432 APPLIED MECHANICS 
362. Transmission of Pressure.—If a fluid at rest have any pre “- rn 
applied to any part of its surface, that pressure is transmitted equ 
to all parts of the fluid. For example, if the vessel 4 
shown in Fig. 703 be full of water or air, and if 
it has attached to its sides equal cylinders fitted with ” 
frictionless pistons, which are kept at rest by suit- 
able forces, any additional force applied to one of 
the pistons will require that an equal additional force 
be applied to each of the other pistons to keep them 
at rest. 
It follows from this that if one of the cylinders be onleniaaly until t 
piston which fits it has double the area, this piston will require dov ble 
the force to keep it in equilibrium against the fluid 
pressure, and generally if a is the area of one piston [~¥ 
and qg the force pushing it in, and if A is the area [ILI] 
of another piston and Q the force pushing it in, then mie 
for equilibrium a/A=q/Q. This is the principle of = < 
the hydraulic press (Fig. 704), in which a compara- Fra. 704. 
tively small force P actifg on a small piston or 
plunger is able to balance a large force W on a large piston or ram, 
363. Pressure at any Point of a Liquid due to its Weight.—Let A 
(Fig. 705) be a very small horizontal dise of area a immersed in a li 
at a vertical depth h below its free surface. The pressure 
of the liquid on the top of the dise will not be altered if a = 
cylindrical tube, open at both ends, and having an internal : 
diameter equal to that of the disc A, be placed over it in a 
vertical position, as shown. This tube above the level of the 
dise contains a cylindrical column of liquid whose volume is 
ah and whose weight is ahw, where w is the weight of a unit 
of volume of the liquid. If the liquid surrounding the tube 
AB be removed, the pressure on the upper surface of the dise A will not 
be altered, because the pressure of the surrounding liquid on the tube is 
horizontal, the sides of the tube being vertical, and therefore se 
balancing. The load on the top of the dise is now ahi, and 
pressure per unit of area is ahw/a=hw =p, which shows that at 
point in a liquid the intensity of the pressure due to the weight 
of the liquid is directly proportional to its depth below the free surface 
of the liquid. a 
If the area a be in square feet, the height h in feet, and w the weight 
of 1 cubic foot of the liquid, then hw will be the pressure per squi we 
foot at the depth h. The depth h is called the head of liquid at A, and 
the head is evidently a measure of the pressure. = 
364. Total Pressure on a Plane Horizontal Surface Immersed in a 
Liquid.—From the preceding Article it follows that the total pressure 
a plane horizontal surface due to the weight of a liquid in which 
immersed is equal to the weight of a right prism of the liquid, whose . ye 
is the given surface, and whose height is the depth of the surface be 
the free surface of the liquid. 
365. Total Pressure on a Plane Inclined Surface Immersed ina 
Liquid.—Let MN (Fig. 706) be a plane inclined surface immersed i 
liquid, and let the surface be divided into a large number of narre : 
