a. What is N-S equations for incompressible flows in cartesian coordinates in long form (in x,y,z...

a. What is N-S equations for incompressible flows in cartesian coordinates in long form (in x,y,z coordinates)?

b. What is continuity equation and N-S equations for incompressible flows in polar coordinates in long form (in r,θ,z)

c. What is N-S equations in x direction for Planar Couette- Pouseille flow and derive an equation for velocity variation using boundary layer conditions

d. Assume an incompressible, steady, axissymmetric, fully developed Pouseille flow in a cylindrical pipe (infinitesimally long in z direction). The flow is in z direction, and radial and tangetial velocity is zero. Derive and simplify the N-S equation in z direction to find out the velocity in z direction. (need to use the boundary conditions to solve for integration constants)

Expert Solution

c) Planar couette flow.

d) Pouseille flow in a cylindrical pipe.

samet mamat answered 1 year ago

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar...

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5. Equations of the form y’ = P(x)y^2 + Q(x)y + R(x) are called Riccati equations....

5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations. i) If we know a solution y = φ(x) of this equation, then any other solution can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is an unknown function which satisfies a certain linear equation. Using the fact that φ and y both solve the above Riccati equation, find the differential equation that v satisfies. ii) Consider the equation 3y’ +...

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Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈ N(400,...

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The velocity components of an incompressible, two-dimensional velocity field are given by the equations u=y^2-x(1+x) v=y(2x+1)...

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Question

a. What is N-S equations for incompressible flows in cartesian coordinates in long form (in x,y,z...

Solutions

Expert Solution

Related Solutions

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar...

Find the coordinates of the point (x, y, z) on the plane z = 4 x...

5. Equations of the form y’ = P(x)y^2 + Q(x)y + R(x) are called Riccati equations....

5. Equations of the form y’ = P(x)y^2 + Q(x)y + R(x) are called Riccati equations....

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