1. The problem statement, all variables and given/known data We have an accelerating vehicle with constant a. Air inside it with mass m. It is kind of closed box of length L and front area S. First objetive: we want to derive the steady state pressure distribution inside the box. Second objetive: we want to derive the transient pressure distribution inside the box. 2. Relevant equations My first guess was to assimilate the problem to an atmosfere with gravitatory field of g=a and use the barometric formula for calculating the pressure distribution. Second try is to use simplified Navier eq. but I don´t know how exactly... 3. The attempt at a solution First try with barometric formula: Force over the mass of air inside: Fa = m a Reaction pressure over the rear side: Pa=Fa/S Assuming barometric distribution inside with g=a (M molar mass of air) P(x)=C exp( -M a x / (RT) ) with initial condition at rear side P(0)=C=Pa This gives a very weak variation with lenght (i.e for 60m it just changes 0,1Pa) so I don´t trust this solution. Second try: Assuming 1D problem, incompressible fluid and no viscosity: dV/dt = f - (1/ro) dP/dx If steady state: f = (1/ro) dP/dx update: checking dimensinally it seems that f is an acceleration so it should be a, and it is in opposite sense of x so: dP = -ro a dx integrating P(x)=-ro a x + C, Now I know that in x=0, I have Pa= m a / S, so P(x)= - ro a x + m a /S With 1m/s2 this gives a linear gradient of pressure about 1.2Pa/m length of the vehicle. ¿it makes sense this result? I would appreciate any comment or help!