Question

(1) In March of 1996 a special release of water, Q = 1270 m3/s, was made from the Glenn Canyon Dam, to create an artificial flood in the Grand Canyon. The flow was through 8 pipes, each with an internal diameter of 2.5 m. Estimate the velocity through those pipes. Estimate the average velocity of the river at some point downstream of the dam, where the width of the river was 61 m and its average depth was 3 m.​

Answer 1

We can use the equation for the flow rate of water, Q = Av, where A is the cross-sectional area of the pipe or river, and v is the velocity of the water.For the pipes, the total cross-sectional area is:A = 8 * π * (2.5/2)^2 = 49.087 m^2Using Q = Av, we can solve for the velocity:v = Q/A = 1270 m^3/s / 49.087 m^2 ≈ 25.88 m/sSo the velocity through each pipe is approximately 25.88 m/s.For the river downstream of the dam, we can estimate the cross-sectional area as:A = width * depth = 61 m * 3 m = 183 m^2Using the same equation, Q = Av, and the given flow rate of water, we can solve for the velocity:v = Q/A = 1270 m^3/s / 183 m^2 ≈ 6.94 m/sSo the average velocity of the river downstream of the dam is approximately 6.94 m/s.