HYDRAULIC MACHINERY, FOR MINES 837 



density. Under the influence of heat, from 40 to 212 Fahr., it increases in bulk to 

 the extent of 1 cubic foot in every 23 feet. 



Expansion at different Temperatures. 40 equal '0000. 



From 40 downwards From 40 upwards 



Expansion Expansion 



32 ... -00022 64 ... -00159 



22 ... .00090 102 . . . -00791 



12 ... -00236 212 . . . -04330 



Gaseous matter. Eiver or canal water contains ^th of its volume. 

 Spring water ^th 



Incompressibility. Experiment has determined that water may be compressed 

 about 1 -46,500,000th part per atmosphere: a quantity so small that, practically 

 speaking, water may be regarded as incompressible. The varying density and volume 

 of water, although small, should be borne in mind by those entrusted with the con- 

 struction of hydraulic apparatus. If it be allowed to freeze in cast-iron pipes, and no 

 means be provided to allow for its free expansion, destruction of the arrangement is 

 sure to follow, since a cubic inch of water exerts within the range of its expansion a 

 force equal to 13g- tons. 



HYDROSTATICS. The pressure, weight, and equilibrium of water are included within 

 this term. 



The pressure of water at any depth is as the depth of the water ; and the pressure 

 upon the bottom of a pressure-column is as the base and perpendicular height. 



Water contained within a cylinder or vessel presses equally in all directions. 



To find the pressure of water upon a cylinder-piston at the bottom of a pressure- 

 column : 



EULE. Multiply the area of the piston in feet by the height of water in the 

 pressure-column in feet, and their sum by the weight of a cubic foot of water, viz. 

 62-5 Ibs. 



Example. What is the pressure upon the surface of a piston 2 feet diameter, 

 the head of water in the pressure-column being 180 feet ? 



Piston, 2 feet diameter, area 3-1416. Then 3-1416 x 180 x 62*5 = 35,343 Ibs. 



Or to find the pressure per square inch on the piston. Divide the product 

 35,343 Ibs. by the number of square inches in the piston. Thus, area of piston 2 feet 

 diameter is 452 square inches : 



452 



THIN CYLINDERS. To determine the thickness of thin hollow cylinders ; the internal 

 diameter, pressure, and tenacity of the material being given. 



KTELE. Multiply the internal diameter in inches by the pressure of water in pounds 

 per square inch, and divide the product by the tenacity per square inch of the 

 material. 



Example. The internal diameter of a cylinder being 30 inches, the water-pressure 

 250 Ibs. to the square inch, and the tenacity of the material of the cylinder 12,000 Ibs. 

 per square inch, what must be the thickness of the cylinder ? 



2 1 5 A X J = -625, or f ths of an inch thick. 

 12,000 



To determine the pressure ; the internal radius, thickness of cylinder, and tenacity 

 of metal being given : 



EULE. Divide the product of the thickness of the cylinder and tenacity of the 

 material per square inch by the internal radius. 



Example. The thickness of the cylinder being of an inch, the tenacity 18,000, 

 and the radius 6 inches, what pressure will the cylinder bear per square inch ? 



18.000 xj 

 6 



THICK CYLINDERS. To determine the thickness of thick cylinders; the internal 

 radius, the pressure, and the tenacity of the material of the cylinder being given: 



EULE. Subtract 1 from the square root of the quotient of the sum and difference 

 of the tenacity per square inch of the material of the cylinder, and the pressure per 

 square inch, and multiply this difference by the internal radius. 



Example. The internal radius of a thick hollow cylinder being 9 inches, the 



