EXPERIMENTAL AERODYNAMICS.
§ 245
Or, |
![{\displaystyle V_{1}=15\ {\mbox{ft. /sec.}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5df92664b94fa333a79a05a851d113411d1ccabc) |
|
|
![{\displaystyle V_{2}=12.5\ {\mbox{ft. /sec.}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ebe64d1b0aa8db991bc2ec205187e03d5b20e48) |
|
|
![{\displaystyle \gamma _{1}={\frac {7.5}{47}}=.160}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a8d2005b4ffb27480e8c93913431c8409e0016e) |
[1]
|
|
![{\displaystyle \gamma _{2}={\frac {7.5}{35}}=2.14}](https://wikimedia.org/api/rest_v1/media/math/render/svg/652aa580720f5cbbd5d1e5783bcaf7d724fcdb74) |
|
|
![{\displaystyle x_{1}+y_{1}=.160\times 5.25=.84}](https://wikimedia.org/api/rest_v1/media/math/render/svg/21983f7f30f8ba2fee21200ef5b3caa7a2416ec9) |
(1)
|
|
![{\displaystyle x_{2}+y_{2}=.214\times 5.25=1.12}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2db897b264eb3da3af7bdcc1f5cd06644a3688db) |
(2)
|
Now we know that and where and are constants,
|
or, |
![{\displaystyle x_{1}=15^{2}n,\quad y_{1}={\frac {m}{15^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cbc8f9a71290fbad86aa7e3208f4aa24a0412cb) |
(3)
|
|
![{\displaystyle x_{2}=12.5^{2}n,\quad y_{2}={\frac {m}{12.5^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/407529ba6055e36d58d6f885d753f53895431e7c) |
(4)
|
By (1) and (3) |
![{\displaystyle 15^{2}n+{\frac {m}{15^{2}}}=.84}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c3482bc3f7e972e2ca99fc6d5da047d24bd5fd5e) |
(5)
|
By (2) and (4) |
![{\displaystyle 12.5^{2}n+{\frac {m}{12.5^{2}}}=1.12}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a2f3befcfa5cdaaa73a70da626101739062036d) |
(6)
|
∴ |
![{\displaystyle 12.5^{2}n+{\frac {(.84-15^{2}n)\times 15^{2}}{12.5^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eda0e520fd797a55fbeb0e58198715f7207d0499) |
|
∴ |
![{\displaystyle 156\ n-325\ n=1.12-1.21}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f70c8a27786a9eb7f7fbfe0ea02acc198d1fde4d) |
|
or, |
![{\displaystyle 169\ n=.09}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c4be9fd45a7e7f90ff5d508a1e29c19e59f7a98d) |
|
|
![{\displaystyle n=.000532}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1536d23a042492fc98713ce64a594f7b97e17dc) |
|
or, |
![{\displaystyle x=.000532\ V^{2}\ {\mbox{grams.}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9bf375772d3e86ac7ff47b041142b041e3edda48) |
|
multiplying by
to obtain grams per square foot, and by
to convert to British absolute units, we have—
But normal plane pressure is given by expression—
or,
In the foregoing calculation no allowance has been made for
- ↑ In these experiments the hypothesis of the small angle is taken as applying to
values;
is expressed in radians.