By J. A. Fox (auth.)
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Additional resources for Hydraulic Analysis of Unsteady Flow in Pipe Networks
Pipe fitted with expansion joints so that it can extend longitudinally without generation of longitudinal stress and free to distend diametrally When a pressure 11pi is applied to a pipe it will distend diametrally. The fluid within it will compress. The pipe distension plus fluid compression effects enable it to contain more fluid than it would do in its normal unpressurised condition. This increase in volume can be calculated as follows. Volume increase due to fluid compression= 11 Vp =~Pix~ d 2 L where K is the fluid bulk modulus and dis the pipe diameter.
As graphical techniques are time consuming this can rarely be done. Any graphical technique consists of the following: (I) Graphically representing the boundary conditions present in the network. (2) Graphically representing the equations of waterhammer which describe the conditions within the pipe as the waves traverse it. e. a hydraulic control) is present. In any waterhammer problem four variables are involved: head, velocity (or flow), position in the pipe ~x, and time ~t. To represent these four variables on a graph an ingenious device is used which employs the fact that a transient is propagated at a speed c.
Therefore Q is another point on the Xt line. The Xt line must be straight so by joining RQ the Xt line is obtained. In some junctions q 1 =q 2 + q 3 . The combination process performed above for the q 1 =q 3 - q 2 equation can be applied with a very simple modification. 18. Ann way junction can be analysed by the methods given in the previous section. The combination of the eagres of two pipes produces a x line, by combining this x line with the eagre of another pipe a further line (say a Aline) can be obtained.