How to calculate the time delay created by a tube.

Hi,

I am trying to model a pressure tube of length 'L', where a fan is attached at one end and the other end is open. I know that Pressure in the tube will vary w.r.to space and time when there is some change in excitation at the input. I got the pressure drop equation ,

f - friction created by the walls of the tube. dx - distance. V - velocity of air flow. D- diameter of the tube. g- gravity

Using the above equation, I can calculate pressure drop at any distance (dp/dx) directly. But how can I get the time delay created by the tube. Please some one guide or teach me how to derive P(x,t).

Thanks srinivas