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

A liquid is observed to rise to a height of 0.6 in. in a 0.02-in. glass tube. The contacting angle is determined to be 54°. Determine the surface tension of the liquid in lb/ft if its density is 1.94 slug/ft3.
Laboratory experiments are being conducted using many opaque, saltwater tanks. Straight glass tubes (with a 0.25 cm inside diameter mounted on the tanks) are proposed to track the depth of the saltwater during the experiment. Determine the measurement error (in cm) resulting from the use of the
A small amount of solvent is added to the ground water to change its electrolytic content. As a result, the contacting angle, 0, representing the adhesion between water and soil material, is increased from 30° to 42° while the surface tension decreases by 10 percent (Figure P 1.5.5). The
The pressure inside a droplet of water is greater than the pressure outside. Split a droplet in half and identify forces. The bursting force is the pressure difference times the area that is balanced by the surface tension acting on the circumference. Derive an expression for the pressure
Detem1ine the percentage change in density of water at 20°C when pressure is suddenly changed from 25 bars to 450,000 N/m2.
A steel tank holds 120 ft3 of water at atmospheric pressure (14. 7 lbs/in∙2 and 68.4°F). The water subjected to a 100-fold increase in pressure. Determine the initial weight and final density of the water if the volume decreases by 0.545 ft3.
The pressure in a 150-cm diameter pipe 2,000 m long is 30 N/cm2. Determine the amount of water that will enter the pipe if the pressure increases to 30 bars. Assume the pipe is rigid and does not increase its volume.
Collapse depth (or crush depth) is the submerged depth that a submarine cannot exceed without collapsing because of the surrounding water pressure. The collapse depth of modem submarines is not quite a kilometer (730 m). Assuming seawater to be incompressible (sp. gr. = 1. 03), what is the crush
A multiple-piston hydraulic jack has two output pistons, each with an area of 250 cm2. The input piston, whose area is 25 cm2, is connected to a lever that has a mechanical advantage of 9:1. If a 50-Nforce is exerted on the lever, how much pressure (kN/m2) is developed in the system? How much force
A cylindrical water tank (Figure P2.2.2) is suspended vertically by its sides. The tank has a 10-ft diameter and is filled with 20°C water to a 3-ft depth. Determine the force exerted on the tank bottom using two separate calculations(a) Based on the weight of the water, and(b) Based on the
The simple barometer in Figure P2.2.3 uses water at 30°C as the liquid indicator. The liquid column rises to a height of 9.8 m from an original height of 8.7 min the vertical tube. Compute the new atmospheric pressure, neglecting surface tension effects. What is the percentage error if the
Mercury is often used in barometers as depicted in Figure P2.2.3. This is because the vapor pressure of mercury is low enough to be ignored, and because it is so dense (sp. gr. = 13. 6) the tube can be shortened considerably. With the atmospheric pressure found in Problem 2.2.3 (99.9
A storage tank (6 m × 6 m × 6 m) is filled with water. Determine the force on the bottom and on each side.
A 30-ft-high, I -fl-diameter pipe is welded to the top of a cubic container (3 ft × 3 ft × 3 ft ). The container and pipe are filled with water at 20°C. Determine the weight of the water and the pressure forces on the bottom and sides of the container.
A closed tank contains a liquid (sp. gr. = 0. 80) under pressure. The pressure gauge depicted in Figure P2.2.7 registers a pressure of 4.50 Ã— 104 N/m2 (pascals). Determine the pressure at the bottom of the tank and the height of the liquid column that will rise in the vertical tube.
An underwater storage tank was constructed to store natural gas offshore. Determine the gas pressure in the tank (in pascals and psi; lb/in2) when the water elevation in the tank is 6 m below sea level (Figure P2.2.8). The specific gravity of seawater is 1.03.
A closed tank contains oil with a specific gravity 0.85. If the gauge pressure at a point 10 feet below the oil surface is 23. 7 psi (lb/in.2), determine the absolute pressure and gauge pressure (in psi) in the air space at the top of the oil surface.
Referring to Figure 2.4 (c), if the height of water (at 4°C) above point 7 is 52.3 cm, what is the height of the oil (sp. g r. = 0.85) above point 8?
A micro-manometer consists of two reservoirs and a U-tube as shown in Figure P2.4.10. Given that the densities of the two liquids are Ï1 and Ï2, determine an expression for the pressure difference (P1 - P2) in terms of Ï1, Ï1, h, d1, and d2.
For the system of manometers shown in Figure P2.4. 11, determine the differential reading h. Two different manometry fluids are being used with different specific gravities.
Determine the air pressure (kPa and cm of Hg) in the sealed left tank of Figure P2.4.12 if EA = 32.5 m.
A significant amount of mercury is poured into a U-tube with both ends open to the atmosphere. If water is poured into one leg of the U-tube until the water column is 3 feet above the mercury- water meniscus, what is the elevation difference between the mercury surfaces in the two legs?
An open tank in a petroleum company lab contains a layer of oil on top of a layer of water. The water height is 4 times the oil height h. The oil has a specific gravity of 0.82. If the gauge pressure at the bottom of the tank indicates 26. 3 cm of mercury, what is the oil height h'?
A mercury (sp. gr. = 13.6) manometer is used to measure water pressure in a pipe. Referring to Figure 2.5 (a), the value of y is 3.40 cm and the value of his 2.60 cm. Determine the pressure in the pipe.
A manometer is mounted on a city water-supply pipe to monitor water pressure, as shown in Figure P2.4.5. However, the manometer reading of 3 ft (Hg) may be incorrect. If the pressure in the pipe is measured independently and found to be 16.8 lb/in.2 (psi), determine the correct value of the reading
An open manometer, shown in Figure P2.4.6, is installed to measure pressure in a pipe carrying an ii (sp. gr. = 1.60). If the monometer liquid is carbon tetrachloride (sp. gr. = l. 60), determine the pipe pressure (in meters of water-column height).
In Figure P2.4.7, a single-reading mercury manometer is used to measure water pressure in the pipe. What is the pressure (in psi) if h1 = 6.9 in and h2 = 24.0 in.?
In Figure P2.4.7, determine the water pressure [in kilo-pascals (kPa)] in the pipe if h1 = 20.0 cm and h2 = 67.0 cm. Also determine the change in liquid height h1 for a 10 cm change in h2 if the diameter of the manometer tube is 0.5 cm and the diameter of the manometer fluid reservoir is 5 cm.
In Figure P2.4.9, water is flowing in pipe A and oil (sp. gr. = 0.82) is flowing in pipe B. If mercury is used as the manometer liquid, determine the pressure difference between A and Bin psi.
A vertical gate keeps water from flowing in a triangular irrigation channel. The channel has a 4-m top width and a 3-m depth. If the channel is full, what is the magnitude of the hydrostatic force on the triangular gate and its location?
In Figure P2.5.10, the wicket dam is 5 m high and 3 m wide and is pivoted at its center. Detem1ine the reaction force in the supporting member AB.
Determine the depth of the water (d) in Figure P2.5.11 that will cause the gate to open (lay down). The gate is rectangular and is 8 ft wide. Neglect the weight of the gate in your computations. At what depth will it close?
Neglecting the weight of the hinged gate, determine the depth h at which the gate will open in Figure P2.5.12.
The circular gate shown in Figure P2.5.13 is hinged at the horizontal diameter. If it is in equilibrium. what is the relationship between hA and hB as a function of Î³A , Î³B, and d?
A sliding gate 10 ft wide and 6 ft high is installed in a vertical plane and has a coefficient of friction against the guides of 0.2. The gate weighs 3 tons, and its upper edge is 27 ft below the water surface. Calculate the vertical force required to lift the gate.
A concrete dam with a triangular cross section (Figure P2.5.2) is built to hold 30 ft of water. Determine the hydrostatic force on a unit length of the dam and its location. Also, if the specific gravity of concrete is 2.67, what is the moment generated with respect to the toe of the dam, A? Is the
A 1-m-diameter circular (plane) gate is mounted into an inclined wall (45°). The center of the gate is located 1 m (vertically) below the water surface. Determine the magnitude of the hydrostatic force and its location with respect to the surface of the water along the incline.
A vertical plate, composed of a square and a triangle, is submerged so that its upper edge coincides with the water surface (Figure P2.5.4). What is the height to length ratio such that the pressure force on the square is equal to the pressure force on the triangle?Front view of vertically
The rectangular gate in Figure P2.5.5 is hinged at A and separates water in the reservoir from the tail water tunnel. If the uniformly thick gate has a dimension of 2 m Ã— 3 m and weighs 20 kN, what is the maximum height h for which the gate will stay closed?
A circular gate is installed on a vertical wall as shown in Figure P2.5.6. Determine the horizontal force? P necessary to hold the gate closed if the gate diameter is 6 ft and h = 7 f t. Neglect friction at the pivot.
Figure P2.5.7 shows a I 0-ft high (H), vertical, rectangular gate. The gate opens automatically when h increases to 4 ft. Determine the location of the horizontal axis of rotation 0-0'.
Calculate the magnitude and the location of the resultant pressure force on the annular gate shown in Figure P2.5.8.
Calculate the magnitude and the location of the resultant pressure force on the annular gate shown in Figure P2.5.8 if the round central hub is replaced by a square hub ( I m by I m).
A 10-m-long curved gate depicted in Figure P2.6.J is retaining a 6-m depth of water in a storage tank. Determine the magnitude and direction of the total hydrostatic force on the gate. Does the force pass through point A? Explain.
In Figure P2.6.10 a homogeneous cone plugs the 0.1-m-diameter orifice between reservoir A that contains water and reservoir B that contains oil (sp. gr. = 0.8). Determine the specific weight of the cone if it unplugs when h0 reaches l.5 m.
What would be the specific weight of the cone if reservoir B in Figure P2.6.10 contains air at a pressure of 8,500 N/m2 instead of oil?
The homogeneous cylinder (sp. gr. = 2.0) in Figure P2.6.12 is 1 m long and ˆš2 min diameter and blocks a l-m2 opening between reservoirs A and B (sp. gr. A = 0.8, sp. gr. 8 = 1.5). Determine the magnitude of the horizontal and vertical components of the hydrostatic force on the cylinder.
A hemispherical viewing pen in a marine museum (Figure P2.6.2) has a 1-m radius, and the top of the port is 3 meters below the surface of the water (h). Determine the magnitude, direction, and location of the total hydrostatic force on the viewing port. (Assume the saltwater has a sp. gr. = 1.03.)
An inverted hemispherical shell of diameter d as shown in Figure P2.6.3 is used to cover a tank filled with water at 20°C. Detuning the minimum weight the shell needs to be to hold itself in place if the diameter is 6 feet.
The corner plate of a barge hull is curved, with a radius of 1.75 m. The barge is leaking, and the depth of submergence (draft) is 4.75 mas depicted in Figure P2.6.4. The water on the inside is up to level A, producing hydrostatic pressure on the inside as well as the outside. Determine the
The tainter gate section shown in Figure P2.6.5 has a cylindrical surface with a 12-m radius; it is supported by a structural frame hinged at 0. The gate is 10 m long (in the direction perpendicular to the page). Determine the magnitude, direction, and location of the total hydrostatic force on the
Calculate the magnitude, direction, and location of the total hydrostatic pressure force (per unit length) on the gate shown in Figure P2.6.6.
A 4-ft-diameter cylindrical tank lays on its side with its central axis horizontal. A 1.5-ft diameter pipe extends vertically upward from the middle of the tank. Oil (sp. gr. = 0.9) fills the tank and pipe to a level of 8 ft above the top of the tank. What is the hydrostatic force on one end of the
Calculate the horizontal and vertical forces acting on the curved surface ABC in Figure P2.6.8.
Calculate the magnitude and location of the vertical and horizontal components of the hydrostatic force on the surface shown in Figure P2.6.9 (quadrant on top of the triangle, both with a unit width). The liquid is water, and the radius R = 4 ft.
A piece of irregularly shaped metal weighs 301 N. When the metal is completely submerged in water, it weighs 253 N. Determine the specific weight and the specific gravity of the metal.
A wooden block is 2 m long, l m wide, and 1 m deep. Is the floating block stable if the metacenter is at the same point as the center of gravity? Explain.
A subway tunnel is being constructed across the bottom of a harbor. The process involves tugboats that pull floating cylindrical sections (or tubes as they are often called) across the harbor and sink them in place, where they are welded to the adjacent section already on the harbor bottom. The
A 12-m-long, 4.8-m-wide, and 4.2-m-deep rectangular pontoon has a draft of 2.8 m in seawater (sp. gr. = 1.03). Assuming the load is uniformly distributed on the bottom of the pontoon to a depth of 3.4 m, and the maximum design angle of list is 15°, determine the distance that the center of gravity
The solid floating prism show in Figure P2.8.2 has two components. Determine Î³A and Î³B in terms of Î³ if Î³B = 1.5 ˆ™ Î³A.
A solid brass sphere of 30-cm diameter is used to hold a cylindrical buoy in place (Figure P2.8.3 l in seawater (sp. gr. = 1.03). The buoy (sp. gr. = 0.45) has a height of 2 m and is tied to the sphere at one end. What rise in tide, h, will be required to lift the sphere off the bottom?
Three people are in a boat with an anchor. If the anchor is thrown overboard, will the Jake level rise, fall, or stay the same theoretically? Explain.
A freshwater cylindrical anchor (h = 1.2 ft and D = 1. 5 ft) is made of concrete (sp. gr. = 2.7). What is the maximum tension in the anchor line before the anchor is lifted from the lake bottom if the anchor line· is at an angle of 60° with respect to the bottom?
In Figure P2.8.6, the spherical buoy of radius R opens the square gate AB when water rises to the half-buoy height. Determine R if the weight of the buoy and the gate are negligible.
The floating rod shown in Figure P2.8.7 weighs 150 lbs, and the water's surface is 7 ft above the binge. Calculate the angle Î¸ assuming a uniform weight and buoyancy distribution.
A rectangular barge is 14 m long, 6 m wide and 2 m deep. The center of gravity is 1.0 m from the bottom, and the barge draws l.5 m of seawater (sp.gr. = 1.03). Find the metacentric height and the righting moments for the following angles of heel (or list): 4 °, 8°, and 12 °.
Figure P2.8.9 shows a buoy that consists of a wooden pole 25 cm in diameter and 2 m long with a spherical weight at the bottom. The specific gravity of the wood is 0.62, and the specific gravity of the bottom weight is J .40. Determine(a) How much of the wooden pole is submerged in the water,(b)
A jet of water ex it~ a nozzle heading in the positive x-direction and strikes a flat plate at a 90° angle. The water then sprays through a 360° arc (y- and z-directions) exiting the plate. If the nozzle has a 20-cm diameter and the flow has a 3.44 m/sec velocity, what is the force exerted on the
At a firefighter's convention, a competition pits two contestants in mock combat. Each is armed with a fire hose and a shield. The object is to push the opponent backward a certain distance with the spray. A choice of shields is offered. One shield is a flat garbage can lid; the other is a
A 1-in.-diameter jet flowing in the negative x-direction hits a fixed blade and deflects the water through a 180° angle. If the force on the blade is 233 lbs, what is the velocity of the jet? (Assume the blade is frictionless.)
At the end of a 0.6-m-diameter pipe, the pressure is 270,000 Nm2. The pipe is connected to a 0.3-m-diameter nozzle. If the flow rate is 1.1 m3/sec in the positive x-direction, what is the total force on-the connection?
Water flows through a horizontal, 0.5-m-diameter pipe with a flow rate of 0. 9 m3/sec. It is ejected from the pipe through a 0.25-m-diameter nozzle. If the force that holds the nozzle in place is -B. 2 k N, determine the water pressure in the pipe just upstream of the nozzle.
Water flowing in a positive x-direction passes through a 90° elbow in a 6-inch-diameter pipeline and heads in a positive y-direction with a flow rate of 3.05 ft3/sec. Compute the magnitude and direction of the force exerted by the elbow. The pressure upstream of the elbow is 15.l psi; just
Determine the magnitude and direction of the reaction force at a 90° pipe bend that is passing a mass flow rate of 985 kg/sec. The diameter of the bend is 60 cm, and the pressure head is 10 m just upstream of the bend and 9.8 m downstream of the bend. (Assume that the water is flowing in a
Water flows through a reducing pipe bend and is deflected 30° in the horizontal plane. The velocity is 4 m/sec entering the bend (15-cm diameter) with a pressure of 250 kPa. The pressure leaving the bend is 130 kPa (7.5-cm diameter). Determine the anchoring force required to hold the bend in
A 30-cm diameter pipe conveys water at the rate of 106 L/sec. Dete1mine the contraction head loss if the diameter is suddenly reduced to 15 cm. Compare this with the head loss incurred when the 15-cm pipe suddenly expands to 30 cm.
A 34-m-high water tower supplies water to a residential area by means of a 20-cm-diameter 800-m-long commercial steel pipe. To increase the pressure head at the delivery point engineers are considering the replacement of 94 percent of the pipe length with a larger (30- cm-diameter) steel pipe
A pipe goes through a sudden contraction to half its diameter and then a sudden expansion back to its original size. Which loss is greater- the expansion loss or the contraction loss? Prove your answer.
In Problem 3.11.1, the head loss from the abrupt contraction and expansion were calculated to be 0.606 m and 1.03 m, respectively. With the same flow rate and geometry, determine the corresponding head losses if a 15° confusor and a 15° diffuser are used to reduce the head losses.
Valve manufacturers want to be able to supply the loss coefficients of their products to prospective buyers. They usually perform experiments to determine the coefficients. Determine the loss coefficient for a valve if water flows through the 8-cm valve at the rate of 0.04 m3 and produces a
A check valve (swing) and a globe valve are installed in series in an 8-in. pipe. Determine the flow rate if the pressure drop across the valves is 5.19 psi (lbs/in.2). Assume that the friction losses are negligible because of the short pipe length.
Water flows through a sudden contraction in a horizontal plane, passing from a 60-cm pipe to a 30-cm pipe. The pressure on the upstream side of the contraction is 285 kPa and on the down-stream side is 265 kPa Determine the flow rate.
Water flows through a 4 -cm, wrought iron, horizontal pipeline from point A to point B. The pipeline is 50 meters long and contains a fully open gate valve and two elbows (RID = 4). If the pressure at B (downstream) is 192 kPa and the flow rate is 0.006m3/s, what is the pressure at point A?
Water flows from a storage tank through a horizontal, 6-inch pipe (cast iron) and discharges water (20oC) into the atmosphere at the end. The pipe is 500 feet long, contains two I-ft-radius bench and a fully open gate valve, and the entrance is square edged. Calculate the flow rate if the depth of
A 75-m long cast-iron pipe, 15 cm in diameter, connects two tanks (open to the atmosphere that have a water (20°C) surface elevation difference of 5 m. The entrance of the pipe from the supply tank is square edged, and the pipe contains a 90° bend with a sharp, 15-cm radius. Determine the flow
A cylindrical tank 5 min diameter is filled with water to a 3-m depth. A very short horizontal pipe with a 20-cm diameter and a rotary value is used to drain the tank from the bottom. How long does it take to drain 50 percent of the tank?
Derive an expression for N pipes in parallel using the Manning equation.
Derive an expression for N pipes in parallel using the Hazen-Williams equation.
Redo Example 3.10 using the Manning equation, assuming that n = 0.013 for all the pipes. Example 3.10 Pipes AB and CF in Figure 3.20 have a diameter of 4 ft, possess a Darcy-Weisbach friction factor of 0.02 and carry a discharge of 120 cubic feet per second (cfs). The length of AB is 1.800 ft and
Redo Example 3.10 using the Hazen-Williams equation and assuming that CHW = 100 for all the pipes. Example 3.10 Pipes AB and CF in Figure 3.20 have a diameter of 4 ft, possess a Darcy-Weisbach friction factor of 0.02 and carry a discharge of 120 cubic feet per second (cfs). The length of AB is
Pipes AB and CF in Figure P3.12.5 have a diameter of 3 m and a Darcy-Weisbach friction factor of 0.02. The length of AB is 1000 m and that of CF is 900 m. The discharge in pipe AB is 60 m3/sec. Branch 1 is 1,000 m long and it has a diameter of 2 m and a friction factor of 0.018. Branch 2 has a
Can the method of equivalent pipes be used to find a single hypothetical pipe that is equivalent to the pipe system of Example 3.10? If your answer is yes, determine an equivalent pipe. If your answer is no, explain your answer. Example 3.10 Pipes AB and CF in Figure 3.20 have a diameter of 4 ft,
Can the method of equivalent pipes be used to find a single hypothetical pipe that is equivalent to the pipe system of Problem 3.12.5? If your answer is yes, determine an equivalent pipe. If your answer is no, explain your answer.
A commercial steel pipe, 1.5 m in diameter, carries 3.5 m3/sec of water at 20°C. Determine the friction factor and the flow regime (i.e., laminar-critical zone; turbulent- transitional zone; turbulent-smooth pipe; or turbulent- rough pipe).
Water at 20°C is transported through a 200-m-long wrought iron pipe with a head loss of 9.8 m. Determine the diameter of the pipe required to convey 10 L/sec.
A water main made of rough concrete loses 43 psi (lb/in.2) of pressure over a 1-mi horizontal length. Estimate the size of the pipe required to carry 16.5 cfs (ft3 /sec) of water at 68°F (20oC Assume minor losses are negligible.
The city water company wants to transport 1, 800 m3 of water per day to a plant from a reservoir 8 km away. The water surface elevation at the reservoir is 6 m above the entrance of the pipe, and the water surface in the holding tank is 1 m above the exit of the pipe. The pipe will be laid on a
Equation 3.19 defines the mean velocity for laminar flow using the Hagen-Poiseuille law. Equation 3.20 gives the Darcy-Weisbach equation applied to a horizontal uniform pipe. Derive Equation 3.20a. showing all steps in the process.Equation 3.19Equation 3.20 Equation 3.20a
Water flows through a 20-cm commercial steel pipe at 20°C. The flow rate is 80 liters per second, and pressure is constant throughout the length of the pipe. Determine the slope of the pipe. Assume losses are negligible.
An old water-supply pipeline contains a long segment that is horizontal and 30 cm in diameter. A leak along an inaccessible portion of the buried pipeline is highly likely. A pair of pressure located upstream of the leak indicate a pressure drop of 23,000 N/m2. Another pair of pressure gauges

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