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Hydraulic Engineering Problems and Solutions

Problem 1: Concrete-lined Channel Analysis

The water surface elevatlon in the reservoir of a dam in a mountainous area is at EL 1510 m (see fiBure below). To transfer the water from the dam reservoir to the communities down the mountains, an underground tunnel of 30 km Jong and 5 m diameter was The tunnel wall has an effective roughness of 5 mm. The tunnel discharges the flow from the dam reservoir to a storage & dlstrlbution (S&D) reservoir from which water Is conveyed to the downstream communities through an open channel. The water flows from the S&D to a stilling basin through a spillway with a crest elevation at El. 1207 m and a rough steep slope. (80/100).


1. Determine the width of the spillway such that the water level in the S&0 remains constant at 1210 m.

The stilling basin 1s at El. 1190 m. Due to the slope roughness, the flow over the spillway hoses 109¢ of its velocity head over the slope.


2. Determine the conjugate depths of the hydraulic jump formed on the stilling basin.

3. A long sloped open channel is connected to the stilling basin. Both stilling basin and channel have the same width as the spillway. Downstream in the channel there is sluice gate. The uniform flow depth of the channel is determined to be 2 5 m. The sluice gate is lowered to a position of 1.0 m above the channel bottom.

Determine the water depths upstream and downstream of the gate.

4. Determine the hydrodynamic force per unit width of the


5. Is hydraulic jump formed downstream of the gate7 If so, determine its conjugate


6. Sketch and identify the water surface profiles of the GVF formed over the length of the sloped channel.

Problem 1. A long, 10 m wide, rectangular, concrete -lined channel (Manning coefficient, n = 0.013) has a bottom slope of 0.001 and a constant-level lake at the upstream end. The lake water level is m above the channel bottom at entrance. (40 Points)

a. Assuming the entrance loss coefficient k=0.0 1, determine the channel

The upstr earn channel is cori meeted to aiiottiei loiig i ectangulai corner etc clia rinel of the same width and bottom frictio n which has with a slope of 0.01. The downstream channel ends at a reservoir. The water surface in the reservoir is at 4.5 ni above the channel bottom at the downstream end.

b. Calculate and show the water depths at control point(s) (including where the slope changes), then, sketch and name the GVI water surface profiles, front the upsti eani entrance to the downstream

Problem 2. A constant head lake delivers water to a basin, through Tunnels (1) and (2) of circular cross-sections. Tunnel (1) is 15,000 m long, 1000 mm in diameter, and has an effective roughness of 1.5 mm. Tunnel (2) is 10,000 m long with a diameter of 1500 mm, and an effective roughness length of 3.5 mm. The lake floor is at El. 1450 and has a mean depth of S0 m. The basin's bottom is at El. 990 m and its depth is 10 ni. An inflow of Q =1 m°/s is added to the tunnel system at the section expansion. To monitor water quality and the spread of pollution in the Lake-Basin system, dye tracing method is carried out. Dye is released at Pint A in the lake. (40 Points)

a. How long would it take for the dye, after its release, to be detected at Point B in the basin, assuming the dye particles travel at the velocity of flow?

Pressure sensors PS 1 and PS2, which monitor the water pressure in the tunnels, are installed at the mid -point of the lengths of Tunnels (1) and (2). respectively.

b. What pressures do PS1 and PS2 record?

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