HW4 Solution

1
2
,
2
This equation must be solved for . However, as noted in Problem 6.4, this equation is a fourth-order
polynomial and, although closed-form solutions to this problem do exist, the simplest way to solve this problem
is by graphical means or by iteration. The method of solving graphically was illustrated in Problem 6.4 and so the
method of iteration will be demonstrated in the Numerical Substitution section of this problem.
Numerical Substitution:
To begin, it is first required to find the density at sea level. From Appendix A, the sea level standard air density is
Next, will be converted into consistent SI units.
1.225
9.8
1020
1 9996
Similarly, the power, , must also be converted into consistent SI units.
Using the equation derived in the analysis,
746 W
85 hp
1 hp
63410
0.963410 1
1.225
2 11.450.03
57069 0.2104
33.65
57069 0.2104
33.65
0.2104
33.65 ·
·
57069 0
29996
1.225
14.85 0.7
First, note that the units are consistent. In other words, for the first term on the left hand side,
For the second term on the left hand side,
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