TANKS AND CISTERNS. 



517 



a force equal to the intensity of the super- 

 incumbent mass. Therefore, the lowest 

 parts of a vessel," tank, or cistern, " con- 

 taining large masses of water, ought to be 

 stronger than the upper. 



" If we take a cistern whose sides are 

 equal in area to the bottom, the pressure 

 on the four upright sides is equal to twice 

 the pressure on the bottom ; but the pres- 

 sure on the bottom is equal to the weight 

 of the fluid contained in the cistern, (sup- 

 posing it to be full;) therefore, the pres- 

 sure on the upright surface is equal to 

 twice the weight of the contained fluid : 

 hence, in a cubical vessel, whose bottom 

 is horizontal, the whole pressure on the 

 bottom and the four sides is equal to 

 three times the weight of the fluid which 

 the vessel contains. 



" Let the box be a cube of 1 foot ; then, 

 since a cubic foot of fresh water weighs 

 62^ pounds, the whole pressure on the 

 bottom and three sides is equal to 

 62.5 x 3 = 187.5 lb. If the vessel be 

 cylindrical, its base horizontal, and its 

 upright surface perpendicular, the pres- 

 sure on the base is to the pressure on the 

 upright surface as the radius of the base 

 is to its altitude. 



" Let the diameter of the base be 3 feet ; 

 then, since the solidity of the vessel is 

 32 x .7954 x 6 = 42.9516 feet, the 

 whole weight will be 42.9516 x 62.5 - 

 2684.465 lb., being exactly the fifth part 

 of the weight which measures the entire 

 pressure — which is, therefore, equal to 

 13422.475 lb., or to 5.992, or nearly 6 

 tons. 



" The pressure exerted by a fluid in a 

 quiescent state, on any portion of a vessel, 

 is equal to the weight of a column of the 

 fluid, having for its base the surface 

 pressed, and for its altitude the mean 

 depth of the incumbent fluid. This mean 

 depth is the same as the distance of the 

 centre of gravity of that portion below 

 the surface of the fluid. 



" But in vessels resembling truncated 

 cones, the pressure on the base may be 

 greater or less than the weight of the con- 

 tained fluid, in any proportion whatever, 

 according as the sides of the vessel con- 

 verge or diverge with respect to the bot- 

 tom. Hence the pressure on the bottom 

 depends solely upon its perpendicular 

 altitude, and not on the quantity of the 

 fluid ; and on this principle any portion 



of the fluid, however small, balances any 

 other portion, however great." — London's 

 Self Instruction, S$c. 



Hence it follows that, in forming heads 

 of water, cisterns, or tanks, to propel the 

 water through close pipes to a distance, 

 depth is of far more consequence than su- 

 perficial area. " In considering," says Mr 

 Loudon, in the work last quoted, "the 

 velocity of water flowing through close 

 pipes, of a given diameter and length, 

 with a given head of water, Eytelwein 

 conceives the whole head of water above 

 the point of discharge to be separated 

 into two portions, one of which he sup- 

 poses to be employed in overcoming the 

 friction and other resistances in the pipe ; 

 and the other portion in producing the 

 velocity, and forcing the water through 

 the orifice. 



" The height which is employed in coun- 

 terbalancing the resistances he considers 

 to be directly proportioned to the diameter 

 of the pipe compounded with its length, 

 and inversely as the area of the transverse 

 section, or the square of the diameter, 

 and, consequently, on the whole, it varies 

 inversely as the diameter. But the fric- 

 tion varies as the square of the velocity ; 

 hence the height equivalent to the friction 

 must vary also as the square of the 

 velocity. 



" The effect of atmospheric pressure on 

 running liquids is, that in a tube of con- 

 siderable length, descending from a reser- 

 voir, it quickens greatly the discharge ; 

 in fact, it much resembles the operation 

 of a piston. Hence we see in a vessel of 

 water, discharging itself by means of a tube 

 in its bottom, a depression of the water 

 surface in the vessel over the tube ; and 

 as the volume of water lessens, this hol- 

 low extends itself like a large funnel." 

 This will readily be seen by withdrawing 

 the waste-pipe out of a cistern of water, 

 and watching the effect. " In fact, the 

 force of the effluent water diminishes the 

 pressure beneath ; on which account the 

 incumbent air, following the stream, finds, 

 as it were, an easier passage, the velo- 

 city of the effluent water being always 

 greater in the middle than towards the 

 sides of the aperture, where it is retarded 

 by tenacity and friction. 



" As regards the friction or resistance 

 of fluids in pipes, an inch tube, 200 feet 

 long, placed horizontally, discharges only 



