Starting from the general expression of the Navier-Stokes
equations in cylindrical coordinates, provide the form of the
equations for an axisymmetric, steady flow. Explicitly write down
the continuity equation as well as the momentum equation in all
relevant directions in terms of partial derivatives. (Hint: How
much is uθ for this flow? Explain why. How much is ∂/∂θ ?
IMPORTANT NOTE: Please have the answer complete,
clear and computer generated!!
The Navier Stokes equation is well known. Make the Navier Stokes
equation dimensionless. Make your assumptions about the different
parameters. Using Reynold's number, show the terms that exist at
high Reynold's number and those at low Reynold's number What do
these represent?
Please explain in full detail.
Write the heat conduction equation (without flow in and out) in
cartesian coordinates for the following case:
1. Steady-state, 1-D, without heat generation (2 points)
2.Transient, 1-D, without heat generation (2 points)
3.Transient, 3-D, with heat generation (3 points)
3. Write the three types of boundary conditions. (3 points)
For the case of incompressible flow, write all 3 components of
the Navier-Stokes equations and the complete form of the
differential continuity equation.
a) Given a vector field à = zỹ +(3y + 2)2 î in cartesian
coordinates, determine whether it is solenoidal (V · À = 0),
conservative (D x X = 0)
I Div x A (Cylinderical Coordinates)
ii) Calculate integral A*dl , where the contour C is the unit
circle (r=1) traversed in anticlockwise direction
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...
Expressed in terms of Cartesian unit vectors, a displacement
vector has the form: A=(3.00m)i-(4.00m)j where the units are given
(meters) Express this vector in polar form