Low Reynolds number Flow
Plane Lubrication Films
Figure: Fluid flow between two plates (basic flow of tribology).
UP = velocity of the moving lower plate;
th
= inclination angle between the plates;
h(x1) = variation of plate distance
1
Low Reynolds numbe
Flow near a plate suddenly set in motion
Stokes first problem
Figure: Flow near a plate suddenly set in motion.
1
Flow near a plate suddenly set in motion
Figure: Transient flow due to the sudden motion of a plate.
Velocity profiles at t/l2=0.0001, 0.001,
Equation of Motion
The equations of motion for
incompressible Newtonian
fluid in Cartesian coordinates
(x, y, z).
1
Equation of Motion
The equations of motion for
incompressible Newtonian
fluid in cylindrical coordinates
(r, , z)
2
Equation of Motion
The
NavierStokes Equations
1
NavierStokes Equations
2
Figure: Momentum fluxes entering
and exiting the volume element dV
NavierStokes Equations
3
Figure: Normal stresses and shear
stresses at the volume element dV
Motion of a Fluid
The motion of a fluid can be determined, when the velocity at every point of
the space is occupied by fluid motion.
Therefore, to express the velocity with independent variables, there are two
distinct methods available,
(i) Lagrangian
Differential operator
Summary of
differential operators
in Cartesian
coordinates (x, y, z);
p, u and are scalar,
vector and tensor
fields, respectively.
1
Differential operator
Summary of
differential operators
in cylindrical polar
coordinates (r, , z);
p
ME 6125: Mechanics of Viscous Fluid
1
3.00 credit hours (Sunday: 4:30-6:00 PM; Wednesday: 7:30-9:00 PM)
Course content
Equations of motion for viscous fluid;
boundary layer analysis for laminar and turbulent flow;
theories of turbulence;
jet, wakes and
Department of Mechanical Engineering, BUET.
ME 6189: Computational Fluid Dynamics
Assignment-5
(Due date: 06 April 2013, Saturday. Submit hard-copy)
Note:
(i) Symbols have their usual meanings.
(ii) Clearly sketch the C.V. (control volume), show the nodal
Department of Mechanical Engineering, BUET.
ME 6189: Computational Fluid Dynamics
Assignment-4
(Due date: 24 March 2013, Saturday. Submit hard-copy, at class)
Note:
(i) Symbols have their usual meanings.
(ii) Clearly sketch the C.V. (control volume), show
Department of Mechanical Engineering, BUET.
ME 6189: Computational Fluid Dynamics
Assignment-3
(Due date: 23 February 2013, Saturday. Submit hard-copy, at class)
Note:
(i) Symbols have their usual meanings.
(ii) Clearly sketch the C.V. (control volume), s
Department of Mechanical Engineering, BUET.
ME 6189: Computational Fluid Dynamics
Assignment-2
(Due date: 30 January 2013, Wednesday. Submit hard-copy, at class)
Note: (i) Symbols have their usual meanings.
(ii) Clearly sketch the C.V. (control volume), s
Department of Mechanical Engineering, BUET.
ME 6189: Computational Fluid Dynamics
Assignment-1
(Due date: 02 March 2013, Saturday. Submit hard-copy, at class)
Note: (i) Symbols have their usual meanings.
(ii) Use finite difference method for discretizatio