PACKING-PRESS. The hydraulic press invented by Mr. Bramah, besidea being used to draw piles, trees, &c., from the ground, or to prove the strength of materials, is frequently employed to pack or compress bales of linen, cotton, and the like goods into small dimen sions for the convenience of transport. A description of this machine has been given under HYDRAULIO PRESS; and it is intended here merely to notice the method employed by Mr. Barlow to determine the thickness which the cylinder should have in order that its strength may be in equilibrio with the strain to which it is subject from the pressure of the fluid within it.
Within any section of the cylinder made by a plane perpendicular to the axis, the tendency of the contiguous particles of metal to separate from one another in a direction perpendicular to a diameter passing through them, in consequence of the expansion produced by the pres sure of the fluid, becomes continually less from the interior to the exterior circumference of the section, and is inversely proportional to the distances of the particles from the axis of the cylinder ; and the cohesive power of the particles is, by the laws of elasticity, proportional to their separation, while the strain produced by the pressure of the fluid varies, at any part of the section, with the distance of that part from the axis. It follows that the resistance opposed at such part of a
section to the momentum of the pressure is inversely proportional tc the square of the distance from the axis.
Therefore r representing the radius of the interior surface of the cylinder, t the whole thickness, and x any variable distance from the interior surface towards the exterior, all in inches; then r2 (IC , if x)' multiplied by 2 e, and also by the force of cohesion on a square inch of the metal, will express the resistance produced by an annulus which is one inch deep in a direction parallel to the axis. That integral, for rt the whole thickness t, is therefore f (in pounds) denoting the 2w rtf force of expresses the whole resistance.
If f' (in pounds) represent the force on a square inch of the interior surface, by which the pressure of the fluid tends to strain the cylinder, 2urf' will denote the whole strain on the same annulus; therefore, equating the strength and strain, there is obtained t= f-f' This value of t expresses the required thickness,