Question

The Los Angeles River is a man-made flood control channel designed to carry the overflow from 3
major reservoirs in the San Gabriel Mountains. For simplicity, we can assume the channel is rectangular
in shape, with a width 20 meters and a depth of 25 meters. During the last major rain year the
overflow of the 3 reservoirs was as follows:
Reservoir 1-Depth over top of spillway was 2. meters, the spillway was 30 meters wide, and the
water was flowing at 5 meters/second.
Reservoir 2- Depth over top of spillway was 0.5 meter, the spillway was 40 meters wide, and
the water was flowing at 3 meters/second.
Reservoir 3-Depth over top of spillway was 1.5 meter, the spillway was 50 meters wide, and
the water was flowing at 6.0 meters/second.
The depth of the water in the Los Angeles River was 10 meters.
a. What was the speed of the water flow Los Angeles River?
b. What was the total pressure at the bottom of the river?

Answer 1

R(1) h = 2 m, b = 30 m, v = 5 m/s R(2) h = 0.5 m, b = 40 m, v = 3 m/s R(3) h = 1.5 m, b = 50 m, v = 6 m/s } h = 10 m (h b v)_1 + (h b v)_2 + (h b v)_3 = (h b v) Rightarrow (2 times 30 times 5) + (0.5 times 40 times 3) + (1.5 times 50 times 6) = (10 times 20 times v) Rightarrow v = 4.05 m/s By Bernouill's theorem Total pressure at bottom = P_atm + delta g h + 1/2 delta v^2 = 101325 + 1000 times 9.8 times 10 + 1/2 times 1000 times (4.05)^2 = 207526.25 p_a = 207.5 k pa