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physics
mechanics

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

Sketch the free surface of the water table produced by a well located in the middle of a circular island as depicted in Figure P7.4.2. If the well yields 7.5 gpm (gal/min), what is the coefficient of permeability? Also determine the drawdown at a distance of 150 ft from the well.
A field test is conducted in a confined aquifer by pumping a constant discharge of 14. 9 m3/hrfrom a 20-cm-diamecer well. After an approximate steady state is reached, adrawdown of 0.98 mis measured in the pumped well. Also measured are draw downs of 0.78 m, 0.63 m, 0.59 m, and 0.56 m.
A field test is conducted in an unconfined aquifer by pumping 1,300 ft 3/hr from an 8- inch diameter well penetrating the aquifer. The undisturbed aquifer thickness is 46 ft. The draw downs, measured at steady state at various locations, are tabulated below. Determine the coefficient of
Explain why a none quilibrium test rather than an equilibrium test is needed to detetmine the storage coefficient of an aquifer.
Derive Equations 7.43 and 7.47.
A pumping test was conducted in a confined aquifer using a constant pump discharge of 6.00 m3/ hr. The draw downs measured at an observation well located 22.0 m from the pumped well are shown in the following table. Determine the aquifer trans missivity, the storage coefficient. and the drawdown
The following drawdown information was collected from an observation well 120 ft away from a 16-in.-diameter well that is pumped at a uniform rate of 1.25 cfs. Determine the permeability and the storage coefficient of the 90-ft-thick unconfined aquifer.
Locate imaginary wells on Figure P7.5. l that will replace the acrual boundaries with an equivalent hydraulic system.
A fully penetrating, 12-in. diameter well pumps groundwater from a 25-ft thick confined aquifer. An impermeable rock stratum is located in the aquifer 105 ft away. Will the impermeable boundary impact the drawdown curve of the well when equilibrium conditions are achieved if tbe pump rate is 20,000
A confined aquifer has a thickness of l 0.0 m and a transmissivity of 1.30 × 10-3 m2/sec. When a 30-cm-diameter well is pumped at the rate of 30 m3 /hr, the drawdown of the piezometric surface at an observation well 30 m away is 9.60 m when it is not impacted by an aquifer boundary. If an
A confined aquifer has a thickness of 10.0 m and a transmissivity of l 30 × LO- 3 m2/sec. When a 30-cm-diameter well is pumped at the rate of 30 m3/ hr, the drawdown in the piezornetric surface at the well is 15.0 m when it is not impacted by an aquifer boundary. If an identical well is installed
An industrial well taps into an 80-ft-thick confined aquifer that has a transmissivity of 0.0455 ft2/sec. The well is located 600 feet from a completely penetrating stream. A farmer's irrigation well is located halfway between the stream and the industrial well. What is the maximum flow rate that
A di scharge well that fully penetrates a confined aquifer is pumped at a constant rate of 300 m3/hr. The aquifer transmissivity is 25. 0 m2/ hr, and the storage coefficient is 0.00025. A fully penetrating stream is located 500 m away. Determine the drawdown at a location between the well and the
A confined aquifer has a thickness of 40.0 ft, a transmissivity of 250 ft2/ hr, and a storage coefficient of 0.00023. A 16-in.-diameter well is extracting a tlow rate of 10,600 ft3/hr from the aquifer. The well is located 330 ft away from a fully penetrating impermeable boundary. Determine the
As previously mentioned, constructing a good flow net is more art than science. Because different people would undoubtedly draw different flow nets, we may wonder about the accuracy of us ing it for seepage calculations. If carefully drawn, there is surprising consistency in seepage predictions
Flow nets yield more information than just seepage rates. For example, the total energy head at an~ location in the flow net can be estimated using equipotential lines. Recall that equal head drop occur from the reservoir water level to the tail water level in sequential equipotentia lines. Given
Sheetpiles are used to keep water out of a bridge pier construction site, as depicted in Figure P7.8.3 (drawn to scale). Determ.ine the quantity of seepage (in m3/hr per unit length of sheetpile) that can be expected in order to design an appropriate pump to dewater the construction site. The
A concrete dam rests on an alluvial solid foundation as shown in the scale drawing of FigureP7.8.4. Estimate the seepage rate (in m3/ day) for the 100-m-long dam if the permeability is 4 .45 X 10-7 m/sec and the upstream water depth is 20 m. Also estimate the energy head (using) the dam bottom as
Place a cutoff wall at the heel of the dam depicted in Figure P7 .8.4 much like Example 7 .18. The cutoff wall should extend downward one-third of the distance to the impervious layer. Estimate the seepage per unit meter width of dam. Assume the permeability is 4.45 × 10- 7 m/sec and the upstream
Determine the seepage in m3/day through the homogeneous earth dam depicted in Figure 7.29. Also determine the seepage velocity when the water surfaces on the downstream embankment at point D. The upstream water depth is 7 .0 m, the dam is 80 m long, and silt is the soil used to construct the dam.
Make a copy of Figure 7.30 and construct a flow net. Use the phreatic line given as the upper streamline with all other streamlines below it terminating in the drain. If the seepage rate is 0.005 m3/day per meter when the upstream water level is 4.24 m, what is the most likely soil type used to
An earth dam, as schematically shown to scale in Figure P7.9.3, is constructed with a uniform material having a coefficient of permeability of 2 .00 X I o-6 m/sec on a relatively imperviousfoundation. The dam is 30 m high, which can be used as the drawing scale. Compute the seepage rate in units of
Determine the flow rate in Problem 8. 9.3 if the outlet was not submerged. Problem 8.9.3 Stage recorders have registered stream depths upstream (4.05 m) and downstream (3.98 m) of a culvert during a flood event. The 2 m by 2 m concrete culvert (square-edged entrance) is 15 m long and has a slope
A concrete culvert is required to convey a design flow of 654 cfs over a length of 330 ft. and a slope of 0. 0 l S ft/ft. Because there is a large lake downstream, the tail water elevation is constant at 526.4 ft MSL, which will submerge the culvert outlet. The headwater elevation cannot exceed
A l. S-m-diameter culvert (concrete barrel, well-rounded entrance) that is 20 m long is installed on a slope of 2 percent. The design discharge is 9.5 m3/sec, and the inlet will be submerged but not the outlet. Determine the depth that will result upstream (above the invert) during the design flood
Determine the size of a circular, corrugated metal culvert with these design conditions: a 60.0-m length, a 0.10-m/m slope, and a flow of 2.5 m3/sec. The outlet will be unsubmerged, but the inlet (square-edged) will be submerged with a headwater depth of 2. 0 m above the culvert invert.
A rectangular concrete culvert (square-edged entrance) is placed on a slope of 0.09 ft/ ft. The culvert is 4. 0 ft × 4 . 0 ft and 140 ft long. The tail water level is 2. 0 ft below the culvert crown at the outlet. Determine the discharge if the headwater level is (a) 1.5 ft above the crown at the
A horizontal rectangular stilling basin (USBR type III) is used at the outlet of a spillway to dissipate energy. The spillway discharges 350 ft3/scc and has a uniform width of 35 ft. At the point where the water enters the basin, the velocity is 30 ft/sec. Compute the following: (a) The sequent
An increase in discharge through the spillway in Problem 8.10.2 to 45 m3/sec will increase the spillway outlet depth to 0. 25 m. Select an adequate USBR stilling basin and deten11ine the sequent depth, the length, the energy loss, and the efficiency of the hydraulic jump (defined as the ratio of
A gravity dam is depicted in Figure P8.3.1. lf a force ratio against sliding of 1.3 is required, is the 33-m-high dam safe? Assume the coefficient of friction between the dam base and the foundation is 0.6, the specific gravity of concrete is 2.5, and fu ll uplift forces exist on the base of the
A gravity dam is depicted in Figure P8.3.1. A force ratio of 2.0 against overturning is required. Determine whether the dam is safe if the water level rises to the top of the 33-m-high dam during a flood event. Assume the specific gravity of concrete is 2.5, and full uplift forces exist on the base
Typical force ratios for a gravity dam are 2.0 for overturning and 1 .2 to 1 .5 for sliding. Determine if these requirements are met in the gravity dam depicted in Figure P8.3.3. Assume that the uplift force takes a triangular distribution with maximum magnitude one-third that of the hydrostatic
The specific gravity of the dam shown in Figure P8.3.4 is 2.63, and the coefficient of friction between the dam and the foundation is 0.53. The depth of the water is 2 7.5 m when the reservoir is filled to design capacity. Assume that the uplift force has a triangular distribution with the maximum
Determine the foundation pressure at the heel and toe of the dam in Problem 8.3.l.Foundation Pressure Problem 8.3.1
For the concrete gravity dam shown in Figure P8.3.3, compute the foundation bearing pressure at the heel and toe. Assume that the uplift force takes a triangular distribution with maximum magnitude one-third that of the hydrostatic pressure at the heel and zero at the toe. The reservoir is full to
Prove that if the resultant vertical force (Rv) passes through the middle one-third of the base in a concrete, gravity dam, none of the concrete along the base of the dam will be in tension.
AV-canyon supports a 100-ft high, constant-angle (120°) arch dam. If the canyon is 60 feet wide at the top and the design freeboard is 6 ft (i.e., the water level is 6 feet below the top of the dam), determine the abutment reactions at dam heights of 25, 50, and 7 5 feet above the bottom of the
A constant-angle arch dam ( θ = 150°) is designed to span a vertical-walled canyon 150 m wide. The height of the dam is 7 8 m, including 3 m of freeboard. If the dam has 4 m thickness at the crest and has a symmetrical cross section that increases its thickness to 11.8 mat the base, determine the
A weir 1.05 min height is built across the floor of a 4-rn-wide rectangular channel. If the water depth just upstream of the weir is 1.52 m, what is the water depth on the crest and the discharge in the channel? Neglect friction loss and the velocity head upstream.
It is necessary to obtain the elevation of the crest of a weir in a channel without stopping the flow. The water surface elevation upstream of the weir is 96.l ft above mean sea level (MSL). Determine the elevation of the crest of the weir above MSL if the weir is 4. 90 ft wide and discharges 30.9
A 3.05-m-wide frictionless weir rises l .10 m above the channel bottom. The water depth upstream of the weir is 1.89 m. Determine the discharge in the channel by two different equations and the velocity of the water going over the weir. Assume the upstream velocity head is negligible.
Verify the following: (a) That Equation 6.14 can be obtained from Equation 6.11; (b) That the discharge coefficient for the weir equation using SI units (Equation 8.8c) is indeed l.70; and (c) That the discharge coefficient would be lower if the weir was not assumed to be frictionless.
A weir 0.78 m in height is built across the floor of a 4-m-wide rectangular channel. If the water depth just upstream of the weir is 2.00 m, what is the flow rate in the channel? Neglect friction loss and the velocity head upstream. Also determine the flow rate if the velocity head is not neglected.
A rectangular channel carries a discharge of 2.00 m3/sec per meter of channel width over a weir crest that is 1.40 min height. The energy grade line upstream of the weir measures 2.70 m above the channel bottom. Determine the true coefficient of discharge in the weir equation, considering the
A weir is being considered for flow measurement in a long, concrete irrigation canal with a bottom slope of 0.002. The maximum depth of flow in the 15-ft-wide canal is 6 feet, but the channel contains an additional 4 feet of freeboard. Determine the maximum height of a flow-measurement weir before
A 31. 2-ft-wide overflow spillway is subject to a head of 3. 25 feet under design conditions. The coefficient of discharge is 3.42 based on model studies. (a) Determine the spillway discharge, assuming a negligible approach velocity. (b) Determine the spillway discharge under flood conditions if
Assume the spillway in Example 8.2 is 6 meters high. Recompute the static head on the spillway by accounting for the approach velocity. What percent error was introduced in the static head by ignoring the approach velocity?
Determine the maximum approach velocity (as a function of Hs) that can occur before an error of 2 percent enters into the calculation for spillway discharge. Compute the function in British units (i.e., g = 32. 2 ft/sec2).
A 21-m-wide overflow spillway has a discharge coefficient of l.96 at flood stage. Flood stage occurs at a static head of between I.7 m and 3. l m. The spillway is 15 m high. Determine the maximum discharge the spillway is able to pass; (a) ignore the approach velocity and (b) include the approach
An overflow spillway is designed to discharge 214 m3/sec under a maximum head of 1.86 m. Determine the width and the profile of the spillway crest if the upstream and downstream slopes are 1:1. Assume C = 2.22.
Determine the maximum discharge for a 104-ft-wide overflow spillway having an available head of 7. 2 ft. Also determine the profile of the spillway crest having a vertical upstream slope and a 1.5:1 downstream slope. Assume C = 4.02.
In Example 8.3, the side-channel spillway passed through critical depth (5.0 I ft) at the end of the channel. Five feet upstream, the depth was determined to be 7. 73 ft in the horizontal (0 percent slope) channel. Determine the depth 5 ft upstream if the side-channel slope is 5 percent.
Answer the following: (a) What happens to the cos θ term in Equation 8.13 (it does not appear in Equation 8.14 )? (b) Verify that Ff = yASfΔx. (c) Determine the largest channel slope that would keep S0 within 1 percent of sin IJ. (Recall that the assumption S0 = sin θ for a reasonably small
The flow at the end of a 30-m-long side channel spillway is 36.0 m3/sec. A 30-m-long overflow spillway, which is under a head of 0. 736 m, contributes the flow to the side-channel spillway. If the side channel has a bottom width of 3 m (n = 0.020) and a bottom slope of 0.01, what is the depth l 0 m
The design engineer working on the spillway described in Example 8.3 would like to try an alternative design. Determine the depth 5 ft and 10 ft upsLream if the overflow spillway is lengthened to 25 ft but still accommodates the design discharge ( 637 ft3 /sec) uniformly along its entire length. In
A 90-m-long, overflow spillway (C = 2.00) operating under a head of 1. 22 m contributes flow to a side-channel spillway. The rectangular side-channel spillway (n = 0. 015) is 4. 6 m wide and has a bottom slope of 0.001. Define the water surface profile (at 30-m intervals) upstream from the location
The overflow spillway of Example 8.2 discharges into a side-channel spillway ( n = 0. 01 3) with a horizontal bottom slope. The wall opposite the overflow spillway crest is vertical, and the depth of water at the exit end of the side channel is critical depth. Determine the depth of water at the
The reservoir level in Example 8.4 will continue to fall as the siphon empties the reservoir. If the water temperature is 20°C, what is the maximum elevation difference between the crown and the falling reservoir level before the pressure at the crown drops below the vapor pressure of water?
Answer the following questions by referring to Example 8.4. (a) If the water temperature is 20°C, what is the allowable (negative) pressure head before the onset of cavitation? (b) Should the bend loss at the crown be included in the computations for determining the pressure head at the crown? (c)
A rectangular siphon (3 ft by 6 ft) discharges into a pool with an elevation of 335 ft MSL Determine the discharge when the siphon primes at an upstream pool elevation of 368 ft MSL if losses are 10.5 ft, excluding the exit loss. Also determine the pressure head at the siphon Crown under these
A 60-m-long siphon spillway discharges water at the rate of 0. 32 m3/sec. The siphon crown is 1.2 m above the water surface elevation of the reservoir and a length of l 0 m away from the siphon entrance. If the siphon diameter is 30 cm, the friction factor is 0.02, and the head loss coefficients
A siphon spillway (Figure P8.8.5) with a cross-sectional area of 12 ft2 is used to discharge water to a downstream reservoir 60 ft below the crest of the spillway. If the upstream reservoir level is 7.5 ft above the intake, what is the pressure head at the crest if the siphon has been primed Assume
Determine the required siphon diameter and maximum height of the siphon crest above the entrance given the following design conditions: Q = 5. 16 m3/sec, K (entrance) = 0.25, K (exit) = l.0 K (siphon bend) = 0.7,f = 0.022, siphon length = 36.6 m, length to crest = 7.62 m, upstream pool elevation=
A siphon spillway is designed to discharge 20 m3/sec with a head above the crest of hs, a crest elevation of 30 m, and an outlet elevation of 0 m. The allowable gauge pressure at the crest -8 m of water column during design flow. The crest section is followed in order by a vertical.: section, a
In Example 8.5, a culvert diameter of l. 5 m may be required if this is the next largest standard size . As the design engineer, you would like to use a I. 25 m diameter culvert to save your client money. Would this smaller diameter culvert meet the design requirements if: (a) A well-rounded
Derive Equation 8.19, the orifice equation, by balancing energy between points (I) and (2) in Figure P8.9.2. Initially, assume no energy losses. What does the variable h represent? What does the variable Cd represent?
Stage recorders have registered stream depths upstream (4.05 m) and downstream (3.98 m) of a culvert during a flood event. The 2 m by 2 m concrete culvert (square-edged entrance) is 15 m long and has a slope of 3.0 percent. Based on this information, determine the flood flow rate that passed
Water is poured into an open-ended U-tube (Figure P9.1.1). Then oil is poured into one leg of the U-tube, causing the water surface in one leg to rise 6 in. above the oil-water interface in the other leg. The oil column measures 8.2 in. What is the specific gravity of the oil?
Determine the pressure in the pipe shown in Figure P9.1.2 if y = 1.24 m, h = 1.02 m, and the manometry fluid is mercury (sp. gr. = 13.6). Also determine the height the pressurized water would climb in a piezometer if it was used to measure pressure at the same location.
An inclined oil manometer is used to measure pressure in a wind tunnel. Determine the specific gravity of the oil if a pressure change of 323 pascals causes a 15-cm reading change on the 15° incline.
A plexiglass tube (piezometer) is mounted on a pipe as shown in Figure P9.2.1. Another plexiglass tube with a 90° bend (i.e., Pitot tube) is inserted into the center of the pipe and directed toward the current. For a given discharge, the piezometer registers a water height of 320 cm, and the
Show that Equation 9.1b can be written in the following formif the pipe fluid is water but the manometry fluid is not (and water from the pipe extends all the way to manometry fluid). Also, sp. gr. is the specific gravity of the manometry fluid.
Pitot tube measurements in a 5-ft-diameter water tunnel indicate that the stagnation pressure and the static pressure differ by a mercury column height of 5.65 inches. What is the water velocity? Estimate the discharge in the tunnel. Why is it just an estimate?
Refer to Figure 9.4 (b) and answer the following questions: (a) If the pipe fluid and the manometry fluid are water (with air in between), determine the pipe velocity if ∆h = 34.4 cm. (b) If the pipe fluid is water, which extends all the way to the manometry fluid (mercury: sp. gr. = 13.6), what
Refer to Figure 9.4 (b) and answer the following questions: (a) If the pipe fluid and the manometry fluid are oil (with air in between), what is the pipe velocity if ∆h = 18.8 in? [sp.gr. (oil) = 0.85.] (b) If the pipe fluid is oil, which extends all the way to the manometry fluid (mercury; sp.
Referring to Figure 9.4 (a), determine the maximum measurable velocity if the maximum Pitot tube scale length is 25 cm. The pipe fluid is water, which extends all the way to the manometry fluid, which is mercury with a specific gravity of 13.6. Estimate the maximum discharge in the 10-cm-diameter
Determine the flow rate in 50-cm diameter pipe that contains a 20-cm (throat) Venturi meter if the pressure taps read 290 kN/m2 and 160 kN/m2.
A Venturi meter with a 4-in. throat is installed in an 8-in. diameter (vertical) waterline. The pressure difference reading between the throat and entry section in a mercury-water manometer is 2.01 feet. Determine the flow rate if the flow is moving downward and the distance between the pressure
A discharge of 0.0820 m3/sec passes through a horizontal, 20-cm waterline containing a 10-cm ASME flow nozzle. Determine the pressure difference that will register across the flow meter in pascals.
Determine the discharge in the 40-cm diameter waterline shown in Figure P9.3.4. The nozzle meter has a throat diameter of 16 cm and is built and installed according to the ASME standard. The distance between pressure taps is 25 cm.
A 12-in. orifice meter (Cv = 0.675) is installed in a vertical segment of a 21-in. -diameter waterline. If the largest flow rate expected is 12.4 ft3/sec, what is the necessary length of a vertical U-tube for the differential (mercury-water) manometer? There is a 9-inch difference between manometer
A maintenance crew discovers an orifice meter while working on an old water line. The engineer in charge would like to know the size of the orifice plate opening without dismantling the delicate meter. A specification plate on the side of the meter reads "Cv = 0.605." For a flow rate of 0.00578
A bend meter is installed in a 75-cm-diameter water pipe as shown in Figure 9.9. The installation delivered 51 m3 of water in 1 min. Determine the pressure head difference (in cm) that will register in a mercury-water manometer when the water pipe and bend are in a horizontal position. The bend
A bend meter is installed in a 75-cm-diameter water pipe with an 80-cm bend radius as shown in Figure 9.9. The flow rate in the pipe is 0.850 m3/sec, and the pressure difference reading between the outside and inside taps registers 5.26 cm on a mercury-water manometer. Determine the coefficient of
An uncontracted, horizontal weir (sharp-crested) is 4.5 m long and 3.1 in high. Determine the discharge if the upstream water depth is 4.4 m. Determine the discharge for the same upstream depth if a contracted weir (both ends) with a 2.4-m crest length and the same height is being proposed as a
Derive Equation 9.18 from the impulse-momentum equation (9.16), showing all steps.
Equation 9.19 is the general expression for a broad-crested weir. Considering the limit of a weir with zero height (h = 0) to infinity (h → ∞), Equation 9.19 may vary from Q = 1.92LH3/2 to Q = 1.36LH3/2 with H in meters and Q in meters per seconds. Verify these expressions and find equivalent
In Chapter 8, it was stated that an essential feature of weirs is that flow achieves critical depth passing over the weir. Because that is the case, derive Equation 9.9 using Equation 6.14, which relates critical depth to the flow rate.
Laboratory tests on a 60° V-notch weir gave the following results: for H = 0.3 m, Q = 0.22 m3/sec; and for H = 0.6 m, Q = 0.132 m3/sec. Determine the discharge equation for this V-notch weir in both SI and BG forms.
The crest of a standard, USBR 90°V-notch weir is 3 feet above the bottom of an irrigation channel. It is used to measure 25.6 cfs of flow to a customer. At this flow rate, the depth of water upstream of the weir is at the channel capacity. If the customer needs to increase the flow rate to 33.3
What is the crest length of the Cipolletti weir (USBR standard trapezoidal weir) required to accommodate a flow up to 0.793 m3/sec if the maximum head is limited to 0.259 m?
A broad-crested rectangular weir is. 1 m high and has a crest length of 3 m. The weir is constructed with a well-rounded upstream corner and a smooth surface. What is the discharge if the head is 0.4 m?
Determine the discharge in cubic meters per second measured by a 15-ft Parshall flume if the gauge reading Ha is 1 m and the gauge reading Hb is 0.5 m.
An uncontracted, horizontal weir is 1.5 m high and 4.5 m long. Determine the discharge over this weir when the upstream depth is 2.2 m. Determine the weir height if the same discharge was desired without exceeding an upstream depth of 1.8 m.
Flow occurs over a sharp-crested, uncontracted horizontal weir 3.5 ft high under a head of 1.0 ft. If this weir replaced another weir, which was one-half its height, what change in depth occurred in the upstream channel?
The flow through an 8-ft Parshall flume is 129 cfs when Ha is 2.50 ft. Determine the downstream water level (Hb) that would produce this flow rate.
The discharge in a rectangular channel 4 m wide is constant. A depth of 2.3 m is maintained by a 1.7-m-high contracted (both ends) horizontal weir (C = 1.86) with a 1-m-long horizontal crest. This weir is to be replaced by an uncontracted horizontal weir that will maintain the same upstream depth.
Uniform flow at a depth of 2 meters occurs in a rectangular channel that is 4 meters wide. The channel is laid on a slope of 0.001, and the Manning coefficient is 0.025. Determine the maximum depth and width of a geometrically similar channel if the flow in the model must be limited to 0.081 m3/sec.
The moment exerted on a gate structure is studied in a laboratory' water tank with a 1:125 scale model. The moment measured on the model is 1.5 N • m on the 1-m long gate arm. Determine the moment exerted on the prototype.
A 1:15 scale model will be used to study the circulation patterns in a rectangular detention pond. The pond has a bottom length of 40 m and a bottom width of 10 m. All sides of the pond have 3:1 (H:V) slopes. If the design depth is 5 m, what is the depth, surface area, and storage volume of the

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