Question

Consider a dam that is in the shape below with height H=80m. the density of water is 1000kg/m^3. The far left side of the dam is vertical wall 140m to the left of point B. The dam is 200m long ( Z direction).

Consider a dam that is in the shape below with height He 80 m. The density of water is 1000kg/m. The far left side of the dam (not shown) is a vertical wall 140 m to the left of point B. The dam is 200 m long (the Z direction). Water 20C 80 m 60 m 1. What is the total energy stored in the dam? By how much would you need to lower the water surface level in order to take 1/4 of the total energy out of the reservoir? 2. Over what time period would must the level in Part 2 be lowered in order to generate one megawatt of power? 3.

Answer 1

(a) potential energy of water filled left to point B . u_1 = mgy_com y_com = location of center of mass = at mid point for rectangle = 4/2 = 80/2 = 40 cm m = rho v = 1000 times 80 times 140 times 200 kg = 2 . 24 times 10^9 kg u_1 = 2 . 24 times 10^9 times 9 . 8 times 40 J u_1 = 8 . 78 times 10^11 J - - - - (1) for right side port over dom y� = y_com of triangle = 1/3 y = 1/3 b = 80/3 energy of right to B u_2 = m_2 g(y - y�) = 1000 times (V) times 9 . 8 (80 - 80/30) v = 1/2 times 60 times 80 times 200 = 480000 m^3