Design of pipe networks in unsteady flow cndition

When a pipe network is designed it is usual to estimate firstly what flows are required at its various outlets, what pipe sizes are needed in the net, and then what type and number of pumps are necessary to deliver the flow under the static and frictional heads imposed by the ground topology and the overall system losses. After all this has been done the classes of pipes are chosen and at this stage it becomes necessary to consider the problem of surge 

All designers are aware of the dangers of surge, and it is commonly realised that pipes burst under the excessive heads that surge can generate What may not be generally appreciated is the fact that negative surges, which impose sub-atmospheric pressures, can in conjunction with positive external pressures applied by over-burden, ground water and perhaps surcharge, cause a flexible pipe to fail in buckling. Large-diameter pipes are particularly at risk in this respect. After a bucking failure has occurred the pipe may burst when exposed to subsequent overpressures applied by surge. uPVC pipes can withstand a number of cycles of buckling before failing by splitting, but no pipe except perhaps very thick walled pipes should be subjected to such a degree of stressing if it can possibly be avoided

The methods of predicting the magnitudes of surge pressures are many and varied, the one in most common current use being the Schnyder-Bergeron graphical method. This method works adequately for a very simple system operating under high static heads and low frictional heads. Friction can be incorporated in the analysis if it can be assumed that it can be lumped at a relatively small number of points in the pipeline length. Wave speeds must be assumed constant. All these assumptions are very limiting as few networks are simple, friction cannot always be ignored, and wave speeds are never constant if even a very small number of gas bubbles are suspended in the fluid passing through the system. For a well chosen example it is possible to obtain excellent agreement between predicted and measured pressure heads using the Schnyder-Bergeron method, but in many cases errors can be as large as 50%.