Answer the following question. The wake velocity of the lift Oseenlet is given by 1 w" = 2 rpU x, (e. K,(kr)) 1. Give the horizontal component of velocity wi in the far-field where x,>0, by using the asymptotic approximation Ko(kr)~, Ie and the asymptotic approximation for r-x.. 2kr 2. Hence give an expression for the upper half outflow given by the integral Wi and show that I→0 as x,+0.
Answer the following question. The wake velocity of the lift Oseenlet is given by 1 w" = 2 rpU x, (e. K,(kr)) 1. Give the horizontal component of velocity wi in the far-field where x,>0, by using the asymptotic approximation Ko(kr)~, Ie and the asymptotic approximation for r-x.. 2kr 2. Hence give an expression for the upper half outflow given by the integral Wi and show that I→0 as x,+0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![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%2Fda3f3234-1c10-4b4b-ba52-d87b2ae88541%2Fxxd9ev_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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