Spherical Cylindrical And One Dimensional Flows of Compressible Fluids

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Spherical Cylindrical And One Dimensional Flows of Compressible Fluids
Joseph B Keller
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-1, B' Xf r. Q q -(n-l)l + ™ + — = (32) q(f) = r^"^3"-^(f) exp J -Xf3"^(f)df . Thus ■X r- (33) h(f) = f^-lB"^-(f) jxp j -\fB~^( f)df df + E Equation (33) yields the solution implicitly. Again we define (3ij-) F(f) = exp Then if X 7^ we have ( 35) /- XfB"-'-(f)df 3(f) = -\fF(F')'- The solution for the flow variables, if y = 1 and \ ^ 0, is again given by (2[|. )-(26) with y = \ and j(t) given by (15). Similarly for y = 1 find X = the solution is given by (27) -(29) with y = 1, G = 1 and j(t) giv...en by ( 30) . 1 ; : " f: . . -r' -. :, • !■ Equations (2l4. )-(26) and (27}-(29) represent non- Isentropic solutions of the flow equations depending upon an arbitrary function. In order to construct these solutions exp]. Icitly one need merely evaluate the integrals in ( Iti. ) or (15) • Some special cases of these integrals yield results which are listed below for later use. N(Y-l) 2 if yj^l, a=0, 11^ = -1 if n(l-'^-)= 1, ci, p arbitrary. If y-n, a=0, iiA-p-i / -1 (37) 3{t)=e' +aV2, :X (38) j(t) = |t^+ at + B IV .

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