116
CALCULUS
[§73
the center, the axis of x horizontal and the axis of y positive down¬
ward. The element of pressure is
and the total pressure is
x is expressed in terms of y by means of the equation of the
ellipse,
Then
Exercises
1. Find the pressure on the vertical parabolic gate, Fig. 51: (a)
if the edge AB lies in the surface of the water; (b) if the edge AB lies
5 feet below the surface.
FIG. 51.
2. Find the pressure on a vertical semicircular gate whose diameter,
10 feet long, lies in the surface of the water.
73. Arithmetic Mean. The arithmetic mean, A, of a series of
n numbers, ai, a2, a3, : : : , an, is defined by the equation
or
That is, A is such a number that if each number in the sum