Geometrical Acoustics I the Theory of Weak Shock Waves
Geometrical Acoustics I the Theory of Weak Shock Waves
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Px. 1 1 16. One such set of equations Is obtained on each side of the wavefront. We now subtract each equation on side tv;o from the corresponding equation on side one. Then remembering that the basic flov; was assioi'ded to be continuous, and that As = As" = 0, we obtain (1+7) [1-u. LC ] A(Pi. ) + [-pV/„ ]A(u. ) = -pAu. - P. , All. -u. ^p-u. A?^^^ X. 1 X. 1 ^ i "^ j t i _2 -1 — -1 — _ _ = [p Px " P ^o ^Ap-P P Apx - ^i ^u. -u. Au. I Px, P i ^x . -J -^ X ()49) [1-u. W. ^ ]A(s. ) = -s„ /^u. J J E...quations (!4. 7)-('!-9} are a set of five linear inhomogeneou£ equations for the five quantities -Ap, , Au. And Z^ s^, . Let us G compare these equations with the shock conditions which are a set of five homogeneous equations for Ap, Au. And As. These latter equations can be rewritten in the form (50) UAp + ov^Au^ = (51) v^p /^p + pUAu^ -I- v^p^Ziks = (52) pUe„As = 1-^ s If (1+7) is multiplied by -^, (1+G) by -2- and (Il9) by ]\-'^ Jvt pe, , ^"k V 'k - — ~ then the coefficient matrix on the left side becomes identical with that of (50)-(52).
What to read after Geometrical Acoustics I the Theory of Weak Shock Waves?
You can find similar books in the "Read Also" column, or choose other free books by Joseph B Keller to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Px. 1 1 16. One such set of equations Is obtained on each side of the wavefront. We now subtract each equation on side tv;o from the corresponding equation on side one. Then remembering that the basic flov; was assioi'ded to be continuous, and that As = As" = 0, we obtain (1+7) [1-u. LC ] A(Pi. ) + [-pV/„ ]A(u. ) = -pAu. - P. , All. -u. ^p-u. A?^^^ X. 1 X. 1 ^ i "^ j t i _2 -1 — -1 — _ _ = [p Px " P ^o ^Ap-P P Apx - ^i ^u. -u. Au. I Px, P i ^x . -J -^ X ()49) [1-u. W. ^ ]A(s. ) = -s„ /^u. J J E...quations (!4. 7)-('!-9} are a set of five linear inhomogeneou£ equations for the five quantities -Ap, , Au. And Z^ s^, . Let us G compare these equations with the shock conditions which are a set of five homogeneous equations for Ap, Au. And As. These latter equations can be rewritten in the form (50) UAp + ov^Au^ = (51) v^p /^p + pUAu^ -I- v^p^Ziks = (52) pUe„As = 1-^ s If (1+7) is multiplied by -^, (1+G) by -2- and (Il9) by ]\-'^ Jvt pe, , ^"k V 'k - — ~ then the coefficient matrix on the left side becomes identical with that of (50)-(52).
What to read after Geometrical Acoustics I the Theory of Weak Shock Waves?
You can find similar books in the "Read Also" column, or choose other free books by Joseph B Keller to read onlineMoreLess
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