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 2 years ago

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

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar coordinates (r, θ) of the point so that r > 0 and 0 ≤ θ ≤ 2π. (b). The polar coordinates (r, θ) = (−3, 5π/6) of a point are given. Find the Cartesian coordinates (x, y) of this point.

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

Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 4 which is closest to the origin.

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’ +...

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’ +...

A Cartesian vector can be thought of as representing magnitudes along the x-, y-, and z-axes...

A Cartesian vector can be thought of as representing magnitudes along the x-, y-, and z-axes multiplied by a unit vector (i, j, k). For such cases, the dot product of two of these fectors {a} and {b} corresponds to the product of their magnitudes and the cosine of the angle between their tails as in {a}⋅ {b} = abcos(theta) The cross product yields another vector, {c} = {a} × {b} , which is perpendicular to the plane defined by...

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

Suppose that X, Y and Z are normally distributed where X ≈ N(100,100), Y ≈ N(400, 400) and Z ≈ N(64,64). Let W = X + Y + Z. a) Describe the distribution of W, give a name and parameters E(W) and Var(W). b) Use Excel or R to generate 200 random values for X, Y and Z. Add these to obtain 200 values for W. Create a histogram for W. In Excel use the NORMINV(rand(),mean, sd) function. c) Estimate...

2.48. Is it true that {ax + by + cz|x, y, z ∈ Z} = {n...

2.48. Is it true that {ax + by + cz|x, y, z ∈ Z} = {n · gcd(a, b, c)|n ∈ Z}? 2.49. What are all the integer values of e for which the Diophantine equation 18x + 14y + 63z = e has an integer solution. Find a solution for each such e. 2.50. For integers a, b and k > 0, is it true that a | b iff a^k | b^k ?

Solve for x,y,z if there if a solution to the given system of linear equations: x...

Solve for x,y,z if there if a solution to the given system of linear equations: x - 3y - 2z = -3 3x + 2y - z = 12 -x - y + 4z = 3

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)...

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) (a)Show that the flow satisfies continuity. (b) Determine the corresponding stream function for this flow field. (c) Determine if the flow is irrotational.

Suppose that an event occurs in the reference frame S with coordinates x = 2m, y...

Suppose that an event occurs in the reference frame S with coordinates x = 2m, y = 0m and z = 0m at t = 4m/c. The frame S’ moves in the positive x-direction with velocity u = 0.2c. The origins of S and S’ coincide at t = t’ = 0. a. Use the Lorentz transformations to find the coordinates of the event in S’. b. Use the inverse transformation on the results of (a) to obtain the original...

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....

A Cartesian vector can be thought of as representing magnitudes along the x-, y-, and z-axes...

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

2.48. Is it true that {ax + by + cz|x, y, z ∈ Z} = {n...

Solve for x,y,z if there if a solution to the given system of linear equations: x...

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)...

Suppose that an event occurs in the reference frame S with coordinates x = 2m, y...