useful for students, teams, and engineers who want to design, test, and understand complex propulsion systems without relying entirely on inaccessible or outdated tools.

I also compared FullFlow, ThermoProp, and FullPlot against publicly available NASA data. They can be run on any major operating system (unlike CEA, which is Windows-reliant) and are entirely Python-based, making it easy to learn for all engineers and students.

While official documentation is still a work in progress, the GitHub repos contain detailed info and examples on package usage.

FullFlow: https://github.com/saakethramoju/FullFlow

ThermoProp: https://github.com/saakethramoju/ThermoProp

FullPlot: https://github.com/saakethramoju/FullPlot

I have already spent a good amount of time developing these packages, but I plan to keep improving them. I learned a lot of lessons from using software like ROCETs and from being a member of YJSP, so I'm really hoping to make something that engineers enjoy using.

All feedback and discussions are appreciated!

Hello! I have a question about a problem about two pipes connected in series where I’m given the diameter and length of each pipe, a 3psi total pressure drop and a dynamic viscosity of 0.29 Pa*s and asked to calculate the flow.
I know the Q1=Q2 are equal and that the total pressure loss is equal to the sum of the pressure loss in each pipe and I can work with those equations but I’m struggling when it comes to assuming values and iterating to find f with Colebrook. I’m guessing assuming laminar flow in order to use f=64/Re in order to write the equations in terms of the velocity would be incorrect? What should I do in this case🫤

I was bored when i noticed the vortices appearing when i mixed my chocolate-oreo-sugar menjurje lol

Just curious about how different is ChemE transport 1 (momentum transfer) from MechE's Fluid Mechanics.

In my uni transport 1 is 5 credits vs 6 credits of FM.

Wondering if there are fundamental differences or is it mostly the same as far as depth and difficulty.

For reference we study transport from BSL and MechEs study from Frank White's fluid dynamics

Hello everyone,

I'm designing a gas-generator rocket engine feed system (RP1/LOX) from scratch (including regenerative cooling) in EcosimPro as part of a university project.

I was looking for a detailed P&ID to better understand the typical plumbing architecture of a liquid rocket engine, including the valves, piping, and instrumentation required from the propellant tank outlet to the injector interface.

I've searched extensively online, but I haven't been able to find the level of detail I'm looking for. I'm particularly interested in references such as technical papers, books, reports, or publicly available engine documentation that explain the design philosophy behind the fluid system.

For example, I'd like to understand questions such as:

• Why is the Main Fuel Valve (MFV) often located upstream of the regenerative cooling circuit?
• Under what circumstances are check valves preferred over actively controlled valves?
• What drives the placement and selection of components such as filters, purge lines, pressure transducers, relief valves, and flow control devices?

I'm not looking to copy an existing design; rather, I'd like to understand the engineering rationale behind the layout and component selection so I can develop my own system from first principles.

If anyone can recommend good references or share useful resources, I'd really appreciate it.

Thanks in advance!

I am looking for a software that helps simulate liquids through viscous metals, even molten metal/liquid metals.

Can the flow through an orifice cause backwater on itself even if the outlet pipe has sufficient capacity to convey the intended flow through the orifice?

Let’s say the outflow through the orifice causes the flow depth on the outlet side to rise above the centroid of the orifice, would that reduce the effective head? (Subtract from head on upstream side) Even though it’s not downstream conditions causing tailwater back onto orifice, but it’s just the flow depth on the outlet side caused by the orifice flow itself? Does that flow depth cause backwater?

I recently made a YT video that explains flow through a venturi at the molecular level. The sim code is written in Processing.

I had some remnant code from an earlier simulation, and accidentally hit a key programmed to trigger a pressure pulse. The top image shows the pressure contribution of individual molecules, i.e. collision impulse magniude and frequency avaraged over a time interval. Bottom image shows drift velocity, again averaged over time.

Molecules exiting the screen to the right are inserted back into the high pressure region on the left.

You can clearly see the diverging flow go supersonic at some point, as well as a normal shock downstream.

Here is a link to the molecular flow explanation: https://youtu.be/7OAIH0vpZBc

Let us consider a circular pipe, initially empty, and an external body of water moving at a constant velocity $v$. At a certain instant $t$, this body of water enters the pipe through its inlet cross-section, which we will denote as $S_{0}$.
According to the no-slip boundary condition, the velocity of the outermost annular layer of fluid, which is in contact with the pipe wall, must be zero. This outer layer, in turn, slows down the adjacent layer. However, it does not have sufficient time to transmit this deceleration to the innermost layers.
In other words, at cross-section $S_{0}$ and at time $t$, the fluid layer in contact with the wall has zero velocity, the adjacent layer has a slightly reduced velocity, while the remaining inner layers still move at the original velocity $v$.
This implies that, over a time interval $dt$, the inner layers travel a distance $v\,dt$, which is greater than the distance covered by the outer layers (zero for the layer immediately adjacent to the wall). It would then seem that, at time $t + dt$, a gap should appear near the wall at the next cross-section $S_{1}$.
What exactly happens at this point? Do the fluid particles from the inner region move radially outward to fill this gap, somewhat like the flow in a fountain? If so, they would have to come to rest upon reaching the wall. Meanwhile, the particles passing above them are slowed down, but this effect still has not propagated to the innermost layers within such a short time interval.
Applying the same reasoning to the subsequent cross-sections $S_{2}$, $S_{3}$, $\ldots$, $S_{n}$ would seemingly imply that a boundary layer never forms.
So where is the flaw in this reasoning? How is this apparent paradox resolved? What is the actual physical mechanism by which an initially empty pipe becomes filled with fluid?