26 HYDRAULICS AND ITS APPLICATIONS 



case a hole should be drilled at one operation through both walls of the 

 pipe. The entering hole may then be plugged up and the second hole, 

 which, with care, will be found to be free from any burr, may be used as 

 the pressure opening. Such an opening should be small one-thirty- 

 second of an inch will usually be found to be ample, the connection 

 appearing as shown in Fig. 10 D. 



The point of attachment of the pressure tubes to the main is im- 

 material, the free surfaces or surfaces of separation in the gauge rising 

 to the same height whether the point of attachment is at the highest or 

 lowest point of the main. 1 



Where a continuously recording gauge is to be used, the possibilities of 

 a single pressure opening becoming choked render it advisable to adopt 

 the arrangement shown in connection with a Venturi meter in Art. 196. 



ART. 10. RESULTANT PBESSURB AND CENTRE OF PRESSURE OF A 

 SUBMERGED AREA. 



If p denote the mean pressure intensity over a small element of area 

 o.l. the total pressure on this element will be given by p SA and the 

 total pressure on the whole submerged area will be the sum of all these 

 small normal pressures, and will be represented by 2 p B A. 



The resultant of all these elementary forces is termed the Resultant 

 Pressure on the area, while the point in which the line of action of this 

 resultant meets the area is termed the Centre of Pressure. 



If the Centre of Gravity or centroid of an element 8 A, be at a depth 

 ./ below the free surface of the liquid, the total pressure on the whole 

 submerged area will thus be given by 



2 Wx 8 A. 



If x be the depth of the centroid of this area it can be easily shown 

 that 2 x b A = 25 A = x A. 



.'. 2 WxSA = W A if, 



/'.'., the total pressure on a single face of any submerged area is equal to 

 the area multiplied by the depth of its centroid below the free surface and 

 by the intrinsic weight of the fluid. 



/'/' 1 . Calculate the total pressure on the internal curved surface of an hemispherical 

 lx>wl of radius r, placed with its diametrical plane horizontal, and just filled with water. 



Here ,T = ^ ; A = 2 w r*. 



.'. Total pressure = (>2-4 x 2 -n r 2 x = 62-4 * r* Ibs. 



1 Confirmed experimentally by Messrs. Marx, Wing & Hoskins. "Trans. American Soo 

 Civil Engineers," 1898. 



