Question

Write the Navier-Stokes (N-S) equations (viscous - incompressible flow) in longer form in x,y,z (Cartesian) coordinates as mentioned in the class today

Answer #1

Kindly appreciate the effort done ,,, If have any doubt please ask me anytime ... Thank you

- write N-S equations for incompressible flows in cartesian
coordinates in long form (in x,y,z coordinates) (1 point)
- also write continuity equation and N-S equations for
incompressible flows in polar coordinates in long form (in r,θ,z)
(since one of your friends ask you can find it easily in online
resources or in books) (1 point)
- Write down N-S equations in x direction for Planar Couette-
Pouseille flow and derive an equation for velocity variation using
boundary layer conditions...

Stokes' Theorem is the generalization of the circulation form of
Green's Theorem in the x y-plane. Use Stokes' Theorem to write the
circulation form of Green's Theorem in the y z-plane.

Stokes' Theorem is the generalization of the circulation form of
Green's Theorem in the x y-plane. Use Stokes' Theorem to write the
circulation form of Green's Theorem in the y z-plane.
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Use Stokes' Theorem to evaluate
S
curl F · dS.
F(x, y, z) = x2 sin(z)i + y2j + xyk,
S is the part of the paraboloid
z = 1 − x2 − y2
that lies above the xy-plane, oriented upward.

Write the augmented matrix of the given system of equations.
x + y - z = 8
5x - 3y = 4
6x + 2y - z = 2

Write these equations in explicit form:
x' = x^(2) - t^(2)
y' = sin(y)
mr' + rm + e^(m+r) = 0

Write these equations in explicit form
x' = x^(2) - t^(2)
y' = sin(y)
mr' + rm + e^(m+r) = 0
Thanks in advance!

Use Stokes' theorem to find the flux curl ∫∫s (CurlG). dS where
G(x,y,z) = <-xy2, x2y, 1> and S is the
portion of the paraboloid z = x2 + y2 inside
the cylinder x2 + y2 = 1. Use an
upward-pointing normal.

Consider the surface S parametrized by the equations x = uv, y =
u + v, z = u − v, where u^2 + v^2 ≤ 4. ) Identify the surface S and
give its equation in rectangular coordinates

3) For the given system of equations:
x+y-z=-6
x+2y+3z=-10
2x-y-13z=3
Rewrite the system as an augmented matrix. [4 pt]
Find the reduced row echelon form of the matrix using your
calculator, and write it in the spacebelow. [4 pt]
State the solution(s) of the system of equations. [3 pt]

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