Environmental Engineering Reference
In-Depth Information
•
Using Equation 10.6, calculate the shear exponent.
•
Assume this exponent remains constant with height. From the power law,
extrapolate the mean speed from 58.5 to 80 m.
•
Using Equation 11.5, in a spreadsheet or with a calculator, find the value
of
z
0
that gives the correct speed at 58.5 m. For this purpose set
h
1
=
32
.
2,
2. (This will take some trial and error with different
values of
z
0
. You can use the Microsoft Excel Solver function if you wish.)
Looking at Table 11-1, does the value you derive make sense?
•
Using the same value of
z
0
, project the mean speed at 58.5 m to 80 m. For
this purpose, set
h
1
=
h
2
=
58
.
5, and
v
1
=
6
.
1.
•
Compare the results from the second and fourth points of this problem. How
much do the extrapolated speeds differ in percentage terms? Relative to the
logarithmic approach, does the power law produce a higher or lower shear
when extrapolating above the top measurement height?
58
.
5,
h
2
=
80
.
0, and
v
1
=
7
.
6. A 60-m meteorological mast has wind speed monitoring heights of 30, 40,
and 60 m. The average wind speeds at each level are 5.3, 5.7, and 6.4 m/s,
respectively.
•
Using the power law, calculate the observed shear exponent between the
following pairs of levels: 30 and 40 m, 40 and 60 m, and 30 and 60 m.
•
Assuming the speeds and heights are all known to the same degree of certainty,
which of these shear values would you say is the most precise?
•
Assume the heights are perfectly known and the speed ratio between any two
heights has an uncertainty of 1.5% (i.e., in Eq. 10.7,
015). What is the
uncertainty of each shear exponent you calculated? Do you think the variation
in shear between heights is statistically significant? Which shear exponent do
you think should be used to extrapolate the 60-m wind speeds to 80 m, and
why?
ε
=
0
.
7. A 60-m meteorological mast is deployed in forested terrain with an approximate
7-m displacement height in all directions. The shear exponent observed at the
mast is 0.32 between 40 and 60 m. Assume the shear exponent with respect
to the displacement height remains constant with height. What would be the
observed shear with respect to ground between the top anemometer height and
an 80-m hub height?
8. A meteorological mast has a thermometer installed at a height of 5 m. By how
many degree Celsius would you expect the average temperature to decrease
between 5 and 80 m?
9. A 50-m meteorological mast observes a 10-min average wind speed of 6.8 m/s
and a corresponding standard deviation of 1.1 m/s. What is TI? If the concurrent
wind speed at a hub height of 80 m is projected to be 7.5 m/s, what would be
a good assumption for the hub-height TI?
Search WWH ::
Custom Search