Assignment 4 (45 pts)
Name: ____________________________
1. The following temperature and flow fields represent the distribution of heat from a
heat source to a heat sink
T  10o C    x  y  cos  x 
where   1 m 1 and   1 m1 are a wave number
constants.
A fan provides an irregular 2-D velocity field,
u    exp  ky   exp  kx  
mˆ
m
i   exp  ky   exp  kx   ˆj
s
s
a. (5 pts) Circle the area(s) on the figure with the largest
warm-air advection and the largest cold-air advection.
Explain your answer.
b. (10 pts) Find the temperature advection at x=-2 m y=2 m and at x=2 m y=2 m. Show
all work. Do your answers agree with what you circled in Part a?
c. (5 pts) At the points in question b, is there cold-air advection or warm-air advection?
Explain.
2. (10 pts) Identify the following vector fields as either Eulerian or Lagrangian
descriptions of flow. Explain your answer in terms of the definition of the Eulerian or
Lagrangian framework.
a) u   ytiˆ  xtjˆ , where  is a constant with units of m 1s 1 and x and y are
positions of the fluid parcel.
mˆ
m
i  exp  ky0  ˆj where k  1 m 1 is a wave number constant and
s
s
x o and y o are constants that indicate the location of a fluid parcel at time t=0.
b) u  sin  kx0 
3. (5 pts) Given
u   ytiˆ  xtjˆ
Find the material acceleration following a fluid parcel a 
Du
Dt
4. (7 pts) Given u  sin  kx0 
mˆ
m
i  exp  ky0  ˆj
s
s
Find the material acceleration following a fluid parcel a 
Du
Dt
5. (3 pts) What is the relationship between the material acceleration in the Lagrangian
framework and the material derivative in the Eulerian framework?