What are the 7 Millennium Problems?

What are the 7 Millennium Problems?

Clay “to increase and disseminate mathematical knowledge.” The seven problems, which were announced in 2000, are the Riemann hypothesis, P versus NP problem, Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier-Stokes equation, Yang-Mills theory, and Poincaré conjecture.

Who has solved the Navier Stokes equation?

Russian mathematician Grigori Perelman was awarded the Prize on March 18 last year for solving one of the problems, the Poincaré conjecture – as yet the only problem that’s been solved. Famously, he turned down the $1,000,000 Millennium Prize.

Who is Diane Adler mathematician?

Diane Adler was a brilliant mathematician, a prodigy whose talent had put her on the fast track to scholarly fame and immortality. She is on the verge of solving one of the most difficult and significant of all mathematical problems.

How many unknowns are there in Navier Stokes equation?

1.8 Navier-Stokes equations

	Number of Equations	Number of Unknowns
continuity	1	1
Navier-Stokes	3 (symmetry)	3
	4	4

When was Navier Stokes equation?

1845

How do you get Navier Stokes equation?

General Form of the Navier-Stokes Equation Denoting the stress deviator tensor as T, we can make the substitution σ=−pI+T. Substituting this into the previous equation, we arrive at the most general form of the Navier-Stokes equation: ρD→vDt=−∇p+∇⋅T+→f.

Is Navier Stokes Eulerian or Lagrangian?

The Navier-Stokes equations are the governing equations of fluid flows. They are deemed to embody all physics in a flow of Newtonian fluids like water, especially when we assume the fluid is incompressible. Thus, the Navier-Stokes equations should be and indeed they are always used in the Eulerian perspective.

What is lambda in Navier Stokes equation?

In the derivation of Navier-Stokes equation, we come across the “Stokes Hypothesis”, where for some fluids, the mechanical and thermodynamic pressures and taken to be equal. Here lambda +2*mu/3 =0. where lambda = second coefficient of viscosity.

Which force is not considered as Navier Stokes equation?

Though surface tension force act on a fluid in motion, it is considered to be negligible for the Navier-Stokes equation.

What is energy per unit head of water called?

total energy

What is a critical depth?

In biological oceanography, ‘Critical Depth’ is defined as a hypothesized surface mixing depth at which phytoplankton growth is precisely matched by losses of phytoplankton biomass within this depth interval. This concept is useful for understanding the initiation of phytoplankton blooms.

When the depth is normal which parameter is zero?

When the depth is normal, which parameter is zero? Explanation: Normal depth is a depth of flow in the channel. It is created when the slope of the water surface and channel bottom is the same and the water depth remains the same throughout the entire flow.

What is the formula for specific energy?

Write pressure in terms of depth (y = p / γ). = 0). i.e. where y is the depth of flow, v is the velocity, Q is the discharge, A is the cross- sectional flow area and E is the specific energy i.e energy w.r.t channel bottom.

What is specific energy of flow?

In open channel flow, specific energy ( e ) is the energy length, or head, relative to the channel bottom. Specific energy is expressed in terms of kinetic energy, and potential energy, and internal energy.

Which fuel has the highest specific energy?

hydrogen

What is the most energy dense fossil fuel?

Another important fossil fuel is Liquefied Natural Gas (LNG). LNG is methane gas cooled to negative 260 degrees Fahrenheit. Liquefication of methane achieves a high energy density for transportation purposes. There is currently a large global trade in LNG….Fossil Fuels: Abundant, Chemically Stable, Energy-dense.

		Fuel Cost
Natural Gas	$2.80/MCF (3)	2.8

Which fuel does not produce least pollution?

Natural gas is a relatively clean burning fossil fuel Burning natural gas for energy results in fewer emissions of nearly all types of air pollutants and carbon dioxide (CO2) than burning coal or petroleum products to produce an equal amount of energy.

Which fuel is less polluting and why?

Answer: the fuels like CNG, LPG, biofuels are the fuels which are less polluting. Explanation: these fuels are less polluting because carbon content is lesser due to which the threat of increase of carbon in the is reduced and the stress of increase of global warming is also reduced.

Which mode of transport does not cause pollution?

Cycle is the vehicle which does not pollute the environment. Cycles do not need fossil fuels, so that they do not emit any harmful gases. So, cycle is an eco-friendly mode of transport. Cycling 10 km each way to work would save 1500 kg of greenhouse gas emissions each year.