HYDROSTATICS. 



11 



fluid, and E F the sloping surface upon 

 which it presses, G its centre of gravity, 

 and G H the depth of G ; the pressure 

 on E F is the weight of a tody of the 

 fluid equal to E F multiplied by G H ; 

 or a body or column of the fluid, whose 

 base is *E F, and height G H. Thus 

 if the surface E F be removed, and 

 the vessel A B C K be a cube, or one 

 with bottom and sides, A K, K C, and 

 B C, equal to each other : the centre 

 of gravity of the sides being in the 

 middle point N, the pressure upon each 

 side is that of the body of fluid found 

 by multiplying K C and N B together, 

 or half the whole fluid in the vessel : 

 while the pressure on the bottom is 

 equal to the weight of the whole fluid. 



In this manner we can easily find 

 the pressure upon a dam, whether it is 

 upright or sloping in the water. We 

 have only to take half the depth of the 

 water, and multiply it by the super- 

 ficial extent of the dam ; this gives the 

 bulk of water whose weight is the 

 pressure on the dam. Suppose the 

 water to be four feet deep, and twelve 

 broad: the dam, if perpendicular, is 

 forty- eight square feet; the centre of 

 gravity being at half the depth, or two 

 feet, the pressure is equal to ninety- six 

 cubic feet of water, or 6000 pounds 

 exactly; about two tons and three- 

 quarters. 



The pressure against the upright 

 sides of a cylinder filled with wafer, 

 such as a pipe, or well, or the cylinder 

 of a steam-engine, may be found in the 

 same way. Multiply the curve surface 

 under water by the 'depth of its centre 

 of gravity, which is half the depth of 

 the water. If the water stands twenty 

 feet high, and the diameter or bore of 

 the cylinder is four feet; the curve 

 surface being a little more than _'">1 

 square feet, and the centre of gravity 

 10 feet deep, the pressure is equal to 

 the weight of above 2510 cubic feet of 

 water, or above 70 tons*. 



It is convenient in practice to bear 

 in mind, that the pressure of fresh water, 

 the fluid most commonly the subject of 

 calculation, is always 'about thirteen 

 pounds upon every square inch of level 

 bottom, at the depth of 30 feet, what- 

 ever the form or position of the sides 



* The circumference of circle i* to its diameter 

 nearly as 3.14159, (or a little less than 3 ^) to 1. 

 The surface of the sphere or globe is in the same 

 proportion to tne square of its diameter. The 

 curved iurface of the cylinder is in the same pro- 

 portion to the product of its length moltipleti by its 

 bore or diameter. 



may be; and so in proportion for 

 greater or lesser depths ; and that if the 

 sides are perpendicular, whatever may 

 be their shape, that is, provided the 

 width of the vessel or pond is the same 

 all the way down, the pressure on every 

 square inch of the sides is nearly thir- 

 teen pounds at the depth of 30 feet ; and 

 so in proportion for greater or lesser 

 depths. 



The same rule extends to finding the 

 pressure upon surfaces, whatever be 

 their shape, whether plain or curve; 

 whatever be their position, horizontal, 

 perpendicular, or slanting : It is always 

 the pressure of a body of water equal 

 to the product of the surface by the 

 depth of its centre of gravity. Thus, if 

 you would find the pressure upon the 

 sloping side of a pond; drop a line 

 from the water to the middle point 

 of the sloping side between the wa- 

 ter's edge and the bottom, and mul- 

 tiply the length of the plum-line under 

 water by the extent of the side co- 

 vered with water. If the plum-line 

 is ten feet, and the side slopes six 

 feet, there will be upon every six feet 

 square of that side a pressure of about 

 ten tons. So if you would find the 

 pressure on a hemispherical vesseJ, (or 

 half globe,) multiply half the depth of 

 the water by the curve surface of the ves- 

 sel. If the diameter is a yard, the surface 

 will be about 14^ feet: consequently 

 the pressure is equal to 13 J- cubic 

 feet of water, or nearly eight hundred 

 weight. 



The pressure upon a number of sur- 

 faces is, in like manner, equal to the 

 pressure of a body of fluid, found by 

 multiplying the whole extent of the sur- 

 faces into the depth of then- common 

 centre of gravity below the surface of 

 the fluid; and thus the finding the 

 pressure is in every case reduced to 

 finding the centre of gravity.. 



The increase of pressure in propor- 

 tion to the depth of the fluid proves 

 the necessity of making the sides of 

 pipes or masonry, in which fluids are to 

 be contained, stronger the deeper they 

 go ; and shows that it is a superfluous 

 expense to make them equally thick 

 and strong from the top downwards. 

 If they are thick enough for the great 

 pressure below, they will be thicker 

 than is required for resisting the smaller 

 pressure above. The same remark 

 applies to floodgates, dams, and banks. 

 If the pipes or cylinders placed up- 

 right have the same bore all the 



