Chapter 24, Problem 23P

Water exerts pressure on the upstream face of a dam as shown in Fig. P24.23. The pressure can be characterized by

FIGURE P24.23

Water exerting pressure on the upstream face of a dam: (a) side view showing force increasing linearly with depth; (b) front view showing width of dam in meters.

$d=\frac{{\int }_0^D\rho gz\omega \left(z\right)\left(D-z\right)dz}{{\int }_0^D\rho g\omega \left(z\right)\left(D-z\right)dz}$

Use Simpson's rule to compute $f_t\text{ and }d$. Check the results with your computer program for the trapezoidal rule.