390 



HYDRAULICS AND ITS APPLICATIONS 



The resistance in tlie direction of motion is given by P' sin 0. 



Probably the experiments by Stanton are the more reliable, and for 

 values of greater than 15, the agreement of these results with those 

 calculated by the formula of Duchemin, is very close. 



As in the case of the normal plane, there is only one point P, this in 

 the median plane of the plate, at which the velocity is zero and at which the 



W r 2 

 maximum pressure -~ is therefore attained. This is in advance of 



the centre of the plane, and its distance from the centre in terms of the 

 length I of the plane, as obtained theoretically, is given in the following 

 table. 1 The distance x of the centre of pressure from the centre of the 



plane, is theoretically given by the formula x = - . - -. - a . I, 1 and 



4 4 -J- 7T sin v 



values of x are also tabulated below. 





It is found, moreover, that with a rectangular oblique plane the total 

 pressure for a given value of depends largely on whether the long or 

 short edges of the plane are perpendicular to the stream, the resistance 

 being greatest when the long edges are so placed. The reason for this is 

 explained by Lord Rayleigh as follows. Although there is only one point 

 of maximum pressure whatever the manner of presentation of the plane, 

 yet with the long edges perpendicular to the stream the motion is approxi- 

 mately in two dimensions, and a region of almost maximum pressure 

 extends over the greater part of the length. The case is very different, 

 however, when the short dimension is perpendicular to the stream, for 

 then, along the greater part of the length the flow is rapid and the 

 tressure in consequence low. 



This is of importance in the design of oar blades, the floats of paddle- 



From Lamb's " Hydrodynamics," p. 94. 



