[datle]

Hi,
I have a pipe with 2 pressure sensors installed at two ends so that I can know two boundary conditions P(0,t) and P(L,t) (see the picture attached). In this figure, p is pressure, u is mean velocity of flow, t is time, x is coordinate in pipe, rho is fluid density, c is speed of sound, lambda is friction coefficient, D is diameter of the pipe.
Assume that I know every parameters, relationship between fluid density and pressure, diameter of the pipe, thickness of the pipe, relationship between fluid bulk modulus and pressure, Young modulus of steel, thickness of the pipe, constant temperature, I want to calculate the flow u(x,t) and pressure P(x,t). I would like to ask if this problem is solvable?
As I investigated, I need to have initial conditions for both u and P. Therefore, I set u(x,0) = 0 and P(x,0) is linear with distance as in the figure. I wonder if an error in this setting (for example offset in u(x,0)) can cause trouble with simulation?
I then used method of characteristics to solve u(x,t) and P(x,t) and does not get a reasonable result to me now. And one problem in using method of characteristics is that I need to know lambda at the initial condition when there is no flow. If I use the equation for lambda as in the figure, then lambda = infinity. I then set lambda = 0 at the beginning. Is this a valid assumption?
I am not working in fluid mechanics, the question then may be simple to everyone. I appreciate your help.
Thanks,