HYDROSTATICS 433 
horizontal strips, of which EF is one. Let y be the depth of the strip EF 
wlow the free surface of the liquid, and let a denote the true area of the 
By Art. 363 the intensity of the 
ssure at the depth y is wy, and there- 
» the total pressure on the strip EF 
8 yt and the total pressure on the 
» surface MN will be the sum of all 
on the separate strips, and 
Il therefore be equal to Zwya or wiya, 
ut by a property of the centre of gravity 
of a surface Yya=hA, where h is the 
_ depth of the centre of gravity of the surface below the free surface of the 
liquid, and A is the true area of the surface. Hence the total pressure 
a the surface MN is whA. But whA is the weight of a right prism of 
e liquid, whose base is the given surface, and whose height is the depth 
f the centre of gravity of the surface ‘below the free surface of the 
7 ho u id. 
a 366. Artificial Head.—In the three preceding Articles the effect of 
any external pressure on the free surface of the liquid has been neglected. 
= 1 the free surface of the liquid is exposed to the atmosphere, or to steam, 
as ina boiler, or if it support a loaded piston in a cylinder, then the 
pressure on the free surface will be transmitted to the surface immersed 
In the Hiquid: Let p, be the intensity of the pressure due to the weight 
f the liquid at a depth 4, below its free surface. Let p, be the intensity 
& of the external pressure on the free surface of the liquid, and let h, be 
the head of liquid, which, by its weight, would cause a pressure of 
intensity Py. Also, let p be the intensity of the total pressure at the 
_ depth hy and lastly, let h be the head of liquid which, by its weight, 
_ would cause a pressure of intensity p. Then p=p,+p,, and since h= £ 
Pat, 
Sy 
Sy 
w 
Se 
oD 
ee =f, = h, =", it follows that h=h, +h,. The head h,, which is the 
9.0 w 
a, of liquid equivalent to the external pressure, may be called the 
a us . al I 1. 
_ 367. Resultant of Pressure.—If a surface be exposed to pressure, 
either uniform or varying, the single force, acting at a point on the 
_ surface, which will produce the same effect on the surface as a whole as 
pressure over the surface, is called the resultant of the pressure. The 
‘magnitude of this resultant is, for plane surfaces, the same as what has 
been called the total pressure in preceding Articles, 
_ _ 368. Centre of Pressure.—If a surface be exposed to pressure, 
either uniform or varying, the point on the surface at which the 
Tesultant of the pressure acts is called the centre of pressure. In 
what follows, the surfaces exposed to pressure will be assumed to be 
ae surfaces. 
If the pressure is uniform over the surface, the centre of pressure is 
Berens at the centre of gravity of the surface. 
__ The other important case is where the pressure varies uniformly in 
one direction, and is uniform in a direction at right angles to this as 
when an inclined surface is immersed in a liquid. i 
E 
