You are the only water resources engineer at the consulting firm Las Maravillas de la Ingenera based out of Lima, Per. You were assigned to work on el ro Marain, a river in Per that is a tributary to the Amazon river. You researched the river Maran and found out that it is 1,737-kilometer long (1,079 miles) and drains a watershed of area 358,000 km (138,225 square miles), an area a little larger than the area of the state of New Mexico. The average discharge in the river Maran is 16,708 m/s, which is very close to the average discharge in the Mississippi river, the longest river in the United States and the second longest river in the world after the Nile river in Africa. You were impressed by the large average discharge in Maran river, knowing that it is only a tributary to the Amazon river, which has an average flow 12 times larger than the Marain river. No wonder why the river Amazon has the largest discharge in the world, you thought. You were tasked to perform a hydrologic analysis on the watershed of el ro Maran. You used HEC-HMS software program to analyze the watershed and evaluate the 100-year flood. The 100-year flow turned out to be Q100=850,000 m/s (or around 3 million cubic feet per second). Later your boss asked you to work on the hydraulic analysis of a diversion structure that diverts part of the flow of the Maran river into a concrete canal with the purpose of irrigating nearby lands and providing water supply to the towns and the city downstream of the diversion. The canal will carry a maximum flow Q = 400 m/s. The rectangular canal has a width B=25 meters and a bed slope S.= 0.0002. Assume Manning's roughness coefficient for the concrete canal to be n = 0.013. Your task is to analyze the effect of placing a sluice gate on this mild-sloped canal (see figure below). The sluice gate opening is 1.0 meter. NDL CDL. Q=400m/s D CANAL BED SLUICE GATE 12 SLOPE So= 0.02% G NDL CDL Q=400 cms (d) Compute the depth of water at point E (YE). Hint: Recall the following equations for evaluating the conjugate depths upstream of a hydraulic jump (y) and downstream (y2). or y = (-1+ 1+ 8 Fr ) Y2 V = (-1+ 1+ 8 Fr ) (e) How far downstream from the sluice gate does the hydraulic jump start? That is, using the Direct Step Method, find the horizontal length (Ax) of the water surface profile DE from the sluice gate with an opening of YD = 1.0 m to point E with a water depth of ye, as computed in question (d) above. Recall that the Direct Step Method gives the curve length Dx as: E-E1 Ax = So-Sf wherein E is the specific energy and Sy is the average friction slope between points 1 and 2. The friction slope at any point is obtained from Manning's equation applied to nonuniform flow: Sf n v 4/3 R Hint: Use only one full step of the Direct Step Method to compute the length of curve DE. In order to structurally design a sluice gate, you first need to find the net external hydraulic force applied on the sluice gate and its direction. Use the momentum equation below to compute the net force applied on the sluice gate and its direction. Assume that the depth of water just upstream of the sluice gate (at point C) is 6.0 m. Assume the yearly average water temperature in the mountains of Per is 20 C. F-PO-V) ext