58 



THE MOVING HYDRAULIC JUMP 



typical jump. Many of the rules and limitations applicable to the 

 stationary jump are no longer true for the moving jump, which may go 

 through such a range of variations that it is difficult to describe them all. 



In considering the different cases only positive values of Di and D2 

 will be considered for there seems to be no useful significance to negative 

 values. Furthermore, to produce the jump a clash of currents seems 

 to be necessary; hence if Di is assumed to be to the left of the line of 

 separation of the two currents and D2 to the right, as shown in Fig. 501, 

 then V\ must be algebraically greater than V2 or there could be no 

 clash. It follows then that V\ — Vq must always be algebraically 

 greater than V2 — Vq, and from equation (502), D2 must be greater 

 than D\. Equations (502) and (503) show that Di and D2 can be 

 interchanged if V\ and V2 are interchanged at the same time. However, 

 as explained above, there would then be no clash unless directions were 

 also reversed, and doing this leads to no additional information. To 

 economize space, therefore, Fig. 502 is drawn to include only the area 

 where D\ is less than D2', a symmetrical lower half is omitted. 



When Vi, V2, and Vq are all positive, Vq cannot be greater than V2. 

 If Fo is negative there are five possible cases that may be considered. 

 First, Vi and V2 may both be positive. Second, V2 may be zero while 

 Vi is still positive. This is the case when a gate is suddenly closed in a 

 canal containing flowing water. Third, V2 may become negative while 

 Vi is still positive. This is the case in the surf and the tidal bore. 

 Fourth, with V2 negative Vi may become zero. Fifth, both Fi and V2 

 may be negative. This may occur in the case of a flood wave traveling 

 down a stream. The special case in which the height of the jump 

 approaches zero is the " solitary wave " observed by J. Scott Russell. 



PROBLEMS 



501. Fill in the blank spaces in the following table in which each horizontal 

 line represents a moving hydraulic jump in a frictionless rectangular channel with 

 horizontal botton. 



