388 



HYDRAULICS AND ITS APPLICATIONS 



back. Experiment also tends to show that the resistance is somewhat 

 greater when the plate is stationary in a moving current than when 

 it is moved through still water. This is probably due to the fact that the 

 water when in motion is in a much more unstable condition than 



when at rest, so that the sphere of 

 influence of eddies projected from 

 the boundaries of the plane is greater, 

 and the consequent dissipation of 

 energy is greater in the former than 

 in the latter case. 



With a plate 1 inch square held in 

 a moving current, Stanton 1 obtained a 

 value of k = '620. 



Submerged Plane in Pipe of Small 

 Cross-Sectional Area. 



The effect of placing the plane in a 

 pipe of restricted area, is to increase 

 the velocity with which the water 

 escapes over the edge of the plane. 

 This causes an increased eddy pro- 

 duction, a consequent reduction of 

 pressure on the rear of the plane, and 

 hence an increased resistance. 



Oblique Motion of Submerged Planes. 

 Where an oblique plane makes 

 an angle 0, with its own direction of motion (Fig. 176), the velocity of 

 the water normal to the plane = v sin 6. 



The column of water whose momentum is affected, is now of sectional 

 area a sin 0, so that the change of momentum produced by the passage of 

 the plane is proportional to 



FIG. 176. 



W v a sin v sin 6 



i.e., to 



W a 



sin 2 0. 



9 9 



It might then be expected that the resistance to the oblique motion of a 

 plane would e^ual 



Direct resistance X sin 2 #. 



Due, however, to the unequal eddy formation at the rear of the plate 

 with the two kinds of motion, and to the fact that as 6 is diminished, 



" Trans. Inst. N.A.," 1909. 



