Question

- 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 mentioned in the last lecture (1 point) (assuming incompressible, steady and fully developed flow)

BONUS: Assume an incompressible, steady, axissymmetric 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) (2 points)

Answer #1

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

Your task will be to derive the equations describing the
velocity and acceleration in a polar coordinate
system and a rotating polar vector basis for an object in general
2D motion starting from a general
position vector. Then use these expressions to simplify to the case
of non-uniform circular motion, and
finally uniform circular motion.
Here's the time-dependent position vector in a Cartesian coordinate
system with a Cartesian vector
basis: ⃗r(t)=x (t)
̂
i+y(t)
̂
j where x(t) and y(t)...

Consider the BVP or the steady-state temperature u(x,y,z) in the
airspace between two infinite (in the y and z directions) stone
walls that are perpendicular to the x-axis, and are 5 centimeters
apart from each other (ie the wall surfaces in contact with the air
space are 5 cm. apart), with the first (or left) wall located at
x=-1 cm. and the second (or right) wall at x= 4 cm, where ux = -10,
and u=100, respectively. Temperature is measure...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 20 minutes ago

asked 39 minutes ago

asked 45 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago