Question

2. During a flood event in the 1980s, a standing wave (hydraulic jump) formed in the Grand Canyon at the Crystal Hole rapid on the Colorado River. Rafters at the time reported entering the rapid at about 30 mph, hitting a 20-ft tall wall of water, and exiting at about 10 mph. Are these pieces of information (upstream and downstream velocities and change in depth) consistent with the principles of a hydraulic jump? Show calculations in support of your conclusion

Answer 1

V_1 = 30 times 5280/3600 = 448 k/s 1/2 = 10 times 5280/3600 write the relation for velocity and depth y_2/Y_1 = V_1/V_2 = 44/14.8 = 2.99 Calculate the provde�s number for the hydraulic jump Y_2/Y_1 = 1/2 (- 1 + squareroot 1 + 8 F^2_1) 2.99 = 1/2 (- 1 + squareroot 1 + 8 F^2_1 F_r_1 = 2.44 Calculate the Upstrem depth F_r_1 = V_1/squareroot g V_1 \r\n 244 = 44/squareroot 32.2 y_1 = Y_1 = Vertical-bar 0.1 F Vertical-bar Calculation the down stream depth y_2/Y_1 = 2.99 y_2/10.1 = 2.94 y_2 = 3028 k Calculate the change in depth y_2 - y_1 = 30.2 - 10.1 Y_2 - Y_1 = 2018k