Water exerts pressure on the upstream face of a dam as shown in Fig. P17.9. The pressure c...

Water exerts pressure on the upstream face of a dam as shown in Fig. P17.9. The pressure can be characterized by

p(z) = Pg(D - z)

where p(z) = pressure in pascals (or N/m2) exerted at an elevation z meters above the reservoir bottom; ρ= density of water, which for this problem is assumed to be a constant 103 kg/m3; g = acceleration due to gravity (9.81 m/s2); and D = elevation (in m) of the water surface above the reservoir bottom. According to Eq. (P17.9), pressure increases linearly with depth, as depicted in Fig. P17.9a. Omitting atmospheric pressure (because it works against both sides of the dam face and essentially cancels out), the total force ft can be determined by multiplying pressure times the area of the dam face (as shown in Fig. P17.9b). Because both pressure and area vary with elevation, the total force is obtained by evaluating

FIGURE P17.9

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.

where w(z) = width of the dam face (m) at elevation z (Fig. P17.9b). The line of action can also be obtained by evaluating

Use Simpson's rule to compute ft and d.