How are head loss and slope related for nonuniform flow, as compared to uniform flow

Why is the Reynolds number for onset of turbulence given by Re > 2000 in fully flowing pipes and Re > 500 in partly nowing pipes and other open channels?

A rectangular open channel has a base oflength 2b, and the water is flowing with a depth of b. a. Sketch this channel. b. What is the hydraulic radius of this channel?

Two channels have the same cross-sectional area, but different geometry, as shown. a. Which channel has the largest wetted perimeter? b. Which channel has more contact between water and channel wall? c. Which channel will have more energy loss to friction?

Consider uniform flow of water in the two channels shown. They both have the same slope, the same wall roughness, and the same cross-sectional area. Then one can conclude that (a) QA = QB, (b) Q.\ < QB, Or (c) QA > QB r["il sn _L ~Joft-..J f----11 LJ:_~r A 1- 7.07 ft ---..J B PROBLDIS 15.3, 15..!

This wood flume has a slope o0.0019. What will be the discharge of water in it for a depth of 1 m? The wood is planed.

Estimate the discharge in a rock-bedded stream (d81 = 30 em) that has an average depth of 1.8 m, a slope of 0.0037, and a width of 52 m. Assume k, = dR4

Estimate the discharge of water (T = I0C} that flows 1.5 m deep in a long rectangular concrete channel that is 3m wide and is on a slope of 0.00 I.

A rectangular concrete channel is 14ft wide and has uniform water flow. If the channel drops 6 ft in a length of 8000 ft, what is the discharge? Assume T = 60F. The depth of flow is 4ft.

Consider channels of rectangular cross section carrying I 00 cfs of water flow. The channels have a slope of 0.001. Determine the cross-sectional areas required for widths of 2 ft, 4ft, 6ft, 8ft, 10ft, and IS ft. Plot A versus y/ b, and see how the results compare with the accepted result for the best hydraulic section.

Determine the discharge in a 5-ft-diameter concrete sewer pipe on a slope of 0.00 I that is carrying water at a depth of 4 ft.

Water flows at a depth of 8 ft in the trapezoidal, concretelined channel shown. If the channel slope is I ft in 1500 ft, what is the average velocity, and what is the discharge?

What will be the depth of flow in a trapezoidal concretelined channel that has a water discharge of 1000 cfs? 1he channel has a slope of 1 ft in 500 ft. The bottom width of the channel is 10 ft, and the side slopes are 1 vertical to 1 horizontal.

What discharge of water will occur in a trapezoidal channel that has a bottom width of 19 ft and side slopes of I vertical to 1 horizontal if the slope of the channel is 2ft/mile and the depth is 5 ft? The channel is lined with troweled concrete.

A rectangular concrete channel4 m wide on a slope of 0.004 is designed to carry a water (T = l0C) discharge of 25 m3 /s. Estimate the uniform flow depth for these conditions. The channel has a rectangular cross section.

A rectangular troweled concrete channelS ft wide with a slope of 10ft in 3000 ft is designed for a discharge of 400 cfs. For a water temperature of 40F, estimate the depth of flow.

A concrete-lined trapezoidal channel having a bottom width of 10 ft and side slopes of I vertical to 2 horizontal is designed to carry a flow of 3000 cfs. If the slope of the channel is 0.00 I, what will be the depth of flow in the channel?

Design a canal having a trapezoidal cross section to carry a design discharge of irrigation water of 900 cfs. The slope of the canal is to be 0.002. The canal is to be lined with concrete, and it is to have the best hydraulic section for the design flow.

How are head loss and slope related for nonuniform flow, as compared to uniform flow?

Critical flow __ . (Select all of the following that are correct.) a. occurs when specific energy is a minimum for a given discharge. b. occurs when the discharge is maximum for a given specific energy. c. occurs when Fr < 1. d. occurs when Fr = I .

Water flows at a depth of 8 in. with a velocity of 35 ft/s in a rectangular channel. (a) Is the flow subcritical or supercritical? (b) What is the alternate depth?

The water discharge in a rectangular channell6 ft wide is 900 cfs. If the depth of water is 3 ft, is the flow subcritical or supercritical?

The discharge in a rectangular channell8 ft wide is 420 cfs. If the water velocity is 9 ft/s, is the flow subcritical or supercritical?

Water flows at a rate of 8m3 /sin a rectangular channel 2 m wide. Determine the Froude number and the type of flow (subcritical, critical, or supercritical) for depths of 30 em, 1.0 m, and 2.0 m. What is the critical depth?

For a rectangular channel3 m wide and discharge of 12m3 , what is the alternate depth to the 30 em depth? What is the specific energy for these conditions?

Water flows at the critical depth with a velocity of 10 m/s. What is the depth of flow?

Water flows uniformly at a rate of 320 cfs in a rectangular channel that is 12 ft wide and has a bottom slope of O.OOS.If n is 0.014, is the flow subcritical or supercritical?

The discharge in a trapezoidal channel is 10 m3 /s. The bottom width of the channel is 3.0 m, and the side slopes are 1 vertical to 1 horizontal. If the depth of flow is 1.0 m, is the flow supercritical or subcritical?

A rectangular channel is 6 m wide, and the discharge of water in it is 18 m3 /s. Plot depth versus specific energy for these conditions. Let specific energy range from Emin toE = 7 m. What are the alternate and sequent depths to the 30-cm depth?

A long rectangu I arc h anne lth at is 8 m wide and has a mild slope ends in a free outfall. If the water depth at the brink is 0.55 m, what is the discharge in the channel?

A rectangular channel that is IS ft wide and has a mild slope ends in a free outfall. If the water depth at the brink is 1.20 ft, what is the discharge in the channel?

A horizontal rectangular channell4 ft wide carries a discharge of water of 500 cfs. If the channel ends with a free outfall, what is the depth at the brink?

What discharge of water will occur over a 3-ft-high, broadcrested weir that is 10ft long if the head on the weir is 1.8 ft?

What discharge of water will occur over a 2-m-high, broad-crested weir that is 5 m long if the head on the weir is 60 em?

The crest of a high, broad-crested weir has an elevation of 100 m. If the weir is 10 m long and the discharge of water over the weir is 25 m3 /s, what is the water-surface elevation in the reservoir upstream?

The crest of a high, broad-crested weir has an elevation of 300 ft. If the weir is 40ft long and the discharge of water over the weir is 1200 cfs, what is the water-surface elevation in the reservoir upstream?

Water flows with a velocity of 3m/sand at a depth of 3m 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 30 em? What would be the depth and elevation changes if there were a gradual downstep of 30 em? What is the maximwn size of upstep that could exist before upstream depth changes would result?

Assuming no energy loss, what is the maximum value of ~z that will permit the unit flow rate of 6 m2 /s to pass over the hump without increasing the upstream depth? Sketch carefully the water-surface shape from section l to section 2. On the sketch give values for ~z. the depth, and the amount of rise or fall in the water surface from section 1 to section 2.

Water flows with a velocity of 3 m/s in a rectangular channel 3 m wide at a depth of 3 m. What is the change in depth and in water-surface elevation produced when a gradual contraction in the charmel to a width of 2.6 m takes place? Determine the greatest contraction allowable without altering the specified upstream conditions.

Because of the increased size of ships, the phenomenon called "ship squat" has produced serious problems in harbors where the draft of vessels approaches the depth of the ship channel. When a ship steams up a channel, the resulting flow situation is analogous to open-channel flow in which a constricting flow section exists (the ship reduces the crosssectional area of the channel). The problem may be analyzed by referencing the water velocity to the ship and applying the energy equation. Thus, at the section of the channel where the ship is located, the relative water velocity in the channel will be greatest, and the water level in the channel will be reduced as dictated by the energy equation. Consequently, the ship itself will be at a lower elevation than if it were stationary; this lowering is referred to as "ship squat." Estimate the squat of the fully loaded supertanker Bellamya when it is steaming at 5 kt (1 kt = 0.515 m/s) in a channel that is 35m deep and 200m wide. The draft of the Bel/amya when fully loaded is 29 m. Its width and length are 63 m and 414 m, respectively.

A rectangular channel that is I 0 ft wide is very smooth except for a small reach that is roughened with angle irons attached to the bottom. Water flows in the channel at a rate of 200 cfs and at a depth of 1.0 ft upstream of the rough section. Assume frictionless flow except over the roughened part, where the total drag of all roughness (all of the angle irons) is assumed to be 2000 lbf. Determine the depth downstream of the roughness for the assumed conditions.

Water flows from a reservoir into a steep rectangular channel that is 4 m wide. The reservoir water surface is 3 m above the channel bottom at the channel entrance. What djscharge will occur in the channel?

A small wave is produced in a pond that is 6 in. deep. What is the speed of the wave in the pond?

A small wave in a pool of water having constant depth travels at a speed of 1.5 m/s. How deep is the water?

As waves in the ocean approach a sloping beach, they curve so that they are nearly parallel to the beach when they finally break (see accompanying figure). Explain why the waves curve like this. Hint: With a sloping beach, where is the water most shallow?

For a hydraulic jump, . (Select all of the following that are correct.) a. the flow changes from subcritical to supercritical. b. the flow changes from supercritical to subcritical. c. significant energy is lost. d. the height of the water abruptly increases from the upstream to the downstream cross-section. e. the downstream and upstream depth arc related quantitatively in terms of the upstream Fr. f. the energy equation is a better tool for analysis than the momentum equation.

The spillway shown has a discharge of2.9 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.

The flow of water downstream from a sluice gate in a horiwntal channel has a depth of 32 em and a flow rate of 5.2 m3 /s per meter of width. The sluice gate is 2 m wide. a. Could a hydraulic jump be caused to form downstream of this section? b. lf so, what would be the depth downstream of the jump?

It is known that the discharge per unit width is 65 cfs/ft and that the height (H) of the hydraulic jump is 14ft. What is the depthy1?

Water flows in a channel at a depth of 40 em and with a velocity of 8 m/s. An obstruction causes a hydraulic jump to be formed. What is the depth of flow downstream of the jump?

Water flows in a trapezoidal channel at a depth of 40 em and with a velocity of 10 m/s. An obstruction causes a hydraulic jump to be formed. What is the depth of flow downstream of the jump? The bottom width of the channel is 5 m, and the side slopes are 1 vertical to I horizontal.

A hydraulic jump occurs in a wide rectangular channel. If the depths upstream and downstream are 0.50 ft and lOft, respectively, what is the discharge per foot of width of channel?

The 20-ft-wide rectangular channel shown has three different reaches. S0,1 = 0.01; 50, 2 = 0.0004; S0,3 = 0.00317; Q = 500 cfs; n1 = 0.015; normal depth for reach 2 is 5.4 ft and that for reach 3 is 2.7 ft. Determine the critical depth and normal depth for reach 1 (use Manning's equation from I 5.3). Then classify the flow in each reach (supcrcritical, subcritical, critical), and determine whether a hydraulic jump could occur. Jn which rcach(es) might it occur if it does occur? Elevation - 1274 ft :: :;,:::D. -Elevation- 1272 ft Elevation~ 1270 fi Reach I Reach 2 PROBU.M l)Y Reach 3 I ..-. Elevation - 1261.2 n

Water flows from under the sluice gate as shown and continues on to a free overfall (also shown). Upstream from the over fall the flow soon reaches a normal depth of 1.1 m. The profile immediately downstream of the sluice gate is as it would be if there were no influence from the part nearer the overfall. Will a hydraulic jump form for these conditions? If so, locate its position. If not, sketch the full profile and label each part. Draw the energy grade line for the system.

Water is flowing as shown under the sluice gate in a horizontal rectangular channel that is 5 ft wide. The depths of y0 and y1 are 65 ft and 1 ft, respectively. What will be the horsepower lost in the hydraulic jump?

For the derivation of Eq. (15.28) on p. 571 of 15.5 it is assumed that the bottom shearing force is negligible. For water flowing uniformly at a depth y1 = 40 em in the concrete channel shown, which is 10m wide, a sill is installed to force a hydraulic jump to form. Estimate the magnitude of the shearing force F, associated with the hydraulic jump and then determine F,/ FH, where FH is the net hydrostatic force on the hydraulic jump. Assume Manning's n value is n = 0.012.

The normal depth in the channel downstream of the sluice gate shown is I m. What type of water-surface profile occurs downstream of the sluice gate? Also, estimate the shear stress on the smooth bottom at a distance 0.5 m downstream of the sluice gate

Water flows at a rate of 100 fe/s in a rectangular channel10 ft wide. The normal depth in that channel is 2ft. The actual depth of flow in the channel is 4 ft. The water-surface profile in the channel for these conditions would be classified as (a) Sl, (b) S2, (c) Ml, or (d) M2.

The water-surface profile labeled with a question mark is (a) M2, (b) S2, (c) H2,or (d) A2.

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

A very long lO-ft-wide concrete rectangular channel with a slope of 0.0001 ends with a free overfall. The discharge in the channel is 120 cfs. One mile upstream the flow is uniform. What kind (classification) of water surface occurs upstream of the brink?

The horizontal rectangular channel downstream of the sluice gate is 10 ft wide, and the water discharge therein is I 08 cfs. The water-surface profile was computed by the direct step method. If a 2-ft-high sharp-crested weir is installed at the end of the channel, do you think a hydraulic jump would develop in the channel? Tf so, approximately where would it be located? Justify your answers by appropriate calculations. Label any watersurface profiles that can be classified.

The discharge per foot of width in this rectangular channel is 20 cfs. The normal depths for parts I and 3 are 0.5 ft and 1.00 ft, respectively. The slope for part 2 is 0.001 (sloping upward in the direction of flow). Sketch all possible water-surface profiles for flow in this channel, and label each part with its classification.

Water flows from under a sluice gate into a horizontal rectangular channel at a rate of 3 m3 /s per meter of width. 1he channel is concrete, and the initial depth is 20 em. Apply Eq. ( I 5.42) on p. 579 of I 5.6 to construct the water-surface profile up to a depth of 60 em. In your solution, compute reaches for adjacent pairs of depths given in the following sequence: d = 20 em, 30 em, 40 em, 50 em, and 60 em. Assume that f is constant with a value of 0.02. Plot your results.

Consider the hydraulic jump shown for the long horizontal rectangular channel. What kind of water-surface profile (classification) is located upstream of the jump? What kind of water-surface profile is located 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 arc likely to occur given the same gate opening? Explai11 and/or sketch the changes.

The steep rectangular concrete spillway shown is 4 m wide and 500 m long. It conveys water from a reservoir and delivers it to a free outfall. The channel entrance is rounded and smooth (negligible head loss at the entrance). If the water-surface elevation in the reservoir is 2 m above the channel bottom, what will the discharge in the channel be?

The concrete rectangular channel shown is 3.5 m wide and has a bottom slope of 0.00 1. The channel entrance is rounded and smooth (negligible head loss at the entrance), and the reservoir water surface is 2.5 m above the bed of the channel at the entrance. a. Estimate the discharge in it if the channel is 3000 m long. b. Tell how you would solve for the discharge in it if the channel were only 100m long.

A dam 50 m high backs up water in a river valley as shown. During flood flow, the discharge per meter of width, q, is equal to 10 m3 /s. Making the simplifying assumptions that R = y and f = 0.030, determine the water-surface profile upstream from the dam to a depth of 6 m. In your numerical calculation, let the first increment of depth change bey,; use increments of depth change of I 0 m until a depth of I 0 m is reached; and then use 2 m increments until the desired limit is reached.

Water flows at a steady rate of 12 cfs per foot of wid~h (q = 12 cfs) in the wide rectangular concrete channel shown. Determine the water-surface profile from section 1 to section 2.