On Jets Produced By Conical Nozzles
On Jets Produced By Conical Nozzles
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In our eReader you can find the full English version of the book. Read On Jets Produced By Conical Nozzles Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book On Jets Produced By Conical Nozzles
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To quickly assess the difficulty of the text, read a short excerpt:
:vWj #J -.
tf^'i - 22 - (15) mR R + sR + (2^ - ST' )R^ + q' = 0.
It is Immediately verified that R = R is a solution of '' o (15) and we shall now show that any solution of (15) v;hich gets close to R performs damped oscillations about R, In a t_ interval where R(t) is monotonic, a unique inverse t(R) is defined. Introducing u(R) defined by (16) u(R) = R(t(R)) one gets from (15) a first order equation for u.
(17) u' = - + su + ( m' ST' )u' mu The point R=R, u=0 is a singular point of this equat...ion, and an easy verification shows that it is, pro- vided that assumption (lU-) holds, a vortex point. Con- sequently, the solutions of (1?) near R = R, u = spiral about this point, see fig. 5» The reinterpretation of this "phase space" diagram in the "physical space" leads to damped oscillatory motion.
locus u'=0 u'0 Fip;ure 5 Since R satisfies a non-linear equation, its "period" (time elapsed between two successive maxima) and its "half time" depend on initial data. One obtains an estimate of - 25 - the period and the half time by assuming a motion of small amplitude and linearizing the differential equation.
What to read after On Jets Produced By Conical Nozzles?
You can find similar books in the "Read Also" column, or choose other free books by Ignace I Kolodner to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
:vWj #J -.
tf^'i - 22 - (15) mR R + sR + (2^ - ST' )R^ + q' = 0.
It is Immediately verified that R = R is a solution of '' o (15) and we shall now show that any solution of (15) v;hich gets close to R performs damped oscillations about R, In a t_ interval where R(t) is monotonic, a unique inverse t(R) is defined. Introducing u(R) defined by (16) u(R) = R(t(R)) one gets from (15) a first order equation for u.
(17) u' = - + su + ( m' ST' )u' mu The point R=R, u=0 is a singular point of this equat...ion, and an easy verification shows that it is, pro- vided that assumption (lU-) holds, a vortex point. Con- sequently, the solutions of (1?) near R = R, u = spiral about this point, see fig. 5» The reinterpretation of this "phase space" diagram in the "physical space" leads to damped oscillatory motion.
locus u'=0 u'0 Fip;ure 5 Since R satisfies a non-linear equation, its "period" (time elapsed between two successive maxima) and its "half time" depend on initial data. One obtains an estimate of - 25 - the period and the half time by assuming a motion of small amplitude and linearizing the differential equation.
What to read after On Jets Produced By Conical Nozzles?
You can find similar books in the "Read Also" column, or choose other free books by Ignace I Kolodner to read onlineMoreLess
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