Water 80.0 m deep presses on a vertical dam wall 500 m wide, and the average pressure on that wall is 3.92 x 10^5 Pa. What force does the water exert on the dam?

1. The force on the dam is the average pressure multiplied by the area of contact. 2. The wetted face of the dam is a rectangle 80.0 m tall by 500 m wide. 3. Area = (80.0 m)(500 m) = 4.00 x 10^4 m^2. 4. Force = (3.92 x 10^5 N/m^2)(4.00 x 10^4 m^2). 5. Multiplying gives 1.57 x 10^10 N. 6. The value 1.96 x 10^13 N is the weight of all the water held in the reservoir, and the force on the dam is only a tiny fraction of that. 7. The values 3.14 x 10^8 N and 4.90 x 10^7 N are too small by factors of about fifty and three hundred, which is what happens if the area is left in the wrong power of ten. _Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.4 Variation of Pressure with Depth in a Fluid_