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Fundamentals Of Hydraulic Engineering Systems 4th Edition Robert J. Houghtalen, A. Osman H. Akan, Ned H. C. Hwang - Solutions

A shipping channel with a design flow rate of 2,650 cfs is experiencing a large accumulation of sediment. A model study is proposed for the 3.20-mile-long channel, but the available model length is only 70 feet. A time ratio of 10 will be used. Select a suitable length scale and determine the model
A proposed reservoir will be drained using a gated opening that is governed by the orifice equation: Q = CdA(2gh)]1/2 (Equation 8.19), where Cd is the coefficient of discharge. A 1:150 scale model is used, and the model reservoir is drained in 18.3 minutes. How many hours should it take to drain
A 1:5 scale model at 1,200 rpm is used to study the prototype of a centrifugal pump that produces 1.00 m3/sec at 30-m head when rotating at 400 rpm. Determine the model discharge and head.
An overflow spillway with a 100-m-long crest will convey a design discharge of 1,150 m3/sec under a permitted maximum head of 3.00 m. The operation of the prototype spillway is studied on a 1:50 scale model in a hydraulic laboratory. The time ratio on the model is LR1/2. The model velocity measured
A 1:20 scale model of a prototype energy dissipation structure is constructed to study force distribution and water depths. A velocity ratio of 7.75 is used. Determine the force ratio and prototype discharge if the model discharge is 10.6 ft3/sec.
A 1:50 scale model is used to study the power requirements of a prototype submarine. The model will be towed at a speed 50 times greater than the speed of the prototype in a tank filled with seawater. Determine the conversion ratios from the prototype to the model for the following quantities: (a)
A seawall has been proposed to dissipate wave forces on a beach front. A 3-ft-long, 1:30 model is used to study the study the effects on the prototype. If the total force measured on the model is 0.510 lbs and the velocity scale is 1:10, what is the force per unit length of the prototype?
The motion of a submarine is being studied in a laboratory. The prototype speed of interest is 5 m/sec in the ocean. Inertial forces and viscous forces govern the motion. At what theoretical speed must a 1:10 model be towed to establish similarity between the model and the prototype? Assume that
Verify the scale ratios given in Table 10.2 (Reynolds Number Law) for(a) Velocity,(b) Time,(c) Acceleration,(d) Discharge,(e) Force, and(f) Power.
A 4-ft diameter oil pipeline is being proposed for a remote location. The oil has a specific gravity of 0.8 and a dynamic viscosity of 9.93 × 10-5 lb-sec/ft2. A model will by used to study the pipeline flow conditions using a 0.5-ft diameter pipe and water at normal conditions (68.4°F). If the
The moment exerted on a ship's rudder is studied with a 1:20 scale model in a water tunnel using the same temperature water as the river water. Inertial and viscous forces govern the fluid motion. The torque measured on the model is 10 N • m for a water tunnel velocity of 20 m/sec. Determine the
A 1:10 scale model of a water-supply piping system is to be tested at 20°C to determine the total head loss in the prototype that carries water at 85ºC. The prototype is designed to carry 5.0 m3/sec. Determine the model discharge.
A structure is built underwater on the ocean floor where a strong current of 5 m/sec is measured. Inertial forces and viscous forces are dominant. The structure is to be studied by a 1:25 model in a water tunnel using seawater that is the same density (p = 1,030 kg/m3) and temperature (4°C) as
If a 1:1,000 scale tidal basin model is used to study the operation of a prototype satisfying the Froude number law, what length of time in the model represents a period of one day in the prototype?
Verify the scale ratios given in Table 10.3 (Froude number law) for(a) Velocity,(b) Time,(c) Acceleration,(d) Discharge,(e) Force,(f) Power.
An ogee spillway has a design flow rate of 14,100 cfs (ft3/sec). An energy dissipater is being designed to force a hydraulic jump at the end of a spillway channel. The initial depth of flow in the 100-ft wide prototype is expected to be 2.60 ft. Assuming inertial and gravity forces are dominant,
An overflow spillway with a 300-m crest is designed to discharge 3,600 m3/sec. A 1:20 model of a portion of the cross section of the dam is built in a laboratory flume 1 m wide. Calculate the required laboratory flow rate assuming viscosity and surface tension effects are negligible.
A 1:25 model is built to study a stilling basin at the outlet of a steep spillway chute assuming inertial and gravity forces are dominant. The stilling basin consists of a horizontal floor (apron) with U.S. Bureau of Reclamation (USBR) type II baffles installed to stabilize the location of the
The 120-m-long crest of an overflow spillway will discharge 1,200 m3/sec of floodwater from a reservoir with a permitted maximum head of 2.75 m. The operation of the prototype spillway is studied on a 1:50 scale model in a hydraulic laboratory assuming inertial and gravity forces are dominant. (a)
A measuring device includes certain small glass tubes of a given geometry. To study the surface tension effect, a 5:1 scale model (larger than prototype) is built. Determine the discharge and force ratios assuming the same liquid is used in the model and the prototype.
Determine the surface tension of a liquid in the prototype if a time ratio of 2 is established with a 1:10 scale model. The surface tension of the liquid in the model is 150 dyn/cm. Also determine the force ratio. Assume the densities of the fluids in the prototype and the model are approximately
A model is built to study the surface tension phenomena in a reservoir. Determine the conversion ratios between the model and the prototype for the following quantities if the model is built with a 1:100 scale: (a) Rate of flow, (b) Energy, (c) Pressure, and (d) Power. The same fluid is used in the
A ship 100 m long moves at 1.5 m/sec in freshwater at 20°C. A 1:100 scale model of the prototype ship is to be tested in a towing tank containing a liquid of specific gravity 0.90. What viscosity must this liquid have for both Reynolds and Froude number laws to be satisfied?
A 1:250 ship model is towed in a wave tank and wave resistance of 10.7 Nis measured. Determine the corresponding prototype wave resistance on the prototype.
A concrete caisson 60 m wide, 120 m long, and 12 m high is to be towed in seawater in the longitudinal direction to an offshore construction site where it will be sunk. The calculated floating depth of the caisson is 8 m, with 4 m remaining above the water surface. A 1:100 model is built to study
A barge model 1 m long is tested in a towing tank at a speed of 1 m/sec. Determine the prototype velocity if the prototype is 150 m in length. The model has a 2-cm draft and is 10 cm wide. The drag coefficient is CD = 0.25 for NR > 5 × 104, and the towing force required to tow the model is 0.3 N.
A model is built to study flow in a stream segment. The stream has an average depth of 1.2 feet and is roughly 20 feet wide with a flow' rate of 94.6 cfs. An undistorted model with a 1:100 scale is constructed to study the velocity-slope relationship. If the reach has a Manning's coefficient of
A new laboratory site is available for modeling the channel of Example 10.8 so that the length is no longer a restriction, but the roughness coefficient of the material to be used in the movable bed is nm = 0.018. Determine the appropriate horizontal scale (using the same vertical scale) and the
Determine the model roughness coefficient, the model velocity, and the model flow7 rate for Example 10.8 if the vertical scale used was 400, just like the horizontal scale. Are the values obtained for the model reasonable? Will the model flow remain fully turbulent?
A 1:300 scale model is constructed to study the discharge-depth relationship in a river reach with Manning's coefficient n = 0.031. If the model discharges 52 L/sec and has Manning's coefficient n = 0.033, what is an adequate vertical scale ratio and the corresponding flow rate for the prototype?
A model study is proposed for a barge channel (np = 0.03) that has a sedimentation problem. The channel conveys a flow rate of 10,600 ft3/sec. The following model parameters have been established: a vertical scale ratio of 1:65 and a roughness coefficient of nm = 0.02. Determine the horizontal
A model of a broad crested weir has been designed and constructed to study the discharge per foot (q) of the prototype. Because the overflowing water sheet is relatively thick, the surface tension and viscosity of the fluid are not critical to the analysis. However, the weir (prototype) discharge
Use the Buckingham Pi theorem to derive an expression for the power developed by a motor in terms of the torque and rotational speed (i.e., Equation 5.3).
Steady flow of an incompressible, Newtonian fluid occurs through a long, smooth-walled horizontal pipe. Use the Buckingham Pi theorem to derive an expression for the pressure drop that occurs per unit length of pipe (∆Pl) using the pipe diameter (D), the pipe velocity (V), and the fluid density
If the viscosity (μ) and density (p) of a liquid are included as variables in the dimensional analysis of Example 10.9, use the Buckingham Pi theorem to develop all of the dimensionless groups if spillway height (h), the gravitational acceleration (g), and the viscosity are selected as the
Determine an expression for the velocity (V) of an air bubble rising through a stationary liquid. The pertinent variables are bubble diameter (D), gravitational acceleration (g), viscosity (μ), density (p), and surface tension (σ). Use bubble diameter, density, and viscosity as repeating
A liquid of density p and viscosity μ flows down an open channel of width W on a channel slope sin θ. The mean speed V is believed to depend on, among other things, the depth (d), the gravitational acceleration (g), and the roughness height (ε). Find the dimensionless parameters that may affect
Components of the hydrologic cycle may be classified as follows:(a) Water-holding elements,(b) Liquid transport phases, and(c) Vapor transport phases.Using Figure 11.1, apply one of these three descriptors to each component of the hydrologic cycle as depicted. Can you think of any other components
As water moves through the hydrologic cycle, water quality changes are common because of natural phenomena or anthropogenic pollution. Using Figure 11.1, describe how water-quality changes occur during each phase of the hydrologic cycle. For example, when lake water is evaporated, trace elements
An in-ground swimming pool may have a leak. The 30-ft by 10-ft by 5-ft (depth) pool is filled on June 1. On June 13, a hose, flowing at a rate of 10 gallons per minute, is used to add water to the pool. The hose is turned off after 1 hr. Four inches of rain fell during the month. Evaporation from a
A water-supply reservoir has been lined with clay to limit leakage (infiltration) through the bottom. An assessment of the effectiveness of the liner is required to fulfill the terms of the construction contract. The following data have been collected for a test week:The surface area of the lake is
A rainfall event occurs over a 150-square-mile watershed. The following incremental depths of precipitation, interception, and infiltration are estimated during a 30-min storm in 5-min increments. Determine the total volume of rainfall (acre-feet) and the total volume of runoff (acre-feet) that
An annual water budget for a critical water-supply basin is needed. During the year, the following data were collected for the 6,200-km2 watershed: precipitation = 740 mm, evaporation and transpiration = 350 mm, average annual streamflow leaving the basin (outflow) = 75.5 m3/sec. groundwater
What are the mechanisms by which air masses laden with water vapor are lifted, resulting in cooling and precipitation? What are the resulting categories (types) of precipitation?
Referring to Figure 11.4, answer the following question:(a) Why does Virginia receive more rain than Kansas?(b) Why does Maine receive less rain than Virginia?(c) Why does northern California receive so much rain?(d) Why does Nevada receive so little rain?(e) Why does western North Carolina receive
A large drainage basin can be divided into four sub-basins. The areas of the sub-basins are 52 km2, 77 km2, 35 km2, and 68 km2. The average annual precipitation in each is 124 mm, 114 mm, 126 mm, and 99 mm, respectively. Determine the average annual precipitation (in cm) for the whole drainage area.
A Kansas farmer wants to determine the average rainfall on his sunflower crop. The sunflower field takes up an entire section (a square of 1 mile per side, or 640 acres). The farmer has rain gauges located at the four corners and in the center. The rainfall depths are NE = 3.2 in., NW = 3.6 in., SE
A Kansas farmer wants to determine the average rainfall on his sunflower crop. The sunflower field takes up an entire section (a square of 1 mile per side, or 640 acres). The farmer has rain gauges located at the four corners and in the center. The rainfall depths are NE = 3.2 in., NW = 3.6 in., SE
Rainfall depths (in centimeters) on a commercial farm during a July storm are depicted at various gauge locations in Figure P11.2.6. (The exact location of each gauge is signified by a dot adjacent to the rainfall depth.) Determine the average depth of rainfall on the field using the Thiessen
Rainfall depths (in cm) on a commercial farm during a July storm are depicted at various gauge locations in Figure P11.2.6. (The exact location of each gauge is signified by a dot adjacent to the rainfall depth.) Determine the average depth of rainfall on the field using the isohyetal method.
Rainfall depths (in cm) on a commercial farm during a July storm are depicted at various gauge locations in Figure P11.2.6. (The exact location of each gauge is signified by a dot adjacent to the rainfall depth.) Determine the average depth of rainfall on the field using the inverse-distance
Precipitation station X was inoperative for one month. A storm occurred during this time. The precipitation depths recorded during the storm at three surrounding stations (A, B. and C) were 6.02 in., 6.73 in., and 5.51 in., respectively. The normal annual precipitation amounts at stations X, A, B,
Determine a 10-yr, 24-hr storm hyetograph for Miami, Florida. Plot a bar graph of the storm (time versus rainfall intensity).
The 10-yr, 24-hr storm hyetograph for Virginia Beach, Virginia, was determined in Example 11.3. From this data, estimate the 10-yr, 6-hr storm hyetograph at the same location.
The following incremental depths of rainfall (inches) are recorded during a 45-minute storm. Determine the total depth of rainfall for the 150-square-mile watershed, the maximum intensity (in./hr), and the total rainfall (acre-feet).
The U.S. Geological Survey maintains a network of stream flow gauges on most of the major rivers and creeks around the country. Many of these gauges are located at bridge crossings. What are the advantages of locating a gauge at a bridge crossing? Are there any disadvantages?
The USGS publishes stream flow information by state and gauge every year in its annual water data reports. Search the service's Internet site (www.usgs.gov) to find information at a particular gauge. What information is provided on individual gauge stations? How frequently are stream flows
The following point velocities (m/sec) and depths (m) were collected in the river cross section shown in Figure 11.12 where the width of each vertical section is 1.0 m. Determine the discharge (m3/sec) of the river.
The following point velocities (ft/sec) and depths (ft) were collected in the river cross section shown in Figure 11.12, where the width of each vertical section is 2.0 ft. Determine the discharge (ft3/sec) of the river.
The following stream flow versus stage information was collected at a stream gauging station during a storm event.(a) Plot a rating curve with the discharge plotted on the abscissa. (b) During a storm event some time later, the following stages were recorded. Plot a hydrograph (discharge vs. time
Refer to Example 11.4 to answer the following questions qualitatively. (a) Would you expect the stream flows measured in the watershed to change if the 12.3 cm of precipitation fell in a 6-hr instead of 24-hr period? If so, how? (b) Why might groundwater contribution to stream flow increase after a
A 2-hr storm (2 cm of runoff) of uniform intensity produces the flows on Wolf Creek shown in the following table. Determine the peak flow and time to peak of a 4-hr design storm that generates 1.5 cm of runoff in the first 2 hours and 3 cm of runoff in the subsequent 2 hrs. Assume a negligible base
The effective part of a 2.5 in. rain (total depth) lasts 4 hours on a 5-sq-mi watershed, producing the stream flows shown in the table below. Assuming a base flow that varies linearly from 20 cfs (at time 0) to 40 cfs (at time 20), determine the 4-hr unit hydrograph for the watershed.
The stream flow given in the following table was produced by a 1-cm rainfall event (total depth). The effective portion of the rainfall lasted 1 hr (from time 9 to time 10). If the watershed is 20 square kilometers, derive a 1-hr unit hydrograph for the watershed. Assume the groundwater
A storm occurs over a 27-square-mile watershed. The measured rainfall and stream flow are shown in the following tables. Derive the unit hydrograph from the data. Is the result a 1-hr, 2-hr, or 3-hr unit hydrograph? What fraction of the precipitation appears as runoff? Assume the groundwater
Measured stream flow data during a storm event on Judith Creek produces a roughly triangular hydrograph shape. The peak occurs 3 hours into the storm and measures 504 cfs. There is no base flow before the event, so the discharge starts at time zero, climbs to the peak in 3 hours, and recedes
Lost Creek's 1 -hr unit hydrograph at the Chamberlain Avenue crossing is shown in the following table. Determine the expected flow rate in the creek at that location if a 2-hr storm produces 2.0 cm of rain in the first hour and 2.5 cm of rain in the second hour. Assume losses to rainfall are
Referring to Example 11.5, determine the stream flow expected from a new storm that produces 6 cm of runoff in the first 24 hours of the storm and 4 cm of runoff in the next 12 hours. Assume the base flow is the same as in Example 11.4.
A 1-hr unit hydrograph for the No Name Creek watershed (307 acres) is given in the following table. Determine the stream flow that would result from a rainfall event on the same watershed if the excess rainfall (runoff) in a 2-hr storm in 30-min increments is 0.5 in., 0.5 in., 0.25 in., and 0.25
In Example 11.4, a 12-hr unit hydrograph (UH12) is computed. Using the UH12, compute a 24-hr unit hydrograph (UH24).
A 200-acre watershed near Chicago, Illinois, includes 169 acres of open space with 90 percent grass cover and a 31 -acre industrial development park. The existing soil has coarse to fine texture based on sieve tests. Determine the runoff depth (in.) and volume (acre-feet) for the 10-yr, 24-hr
A 100-hectare watershed is composed of three different land uses: 20 hectares of golf course (40% in Drexel soils and the rest in Bremer soils), 30 hectares of commercial area (Bremer soils), and 50 hectares of residential area (half-acre lots and Donica soils). Determine the runoff volume (cubic
Determine the rainfall excess (i.e., runoff) resulting from the 10-yr, 24-hr rainfall for the watershed in Example 11.8. This amounts to completing steps 1, 2, and 3 of the design process described in Section 11.6.4 and elaborated in Example 11.6. Albemarle County, in western Virginia, receives 6.0
The hydraulic length (longest flow path) for a watershed is 2,800 ft. Along this path, runoff initially travels over the land surface (dropping 4 ft in elevation over 200 ft in length through short grass) and then moves into shallow concentrated flow for a distance of 600 feet with an average
A 100-acre watershed with type B soils has been commercially developed. The length of the longest flow path is 3,000 feet, and the average watershed slope is 2.5 percent. Determine the peak discharge and time to peak for an SCS dimensionless unit hydrograph.
Referring to Example 11.8, plot the unit hydrograph using a spreadsheet program. Determine the volume of runoff in acre-feet and the depth of runoff in inches.
Referring to Example 11.8, determine the SCS unit hydrograph after development if half the watershed is developed commercially and the rest with townhouses.
A 400-acre watershed just south of Chicago is currently farmed with small grain crops. The soils are primarily clay, the hydraulic length of the watershed is about 1 mile, and the average land slope is 2 percent. Determine the SCS synthetic unit hydrograph before development.
Determine the change in SCS synthetic unit hydrograph of Problem 11.6.8 if the farmland is developed into an industrial park. Problem 11.6.8 A 400-acre watershed just south of Chicago is currently farmed with small grain crops. The soils are primarily clay, the hydraulic length of the watershed is
Build a 2S/∆t + O versus O relationship in 0.2-m increments for a pond that is expected to reach a depth of 1.0 m over the top of the service spillway (normal pond level). The elevation-storage relationship for the pond is described by S = 600 h1.2, where S = storage in the pond in m3 and h =
Build a 2S/∆t + O versus O relationship in half-foot increments for an underground cistern that is 2 ft deep, 4 ft long, and 3 ft wide. A 2-in.-diameter bottom drain acts as an orifice with a discharge coefficient of 0.6. Assume a routing interval of 10 seconds.
Referring to Example 11.9, continue computations in the routing table through time 13:45. Additional inflows are given in the following table. Graph the inflow and outflow hydrograph on the same set of axes. Determine the maximum elevation and storage attained in the pond during the design storm.
A flood occurs before the storage pool of a reservoir is empty. Given the information in the following tables, determine the peak outflow during the flood.
A portion of a reservoir routing table immediately follows (90 min into the flood). Fill in the blanks (?) in the table. Also determine the peak reservoir outflow, stage (H), and volume in the reservoir at 120 minutes. (1 acre = 43,560 ft2.)
Referring to Example 11.9, perform the storage routing computations again using a 10-min routing increment starting with the flow at time 11:30 and progressing to 11:40, then 11:50, and so on and dropping the flows in between. Will this require a new (2S/∆t + O) versus O relationship? If so,
The following table shows the elevation-outflow-storage data for a flood-control reservoir. Determine the maximum pool elevation and peak outflow rate during a 6-day storm that produces the displayed inflow hydrograph values.
The stage storage relationship at a pond site is described by S = 600 h1.2, where S = storage in the pond in m3 and h = water level in meters above the spillway crest. The discharge over the spillway is described by O = kwL(2g)0.5h1.5, where the discharge (()) is in m3/sec, kw = 0.45 (discharge
An empty water storage tank (cylindrical shape) with a diameter of 20 m and a height of 5 m is being filled at a rate of 2.5 m3/sec. However, it is also losing water (because of a hole in the bottom of the tank) at the rate of O = 0.7(h)0.6, where h is the depth of water in meters and O is the
The peak discharge from a 20-acre watershed is required for a new culvert installation. The hilly watershed (average slope 7%) is composed of pastureland with dense grass and clay soils. The hydraulic length of the watershed is 1,200 feet. The watershed is slated for commercial development in the
Referring to Example 11.11, determine the pipe size (concrete) that would be required to convey the design flow away from the first inlet. If the minimum pipe size specified by community standards is 12 in., what is the depth of flow in the pipe at peak flow (0.914 cfs)? What is the travel time per
Referring to Example 11.12, finish the problem by sizing the pipes from MH-4 to MH-6. Pipe lengths are as follows: MH4A to 4, 350 ft; MH4 to 5, 320 ft; MH5A to 5, 250 ft; MH-5 to 6, 100 ft.
Design the stormwater-collection pipes (concrete; minimum size of 12 in.) for the housing subdivision in Figure P11.8.13. The data for each drainage area (basin) contributing flow to the manholes is provided in the following table, including the inlet time (Ti) and the runoff coefficient (C). In
Design the stormwater-collection pipes in Problem 11.8.13 given the following data changes. The upstream elevation for pipe AB is 23.9 ft instead of 24.9 ft, the inlet time for basin 1 is 14 min instead of 12 min, and the inlet time for basin 3 is 10 min instead of 13 min.Problem 11.8.13Design the
Design the stormwater-collection pipes in Problem 11.8.13 given the following data changes. The upstream elevation for pipe CB is 23.5 ft instead of 24.4 ft, the inlet time for basin 2 is 14 min instead of 10 min, and the downstream elevation for pipe DR is 22.0 ft instead of 21.6 ft.Problem
A large circular parking lot with a diameter of 400 feet is being constructed as overflow parking for the state fairgrounds. All stormwater will drain as sheet flow to the center, flow into a drop inlet, and travel through a pipe system to the nearest stream. The parking lot will be mowed grass
Determine the 10-year peak discharge using the rational equation for a concrete parking lot that is 300 ft wide by 600 ft long. The longest flow path is 300 ft of sheet flow across the lot on a slope of 0.5 percent and 600 ft of shallow concentrated flow along the parking lot's length in a paved
The paved parking lot depicted in Figure P11.8.4 drains as sheet flow into a concrete drainage channel. The rectangular channel discharges into a stormwater-management pond. Determine the 5-yr peak discharge. Assume the 2-yr, 24-hr rainfall is 2.8 in. Use Figure 11.26 for the rainfall intensity in
A 150-acre forested watershed with a time of concentration of 90 min will soon be developed with the following land uses: 60 acres of single-family homes, 40 acres of apartments, and the rest in native forest. After development, the longest flow path is 5,600 feet. A 100-foot sheet flow segment
The paved parking lot depicted in Figure P11.8.4 drains as sheet flow into a concrete side channel that discharges into a stormwater-management pond. The travel time across the parking lot as sheet flow is 5 min, and the travel time through the entire drainage channel is 2 min. Thus, the time of
Referring to Example 11.11, describe subjectively (no analysis required) how the location of the inlet would change (one change at a time, not collectively) if:(a) The 10-year design storm is the standard.(b) The pavement-encroachment criterion is 8 feet.(c) The lawns are Bermuda grass.(d) The

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