Answer the following question. The wake velocity of the lift Oseenlet is given by 1 (e*i K,(kr)) 2 πρυx (2) 1. Give the horizontal component of velocity w in the far-field where x,>0, by using the asymptotic approximation K,(kr)~ire -kr and the asymptotic approximation for r-x. V 2 kr
Answer the following question. The wake velocity of the lift Oseenlet is given by 1 (e*i K,(kr)) 2 πρυx (2) 1. Give the horizontal component of velocity w in the far-field where x,>0, by using the asymptotic approximation K,(kr)~ire -kr and the asymptotic approximation for r-x. V 2 kr
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Please solve last two parts
![Answer the following question.
The wake velocity of the lift Oseenlet is given by
1
w=;
(e K(kr))
Ey3
2 πρυ
дх,
1. Give the horizontal component of velocity w in the far-field where x,>0, by using the
asymptotic approximation Ko(kr)~2kr
e
and the asymptotic approximation for r-x.
2. Hence give an expression for the upper half outflow given by the integral
1=S, w"dx,
and show that 1+0 as x,.
Consider the expression for the upper half moment
S, x,w"dx,.
M =
3. Evaluate the integral to give M and show that it is a constant as x,o. (Help: Consider
k x2
and use the integration by parts fq'e"dq=;e*]-Se dq. )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9a958a9-a9d7-40b5-a676-5a325bc0b99d%2Feee9af6e-0c74-4208-862a-f819a6eae877%2Fm2smj8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Answer the following question.
The wake velocity of the lift Oseenlet is given by
1
w=;
(e K(kr))
Ey3
2 πρυ
дх,
1. Give the horizontal component of velocity w in the far-field where x,>0, by using the
asymptotic approximation Ko(kr)~2kr
e
and the asymptotic approximation for r-x.
2. Hence give an expression for the upper half outflow given by the integral
1=S, w"dx,
and show that 1+0 as x,.
Consider the expression for the upper half moment
S, x,w"dx,.
M =
3. Evaluate the integral to give M and show that it is a constant as x,o. (Help: Consider
k x2
and use the integration by parts fq'e"dq=;e*]-Se dq. )
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