Background: At dams, a usually rectangular channel is used as an overflow channel to drain the reservoir formed behind the dam when the water level in the reservoirs gets too high. Since dams are usually quite large structures, this means that the water moving through the spillway has a lot of energy and the velocity will be very high at the bottom of the spillway. Therefore, a stilling basin is used at the base of the spillway to dissipate some of this energy before the high velocity fluid moves in into the downstream river channel. Since hydraulic jumps are very good energy dissipators, the basins are often designed so that a jump forms within the basin. A jump will form if the river water depth is equal to the subcritical sequent depth of the flow into the stilling basin. If the river depth is larger than the subcritical sequent depth, a submerged hydraulic jump forms. Sometimes, concrete blocks called "baffle blocks" are placed on the stilling basin floor to help the hydraulic jump form within the basin. The baffle blocks decrease the momentum of the flow (by an amount equal to the drag on the blocks) and allow a jump to form under a larger range of tailwater (water depths in the downstream river channel) than would normally occur. Consider a spillway and stilling that are rectangular in shape with a width of 22.5 m.
The floor of the stilling basing is at an elevation 240.0 m above a datum. The incoming flow has a flow depth of 1.0 m at the design discharge of 275 m3/s. Within the basin are 17 baffle blocks placed on the bed of the channel, each 0.5 m high and 0.85 m wide.
a. Assuming a drag coefficient Cd of 0.6 for the baffle blocks based on the upstream velocity and combined frontal area of the blocks, calculate the sequent depth required to form a jump with the blocks and compare this value to the sequent depth required to form a jump without baffle blocks.
b. What is the energy loss in the basin with and without the blocks?
c. If the tailwater elevation for Q=275 m3/s is 246.5 m, will the stilling basin performed as designed? (i.e. Do you have enough tailwater for the jump to form and, if it does, it is submerged?)