Question 5 A smooth hump with height Az = 0.25 m is positioned on the bed of an inclined rectangular channel, as schematically represented in Figure 1 (not to scale). The channel has width B = 2 m, slope S. = 0.003 and Manning n = 0.03, and the discharge in the channel is Q = 1 m/s. The flow at position 1 (just upstream of the hump) is subcritical and the flow at position 2 (over the hump) is critical. Downstream the hump, the channel is long enough, so normal flow conditions (uniform flow) are achieved at position 4. For the calculations restricted only around the hump (i.e., from position 1 to position 3), related to tasks (a), (b), (c) and (d) below, you can assume that the pressure distributions are hydrostatic at positions 1 and 3; that local or friction losses can be neglected; and that the channel slope has no effect (i.e., the elevations of the channel bed at positions 1 and 3 can be considered approximately the same). Complete the following tasks: Note: For any tasks involving drawing, you must draw on you answer booklet (with the white pages); any drawings you make in the exam paper will not be considered. (a) Calculate the flow depth at position 2 (i.e., the critical flow depth yc). (b) Calculate the flow depth y1 at position 1. (c) Calculate the flow depth yg at position 3. (d) Calculate the horizontal force that the water exerts on the hump and indicate the direction of this force. (e) Calculate the normal flow depth y, at position 4 and classify the slope of the channel. Question 5 A smooth hump with height Az = 0.25 m is positioned on the bed of an inclined rectangular channel, as schematically represented in Figure 1 (not to scale). The channel has width B = 2 m, slope S. = 0.003 and Manning n = 0.03, and the discharge in the channel is Q = 1 mls. The flow at position 1 (just upstream of the hump) is subcritical and the flow at position 2 (over the hump) is critical. Downstream the hump, the channel is long enough, so normal flow conditions (uniform flow) are achieved at position 4. For the calculations restricted only around the hump (i.e., from position 1 to position 3), related to tasks (a), (b), (c) and (d) below, you can assume that the pressure distributions are hydrostatic at positions 1 and 3; that local or friction losses can be neglected, and that the channel slope has no effect (i.e., the elevations of the channel bed at positions 1 and 3 can be considered approximately the same). Complete the following tasks: Note: For any tasks involving drawing, you must draw on you answer booklet (with the white pages); any drawings you make in the exam paper will not be considered (a) Calculate the flow depth at position 2 (ie., the critical flow depth yd). (6) Calculate the flow depth y, at position 1. (c) Calculate the flow depth y, at position 3. (d) Calculate the horizontal force that the water exerts on the hump and indicate the direction of this force. (e) Calculate the normal flow depth y. at position 4 and classify the slope of the channel. (1) Copy Figure 1 in your answer booklet and draw the following (only schematically, not required to be to scale); The free-surface profile along the channel, from position 1 to position 4, including any relevant features: m) Indicate and label all regions and/or positions of critical, supercritical and subcritical flow; (M) Indicate and label all regions of uniform, gradually varying and rapidly varying flow 3 Channel bed: S, -0.003
