56 THE MOVING HYDRAULIC JUMP 



which, when Vq = 0, reduces to 



From equations (505) and (507) numerical values were calculated by 

 means of which the curved lines on the right-hand part of Fig. 502 were 

 plotted. Values of Vi and V2 are read along the coordinate axes, and 

 the two sets of curved lines represent equal values oi Di and Z>2 respec- 

 tively. The axes for Vi and V2 are inclined at 120 degrees, instead of 

 being rectangular, for two reasons: first, in order to utilize the space 

 more efficiently; second, in order to obtain subsequently the same scale 

 for Vq as is used for V\ and F2. It should be carefully noted that lines 

 for constant values of Vx run from the bottom of the diagram upwards 

 and towards the left, while lines for constant values of V2 run from the 

 bottom of the diagram upwards and towards the right. 



The diagram as so far described suffices for the solution of problems 

 on the stationary jump. Of the four variables V\, V2, D\, and D2, 

 values for any two may be given. These values will locate a point on 

 the diagram, where the corresponding values of the other two variables 

 may be instantly read. For example, assume that the given data are 

 Fi = 15 feet per second and Di = 2 feet. These locate the point 

 marked P on Fig. 502, showing that V2 = 6.8 feet per second and 

 D2 = 4.4 feet. It is apparent that the given data might have been 

 Fi = 15 and V2 — 6.8, locating the same point, from which the corre- 

 sponding values of Di and D2 could be read. 



To use the diagram for the solution of problems on the moving 

 hydraulic jump it is necessary to introduce the fifth variable Vq. This 

 is done by moving the point on the diagram horizontally a distance 

 equal to Vq measured on the velocity scale along the bottom of the 

 diagram. For example, suppose the given data to be Z)i = 2, P2 = 4.4, 

 Fo = 5. The values of Di and £>2 give the point P in the diagram. 

 From P a distance is measured horizontally to the right equal to 5 on 

 the velocity scale, locating the point Q, from which may be read the 

 values Fi = 20 feet per second, F2 = 11.8 feet per second. It is 

 evident that the operation would be equally easy if the given values 

 were Fi, F2, and Vq. It is not quite so convenient, however, when 

 such data are given as Di = 2, Fi = 20, and Fo = 5. In such a case 

 it is necessary by careful inspection or by using a movable horizontal 

 scale to determine just where the Hne for Di = 2 and the line for Fi = 20 

 are apart, measured horizontally, a distance exactly equal to the given 

 value of Vq. This can be done by the exercise of some care and at the 

 cost of a little inconvenience. If the given value of Fo is negative, then 



