Water exerts pressure on the upstream face of a dam as shown in Figure. 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; p = density of water, which for

this problem is assumed to be a constant 103 kg/m3; g = acceleration due to gravity (9.8 m/s2); and D = elevation (in m) of the water surface above the reservoir bottom. According to Eq. (P24.22), pressure increases linearly with depth, as depicted in Figure. Omitting atmospheric pressure (because it works against both sides of the dam face and essentially cancels out), the total force Æ’t can be determined by multiplying pressure times the area of the dam face (as shown in Figure). Because both pressure and area vary with elevation, the total force is obtained by evaluating

Where w(z) = width of the dam face (m) at elevation z (Figure). The line of action can also be obtained by evaluating

Use Simpson’s rule to compute ƒ_t and d. Check the results with your computer program for the trapezoidal rule.

Transcribed Image Text:

pgw(z)(D - 2) dz