Converting from Static to Dynamic Understanding the Darcy Weisbach

[joejoekelly1]

Trying to get my head around something with the Darcy Weisbach. It is used to calculate the head loss of a moving fluid within a pipe. So for example if we take a pipe with an entry point 6m above a datum plane and an exit point 1m above the same datum plane. The pipe length is very long, say 10,000 meters. In this scenario the fluid would flow from the entry point to the exit point and using the Darcy Weisbach equation there would be a loss in pressure at the exit point when compared to 1m above the entry point.

While the above holds true for a dynamic system, if the exit point was closed off and no water was allowed to flow this would make the system static. In a static system the pressure across a level plane is the same, therefore the pressure at the exit point would equal the pressure 1m above the datum plane at the entry point. If the exit point was opened again the fluid would start to flow. The Darcy Weisbach tells us that once the fluid is flowing there will be a pressure drop; however would the pressure drop be more gradual rather than instantaneous? In other words would it take X amount of time before the shear stresses between the fluid and the pipe wall reach a nominal level which ultimately results in the pressure drop we see in a dynamic system?

Also when the Darcy Weisbach asks for L (Length of pipe) in its equation, is it basing its analysis on the movement of the entire length of fluid within the pipe or the movement of some cross-section of fluid within the pipe?

Any thoughts on these would be appreciated!

 

[SteamKing]

In a static system the pressure across a level plane is the same, therefore the pressure at the exit point would equal the pressure 1m above the datum plane at the entry point.

The datum chosen for the piping system must be the same throughout the length of the entire system. You can't chose one datum at the entrance and a different datum at the exit.

Piping system friction for D-W is modeled as f*L/D, where f is a friction factor which is based on the pipe material and the Reynold's No. of the flow, L is the length of the pipe, and D is the internal diameter of the pipe. In between the entrance and the exit, the flow due to friction in the pipe is assumed to be directly proportional to the distance from the entrance, IOW, there will be one-half of the total friction at a point which is midway between the entrance and the exit.