How do you use the Navier-Stokes equation?
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How do you use the 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.
What do the Navier Stokes equation represent?
The Navier-Stokes equations represent the conservation of momentum, while the continuity equation represents the conservation of mass.
Who proved the Navier-Stokes equation?
Jean Leray in 1934 proved the existence of so-called weak solutions to the Navier–Stokes equations, satisfying the equations in mean value, not pointwise.
Who invented spherical coordinates?
Bernoulli’s work extended to finding the radius of curvature of curves expressed in these coordinates. The actual term polar coordinates has been attributed to Gregorio Fontana and was used by 18th century Italian writers.
Who Solved the Navier Stokes problem?
Is equation of sphere a function?
Spheres, just like circles in R2, aren’t functions since there are points in its domain which give more than one output. Functions should only return one output point at most; since the equation outputs 2 values for z for every input of x and y (with a few exceptions in its domain), then it is not a function.
What is the origin in spherical coordinates?
In spherical coordinates a point is specified by the triplet (r, θ, φ), where r is the point’s distance from the origin (the radius), θ is the angle of rotation from the initial meridian plane, and φ is the angle from the polar axis (analogous to a ray from the origin through the North Pole).
What is dS in spherical coordinates?
On the surface of the sphere, ρ = a, so the coordinates are just the two angles φ and θ. The area element dS is most easily found using the volume element: dV = ρ2 sin φ dρ dφ dθ = dS · dρ = area · thickness so that dividing by the thickness dρ and setting ρ = a, we get (9) dS = a2 sin φ dφ dθ.
What is the general equation of sphere?
x2 + y2 + z2 = r2 which is called the equation of a sphere.
