EML 5060 Homework Set 4 Fall 1996 | |||
Page | HW | Class | |
17 | 2.19afh | 2.19e | Classification |
17 | 2.20 | Classification | |
17 | 2.21ab | 2.21c | Classification: assume u=u(x,y,z) |
18 | 2.24 | 2.26 | Canonical form |
18 | 2.25 | Canonical form | |
18 | 2.22cef | 2.22d | Characteristics |
18 | 2.27ab | 2.27d | 2D Canonical form |
18 | 2.28dejo | 2.28nml | 2D Canonical form |
98 | 7.20 | 7.19 | Unsteady heat conduction in a bar |
98 | 7.22 | 7.21 | Unsteady heat conduction in a bar |
98 | 7.24 | 7.26 | Unidirectional viscous flow |
98 | 7.26 | Unidirectional viscous flow | |
99 | 7.27 | 7.28 | Acoustics in a pipe |
99 | 7.31 | 7.29 | Vibrations of a string |
99 | 7.35 | 7.36 | Acoustics above a plate |
99 | 7.37 | 7.37 | Steady heat conduction in a plate |
99 | 7.38 | 7.39 | Steady heat conduction in a disk |
Solve the problem below |
The boundary condition on the pipe wall is
For initial condition, assume that is a delta function at r=0.5 and , in other words that
for any function . Sketch the velocity profile u(r,0,t) at for a small time t. Determine and draw the shape of the velocity profile (i.e. u(r,0,t)/u(0,0,t)) for a large time t. Does u become independent of for large times?