FluidPower.Pro – Hydraulic and pneumatic professionals

OpenAI Solved the Navier–Stokes Problem

Dzyanis September 11, 2026 0 News 11 Views

I recently read some exciting news: OpenAI says its AI system has solved the famous Navier–Stokes existence and smoothness problem, one of the hardest questions in mathematics.

So, what are the Navier–Stokes equations? In simple words, they describe how fluids move. They help scientists study air around airplanes, water in oceans, weather systems, and even blood moving through our bodies.

The problem is difficult because fluids can behave in incredibly complicated ways. A smooth flow can suddenly form a tiny, violent swirl called a singularity. Mathematicians have spent about 90 years trying to prove whether this can happen in three-dimensional fluids. Even viscosity, which normally makes fluid motion smoother, does not make the mathematics easy.

This problem is one of the seven Millennium Prize Problems. The Clay Mathematics Institute offered a prize of $1 million for a correct solution. However, it is important to clarify one common misunderstanding: there is no Nobel Prize for solving this problem. Nobel Prizes are awarded in areas such as physics, chemistry, and medicine, while this is a mathematics prize.

According to OpenAI, its internal AI system used around 10,000 cooperating AI agents. They explored many possible approaches, shared useful ideas, and eventually produced both a written proof and a computer-checked version written in Lean. OpenAI says the proof shows that a smooth fluid can develop a singularity in a finite amount of time. The key idea is a vortex that spirals inward and stretches like spaghetti while its speed grows dramatically.

One surprising fact is that the AI reportedly found the result in about 88 hours, with another 17 hours used for verification. The agents exchanged about 2.7 million messages and produced around 130 billion tokens.

This does not mean that computers have replaced mathematicians. The result still needs careful review by independent experts. But if the proof is confirmed, it could become an important moment in the history of mathematics—and a fascinating example of how AI may help humans explore problems that once seemed impossible.

Source: OpenAI’s announcement
Source: Wikipedia: Navier–Stokes equations

Vacuum pressure understanding

Dzyanis April 2, 2025 0 Articles 4390 Views

vacuum pressure vs atmospheric

Recently I was involved in test of the suction pressure of pump, that faulty because cavitations. It was an interesting experience and I noted that not everyone understand requirements for pump’s inlet pressure from manufacturers. I made a diagram above to add more clarity for everyone and added below my answers for most popular questions about vacuum pressure.

Oil deaeration options

Dzyanis April 18, 2024 0 Articles cavitation, deaeration, tank 5269 Views

Air in oil is not good, if there’s a lot of air in the oil, the hydraulics don’t behave the way you expect them to:

– efficiency losses
– cavitation
– loud noise
– faster oil ageing
– higher temperatures
– changes in oil properties
– control problems

Air in oil impacts the life of the oil and the life of the components in the system. The components can be damaged because of the air in the system. The cavitation effects cause damage to components and create loud noise, micro-diesel effects and increases in temperature make oil age more quickly. This causes deposits to alter the oil viscosity and reduces the fluid thermal conductivity. Free air in the oil also increases the compressibility of oil and makes control unresponsive and imprecise leading to certain safety problems.

How does the air get into the oil?

There are a lot of ways, but the major ones are:
– by liquid sloshing in the tank
– by the pump suction the air
– through damaged seals in cylinders
– as a result of flawed filter tank design
– during maintenance works
– when equipment is connected

So what are the ways to decrease air bubbles in the hyd tank?

Fluid Power world-wide pressure gauges

Dzyanis February 15, 2024 0 Articles gauge 3345 Views

The company where I’m currently working manufactures and ships equipment around the world.
Although the SI unit for pressure is the Pascal (Pa), different countries use their own kind of “standards” for pressure measuring, and when designing the system I need to keep in mind what country our equipment is shipping to. Below are just my notes/recommendations, which I personally use in my practice in case if customer doesn’t have specific requirements for pressure gauges (brand/units). Since our equipment is designed and manufactured in Alberta and Texas, I use a primary scale that matches the region and “psi” scale as a secondary one.

Region	Unit	Gauge unit(s) scale
North America South America	psi (Pounds per Square Inch)	psi
Australia China	kPa or MPa (KiloPascal or MegaPascal)	Dual: psi/kPa
Western Europe Arabic Countries	bar (Bar)	Dual: psi/bar
India South Korea South Asia	kg/cm² (Kilogram per square centimetres)	Dual: psi/kg/cm²

The unit converter you can find by this link.

Most popular pressure gauge scale ranges:


   30 psi =    207 kPa = 0.207 MPa = 2.068 bar
   60 psi =    413 kPa = 0.414 MPa =  4.14 bar
  160 psi =  1,103 kPa =   1.1 MPa = 11.03 bar
  200 psi =  1,379 kPa =  1.38 MPa = 13.79 bar
  600 psi =  4,136 kPa =   4.1 MPa =  41.4 bar
1,000 psi =  6,895 kPa =   6.9 MPa =    69 bar
2,000 psi = 13,789 kPa =  13.8 MPa =   138 bar
3,000 psi = 20,684 kPa =  20.7 MPa =   207 bar
5,000 psi = 34,474 kPa =  34.5 MPa =   345 bar