http://www.ck12.org Chapter 5. Applications of Definite Integrals
Figure 24
Solution:
Letx=the depth of the water. At an arbitrary pointxon the dam, the width of the dam isL(x) =300 m and the
depth ish(x) =xm. The weight density of water is
wwater=ρg
= ( 1000 )( 9. 8 )
=9800 N/m^2.Using the fluid force formula above,
F=
∫b
a wh(x)L(x)dx
=∫ 100
0 (^9800 )(x)(^300 )dx
= 2. 94 × 106∫ 100
0 xdx
= 2. 94 × 106[x 2
2] 100
0
= 1. 47 × 1010 N.