Problem 4.2

A concrete sewer pipe 4 ft in diameter is laid so it has a drop in elevation of 1.00ft per 1000 ft of length. If sewage (assume the properties are the same as those of water) flows at a depth of 2 ft in the pipe, what will be the discharge?

Problem 4.4
A rectangular troweled concrete channel 12 ft wide with a slope of 10 ft in 8000 ftis designed for a discharge of 600 cfs. For a water temperature of 40?F, estimate the depth of the flow.

Problem 4.7
A concrete-lined trapezoidal channel with bottom width of 10 ft and side slopes of 1 vertical to 2 horizontal is designed to carry a flow of 3000 cfs. If the slope of the channel is 0.001, what would be the depth of flow in the channel?

Problem 4.12
Estimate the discharge in the Moyie River near Eastport, Idaho, when the depth is 4 ft.
Assume S 0 = 0.0032.

Problem 4.16
A trapezoidal irrigation canal is to be excavated in soil and lined with coarse gravel. The canal is to be designed for a discharge of 200 cfs, and it will have slope of 0.0016. What should be the magnitude of the cross-sectional area and hydraulic radius for the canal if it is to be designed so that erosion of the canal will not occur? Choose a canal cross section that will satisfy the limitations.

Problem 4.22
Water flows at a depth of 10 cm with a velocity of 6 m/s in a rectangular channel. Is the flow subcritical or supercritical? What is the alternate depth? Problem 4.31
Derive a formula for critical depth, dc in the V-shaped channel shown below.
Problem 4.34
A 10-ft wide rectangular channel is very smooth except for a small reach that is rough- ened with angle irons attached to the bottom of the channel. Water flows in the channel at a rate of 200 cfs and at a depth of 1.00 ft. Assume frictionless flow except over the roughened part where the total drag of all the roughness (all the angle irons) is assumed to be 2000 lb. Determine the depth at the end of the roughness elements for the assumed conditions.

Problem 4.36
Water flows with a velocity of 2 m/s and at a depth of 3 m in a rectangular channel. What is the change in depth and in water surface elevation produced by a gradual upward change in bottom elevation (upstep) of 60 cm? What would be the depth and elevation changes if there were a gradual downstep of 15 cm? What is the maximum size of upstep that could exist before upstream depth changes would result? Neglect head losses.

Problem 4.39
The spillway shown has a discharge of 1.2 m3/s per meter of width occurring over it. What depth y2 will exist downstream of the hydraulic jump? Assume negligible energy loss over the spillway.

Problem 4.43
Water is flowing as shown under the sluice gate in a horizontal rectangular channel that is 6 ft wide. The depths y0 and y1 are 65 ft and 1 ft respectively. What will be the horsepower lost in the hydraulic jump?

Problem 4.48
The partial water surface profile shown is for a rectangular channel that is 3 m wide and has water flowing in at a rate of 5 m3/s. Sketch in the missing part of water surface profile and identify the type(s).

Problem 4.50
A horizontal rectangular concrete channel terminates in a free outfall. The channel is 4 m wide and carries a discharge of water of 12 m3/s. What is the water depth 300 m upstream from the outfall?

Problem 4.51
Given the hydraulic jump for the long horizontal rectangular channel, what kind of water surface profile (classification) is upstream of the jump? What kind of water surface profile is downstream of the jump? If baffle blocks are put on the bottom of the channel in the vicinity of A to increase the bottom resistance. What changes are apt to occur given the same gate opening? Explain or sketch the changes.

Problem 4.59
Theory and experimental verification indicate that the mean velocity along a vertical line in a wide stream is closely approximated by the velocity at 0.6 depth. If the indicated velocities at 0.6 depth in a river cross section are measured, what is the discharge in the river?

Problem 4.63
A flood caused water to flow over a highway as shown below. The water surface ele- vation upstream of the highway (at A) was measured to be 101.00 ft. The elevation at the top of the crown of the pavement of the highway is 100.10 ft. Estimate the discharge over a stretch of highway with this elevation, which is 100 ft long. What was the depth of flow at the crown of the highway?