When a fluid completely fills a vessel, and a pressure is applied to it at any part of the surface, that pressure is transmitted equally throughout the whole of the enclosed fluid. This is known as Pascal’s.principle (see also page 122).

This principle finds an important industrial application in the hydraulic press (Fig. 8.16). This type of machine has numerous uses, from the compression of soft materials such as waste paper and cotton into compact bales to the shaping of motor-car bodies and the forging of steel armour plate and light alloys (Fig. 8.17, 13.11).

In its simplest form the hydraulic press consists of a cylinder and piston of large diameter, connected by a pipe to a force pump of much smaller diameter. Oil from a supply tank is pumped into the cylinder and the piston (or ram) moves out, exerting considerable force. A valve is provided to release the pressure and allow the oil to return to the tank, after the press has done its work. In order to understand how very large forces may be so easily produced by this press, look at Fig. 8.18. Suppose the pump barrel has an area of 2 ern? and that a force of 100 N is applied to its plunger, force 100 the pressure produced = 50 Njcm? area 2

This pressure is transmitted equally throughout the whole of the liquid and so also to the piston in the large cylinder. If the area of the large piston is 800 ern”, then the total force or thrust exerted is given by, thrust = pressure x area = 50 x 800 = 40 000 N A force of 40000 N is therefore obtained simply by exerting a force of only 100 N. The velocity ratio between the two cylinders of a hydraulic system may be found by using the fact that the volume of liquid which leaves the pump ylinder is equal to hat which enters the ram cylinder.

If x is the distance moved by the pump piston and y the distance moved by the ram piston, then equating volumes, x x area of pump piston = y x area of ram piston . . x area of ram piston nR 2 R 2 or velocity ratio = -y = area of pump piston -n-r2 = -r2 where R = radius of ram piston, and r = radius of pump piston. The above expression gives the velocity ratio between the two pistons only. If the total velocity ratio of the whole press is required we must multiply Rr: by the velocity ratio of the pump handle treated as a lever.