!$ { \Large { \partial \bar{u}\over \partial\,t}} + u^{ \prime} { \Large { \partial \bar{u}\over \partial\,x}+ { \Large { 1 \over p^{\prime}}}} { \Large { \partial \bar{p}\over \partial\,x}} = 0 !$

!$ { \Large { \partial u^{ \prime} \over \partial t}} + \bar{u} { \Large { \partial u^{ \prime} \over \partial x}} + { \Large { 1 \over p}} { \Large { \partial p^{ \prime} \over \partial x}} = 0 !$

!$ { \Large { \partial (p^{\prime} + \bar{p}) \over \partial t}} + \bar{u} { \Large { \partial (\bar{u} + u^{ \prime}) \over \partial x}} + { \Large { 1 \over p}} { \Large { \partial (\bar{p} + p^{\prime}) \over \partial x}} = 0 !$

!$ { \Large { \partial (p^{\prime} + \bar{p}) \over \partial z}} = ( p^{\prime} + \bar{p} ) g !$

!$ { \Large { \partial p^{ \prime} \over \partial t}} + \bar{u} { \Large { \partial p^{ \prime} \over \partial x}} + \bar{p} { \Large { \partial u^{ \prime} \over \partial x}}= 0 !$