Water to a residential area is transported at a rate of 1.5 m3/s via 70-cm-internal-diameter concrete pipes with a surface roughness of 3 mm and a total length of 1500 m. In order to reduce pumping power requirements, it is proposed to line the interior surfaces of the concrete pipe with 2-cm-thick petroleum-based lining that has a surface roughness thickness of 0.04 mm. There is a concern that the reduction of pipe diameter to 66 cm and the increase in average velocity may offset any gains. Taking ρ = 1000 kg/m3 and ν = 1 × 10−6 m2/s for water, determine the percent increase or decrease in the pumping power requirements due to pipe frictional losses as a result of lining the concrete pipes.
> A 0.80-m-diameter, 1.2-m-high garbage can is found in the morning tipped over due to high winds during the night. Assuming the average density of the garbage inside to be 150 kg/m3 and taking the air density to be 1.25 kg/m3, estimate the wind velocity d
> Bill gets a job delivering pizzas. The pizza company makes him mount a sign on the roof of his car. The frontal area of the sign is A = 0.612 ft2, and he estimates the drag coefficient to be CD = 0.94 at nearly all air speeds. Estimate how much additiona
> Reconsider Prob. 15–32. Using appropriate software, investigate the effect of car speed on the required power to overcome (a) rolling resistance, (b) the aerodynamic drag, and (c) their combined effect. Let the car speed vary from 0 to 150 km/h in increm
> During steady motion of a vehicle on a level road, the power delivered to the wheels is used to overcome aerodynamic drag and rolling resistance (the product of the rolling resistance coefficient and the weight of the vehicle), assuming the friction at t
> Reconsider Prob. 15–30. Using appropriate software, investigate the effect of wind speed on the torque applied on the pivot. Let the wind speed vary from 0 to 50 m/s in increments of 5 m/s. Tabulate and plot the results. Data from Prob
> A wind turbine with two or four hollow hemispherical cups connected to a pivot is commonly used to measure wind speed. Consider a wind turbine with four 8-cm-diameter cups with a center-to center distance of 40 cm, as shown in Fig. P15–
> Which bicyclist is more likely to go faster: one who keeps his head and his body in the most upright position or one who leans down and brings his body closer to his knees? Why?
> A 70-kg bicyclist is riding her 15-kg bicycle downhill on a road with a slope of 8° without pedaling or braking. The bicyclist has a frontal area of 0.45 m2 and a drag coefficient of 1.1 in the upright position, and a frontal area of 0.4 m2 and a drag co
> An adiabatic closed system is accelerated from 0 m/s to 30 m/s. Determine the specific energy change of this system, in kJ/kg.
> A submarine can be treated as an ellipsoid with a diameter of 5 m and a length of 25 m. Determine the power required for this submarine to cruise horizontally and steadily at 40 km/h in seawater whose density is 1025 kg/m3. Also determine the power requi
> At highway speeds, about half of the power generated by the car’s engine is used to overcome aerodynamic drag, and thus the fuel consumption is nearly proportional to the drag force on a level road. Determine the percentage increase in fuel consumption o
> Advertisement signs are commonly carried by taxicabs for additional income, but they also increase the fuel cost. Consider a sign that consists of a 0.30-m-high, 0.9-m-wide, and 0.9-m-long rectangular block mounted on top of a taxicab such that the sign
> Suzy likes to drive with a silly sun ball on her car antenna. The frontal area of the ball is A = 2.08 × 10−3 m2. As gas prices rise, her husband is concerned that she is wasting fuel because of the additional drag on the ball. He runs a quick test in th
> A circular sign has a diameter of 50 cm and is subjected to normal winds up to 150 km/h at 10°C and 100 kPa. Determine the drag force acting on the sign. Also determine the bending moment at the bottom of its pole whose height from the ground
> Reconsider Prob. 15–22E. Using appropriate software, investigate the effect of frontal area on the annual fuel consumption of the car. Let the frontal area vary from 10 to 30 ft2 in increments of 2 ft2. Tabulate and plot the results. Data from Prob. 15-
> To reduce the drag coefficient and thus to improve the fuel efficiency, the frontal area of a car is to be reduced. Determine the amount of fuel and money saved per year as a result of reducing the frontal area from 20 to 13 ft2. Assume the car is driven
> The drag coefficient of a car at the design conditions of 1 atm, 25°C, and 90 km/h is to be determined experimentally in a large wind tunnel in a full-scale test. The height and width of the car are 1.25 m and 1.65 m, respectively. If the horizontal forc
> During a high Reynolds number experiment, the total drag force acting on a spherical body of diameter D = 12 cm subjected to airflow at 1 atm and 5°C is measured to be 5.2 N. The pressure drag acting on the body is calculated by integrating the pressur
> What is lift? What causes it? Does wall shear contribute to the lift?
> On a hot summer day, a student turns his fan on when he leaves his room in the morning. When he returns in the evening, will the room be warmer or cooler than the neighboring rooms? Why? Assume all the doors and windows are kept closed.
> The resultant of the pressure and wall shear forces acting on a body is measured to be 430 N, making 30° with the direction of flow. Determine the drag and the lift forces acting on the body.
> A car is moving at a constant velocity of 110 km/h. Determine the upstream velocity to be used in fluid flow analysis if (a) the air is calm, (b) wind is blowing against the direction of motion of the car at 30 km/h, and (c) wind is blowing in the same d
> In general, how does the drag coefficient vary with the Reynolds number at (a) low and moderate Reynolds numbers and (b) at high Reynolds numbers (Re > 104)?
> Consider laminar flow over a flat plate. How does the local friction coefficient change with position? Answer: We are to discuss how the local skin friction coefficient changes with position along a flat plate in laminar flow. Analysis The local fric
> What is drafting? How does it affect the drag coefficient of the drafted body?
> What is flow separation? What causes it? What is the effect of flow separation on the drag coefficient?
> What is the effect of streamlining on (a) friction drag and (b) pressure drag? Does the total drag acting on a body necessarily decrease as a result of streamlining? Explain.
> What is the effect of surface roughness on the friction drag coefficient in laminar and turbulent flows?
> What is the difference between skin friction drag and pressure drag? Which is usually more significant for slender bodies such as airfoils?
> The cylindrical chimney of a factory has an external diameter of 1.1 m and is 20 m high. Determine the bending moment at the base of the chimney when winds at 110 km/h are blowing across it. Take the atmospheric conditions to be 20°C and 1 atm.
> For a cycle, is the net work necessarily zero? For what kinds of systems will this be the case?
> What is terminal velocity? How is it determined?
> What is drag? What causes it? Why do we usually try to minimize it?
> Water is to be withdrawn from a 7-m-high water reservoir by drilling a well-rounded 5-cm diameter hole with negligible loss near the bottom and attaching a horizontal 90° bend of negligible length. Taking the kinetic energy correction factor t
> Repeat Prob. 14–97 for hot-water flow of a district heating system at 100°C. Data from Prob. 14-97: A pipeline that transports oil at 40°C at a rate of 3 m3/s branches out into two parallel pipes made of commercia
> A pipeline that transports oil at 40°C at a rate of 3 m3/s branches out into two parallel pipes made of commercial steel that reconnect downstream. Pipe A is 500 m long and has a diameter of 30 cm, while pipe B is 800 m long and has a diameter
> Reconsider Prob. 14–95. Using appropriate software, investigate the effect of the second pipe diameter on the required pumping head to maintain the indicated flow rate. Let the diameter vary from 1 to 10 cm in increments of 1 cm. Tabula
> Water at 15°C is to be discharged from a reservoir at a rate of 18 L/s using two horizontal cast iron pipes connected in series and a pump between them. The first pipe is 20 m long and has a 6 cm diameter, while the second pipe is 35 m long an
> Shell-and-tube heat exchangers with hundreds of tubes housed in a shell are commonly used in practice for heat transfer between two fluids. Such a heat exchanger used in an active solar hot water system transfers heat from a water-antifreeze solution flo
> Repeat Prob. 14–92 except let the length of pipe A be three times that of pipe B. Compare this result to that of Prob. 14–92. Does the difference agree with your intuition? Explain. Data from Prob. 14-92: Two pipes of identical diameter and material ar
> Two pipes of identical diameter and material are connected in parallel. The length of pipe A is five times the length of pipe B. Assuming the flow is fully turbulent in both pipes and thus the friction factor is independent of the Reynolds number and dis
> What are the different mechanisms for transferring energy to or from a control volume?
> The velocity profile in fully developed laminar flow in a circular pipe, in m/s, is given by u(r) = 6(1 − 100r2), where r is the radial distance from the centerline of the pipe in m. Determine (a) the radius of the pipe, (b) the average velocity through
> A house built on a riverside is to be cooled in summer by utilizing the cool water of the river. A 20-m-long section of a circular stainless-steel duct of 20 cm diameter passes through the water. Air flows through the underwater section of the duct at 4
> How does surface roughness affect the pressure drop in a pipe if the flow is turbulent? What would your response be if the flow were laminar?
> The compressed air requirements of a manufacturing facility are met by a 120-hp compressor that draws in air from the outside through a 9-m-long, 22-cm-diameter duct made of thin galvanized iron sheets. The compressor takes in air at a rate of 0.27 m3/s
> In a geothermal district heating system, 10,000 kg/s of hot water must be delivered a distance of 10 km in a horizontal pipe. The minor losses are negligible, and the only significant energy loss arises from pipe friction. The friction factor is taken to
> In a laminar flow through a circular tube of radius of R, the velocity and temperature profiles at a cross section are given by u = u0(1 − r2/R2) and T(r) = A + Br2 − Cr4 where A, B, and C are positive constants. Obtain a relation for the bulk fluid temp
> Two pipes of identical length and material are connected in parallel. The diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to be the same in both cases and disregarding minor losses, determine the ratio of the flow rates i
> Water is transported by gravity through a 10-cm diameter 550-m-long plastic pipe with an elevation gradient of 0.01 (i.e., an elevation drop of 1 m per 100 m of pipe length). Taking ρ = 1000 kg/m3 and ν = 1 × 10−6 m2/s for water, determine the flow rate
> Repeat Prob. 14–82 for cast iron pipes of the same diameter. Data from Prob. 14-82: A geothermal district heating system involves the transport of geothermal water at 110°C from a geothermal well to a city at about the same elevation for a distance of 1
> A steel rod of 0.5 cm diameter and 10 m length is stretched 3 cm. Young’s modulus for this steel is 21 kN/cm2. How much work, in kJ, is required to stretch this rod?
> A geothermal district heating system involves the transport of geothermal water at 110°C from a geothermal well to a city at about the same elevation for a distance of 12 km at a rate of 1.5 m3/s in 60-cm-diameter stainless-steel pipes. The fluid pressur
> Repeat Prob. 14–80 assuming pipe A has a halfway closed gate valve (KL = 2.1) while pipe B has a fully open globe valve (KL = 10), and the other minor losses are negligible. Data from Prob. 14-80: A certain part of cast iron piping of
> A certain part of cast iron piping of a water distribution system involves a parallel section. Both parallel pipes have a diameter of 30 cm, and the flow is fully turbulent. One of the branches (pipe A) is 1500 m long while the other branch (pipe B) is 2
> Consider laminar flow in a circular pipe. Is the wall shear stress τw higher near the inlet of the pipe or near the exit? Why? What would your response be if the flow were turbulent?
> Water at 15°C is to be pumped from a reservoir (zA = 2 m) to another reservoir at a higher elevation (zB = 9 m) through two 25-m-long plastic pipes connected in parallel. The diameters of the two pipes are 3 cm and 5 cm. Water is to be pumped
> A vented tanker is to be filled with fuel oil with ρ = 920 kg/m3 and μ = 0.045 kg/m·s from an underground reservoir using a 25-m-long, 4-cm-diameter plastic hose with a slightly rounded entrance and two 90Â
> Two water reservoirs A and B are connected to each other through a 40-m-long, 2-cm-diameter cast iron pipe with a sharp-edged entrance. The pipe also involves a swing check valve and a fully open gate valve. The water level in both reservoirs is the same
> A water tank filled with solar-heated water at 40°C is to be used for showers in a field using gravity-driven flow. The system includes 35 m of 1.5-cm-diameter galvanized iron piping with four miter bends (90°) without vanes and a wide-open globe valve.
> Reconsider Prob. 14–74E. Using appropriate software, investigate the effect of the pipe diameter on the required electric power input to the pump. Let the pipe diameter vary from 1 to 10 in, in increments of 1 in. Tabulate and plot the results, and draw
> A farmer is to pump water at 70°F from a river to a water storage tank nearby using a 125-ft-long, 5-in-diameter plastic pipe with three flanged 90° smooth bends. The water velocity near the river surface is 6 ft/s, and the pipe inlet is placed in the ri
> As a spherical ammonia vapor bubble rises in liquid ammonia, its diameter changes from 1 cm to 3 cm. Calculate the amount of work produced by this bubble, in kJ, if the surface tension of ammonia is 0.02 N/m.
> A 4-m-high cylindrical tank having a cross-sectional area of AT = 1.5 m2 is filled with equal volumes of water and oil whose specific gravity is SG = 0.75. Now a 1-cm-diameter hole at the bottom of the tank is opened, and water starts to flow out. If the
> Gasoline (ρ = 680 kg/m3 and ν = 4.29 × 10−7 m2/s) is transported at a rate of 240 L/s for a distance of 2 km. The surface roughness of the piping is 0.03 mm. If the head loss due to pipe friction is not to exceed 10 m, determine the minimum diameter of t
> Reconsider Prob. 14–70. In order to drain the tank faster, a pump is installed near the tank exit as in Fig. P14–71. Determine how much pump power input is necessary to establish an average water velocity of 4 m/s when
> A 3-m-diameter tank is initially filled with water 2 m above the center of a sharp-edged 10-cm diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere through a 100-m-long pipe. The friction coefficie
> Consider the flow of air and water in pipes of the same diameter, at the same temperature, and at the same mean velocity. Which flow is more likely to be turbulent? Why?
> A 2.4-m-diameter tank is initially filled with water 4 m above the center of a sharp-edged 10-cm diameter orifice. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere. Neglecting the effect of the kinetic energy cor
> Water at 70°F flows by gravity from a large reservoir at a high elevation to a smaller one through a 60-ft-long, 2-in-diameter cast iron piping system that includes four standard flanged elbows, a well-rounded entrance, a sharp-edged exit, and a fully op
> The water needs of a small farm are to be met by pumping water from a well that can supply water continuously at a rate of 5 L/s. The water level in the well is 20 m below the ground level, and water is to be pumped to a large tank on a hill, which is 58
> A semi-spherical tank of radius R is completely filled with water. Now a hole of cross-sectional area Ah and discharge coefficient Cd at the bottom of the tank is fully opened and water starts to flow out. Develop an expression for the time needed to emp
> Water at 15°C is drained from a large reservoir using two horizontal plastic pipes connected in series. The first pipe is 13 m long and has a 10-cm diameter, while the second pipe is 35 m long and has a 5-cm diameter. The water level in the re
> A damaged 1200-kg car is being towed by a truck. Neglecting the friction, air drag, and rolling resistance, determine the extra power required (a) for constant velocity on a level road, (b) for constant velocity of 50 km/h on a 30° (from horizontal) uphi
> A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in parallel. How would you compare the (a) flow rates and (b) pressure drops in these two pipes?
> A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in series. How would you compare the (a) flow rates and (b) pressure drops in these two pipes?
> Consider two identical 2-m-high open tanks filled with water on top of a 1-m-high table. The discharge valve of one of the tanks is connected to a hose whose other end is left open on the ground while the other tank does not have a hose connected to its
> A person filling a bucket with water using a garden hose suddenly remembers that attaching a nozzle to the hose increases the discharge velocity of water and wonders if this increased velocity would decrease the filling time of the bucket. What would hap
> For a piping system, define the system curve, the characteristic curve, and the operating point on a head versus flow rate chart.
> Which fluid at room temperature requires a larger pump to flow at a specified velocity in a given pipe: water or engine oil? Why?
> Water is pumped from a large lower reservoir to a higher reservoir. Someone claims that if the head loss is negligible, the required pump head is equal to the elevation difference between the free surfaces of the two reservoirs. Do you agree?
> A piping system equipped with a pump is operating steadily. Explain how the operating point (the flow rate and the head loss) is established.
> Water is to be withdrawn from an 8-m-high water reservoir by drilling a 2.2-cm-diameter hole at the bottom surface. Disregarding the effect of the kinetic energy correction factor, determine the flow rate of water through the hole if (a) the entrance of
> Repeat Prob. 14–55 for a slightly rounded entrance (KL = 0.12). Data from Prob. 14-55: Consider flow from a water reservoir through a circular hole of diameter D at the side wall at a vertical distance H from the free surface. The flow
> The engine of a 1500-kg automobile has a power rating of 75 kW. Determine the time required to accelerate this car from rest to a speed of 100 km/h at full power on a level road. Is your answer realistic?
> Consider flow from a water reservoir through a circular hole of diameter D at the side wall at a vertical distance H from the free surface. The flow rate through an actual hole with a sharp-edged entrance (KL = 0.5) is considerably less than the flow rat
> A horizontal pipe has an abrupt expansion from D1 = 5 cm to D2 = 10 cm. The water velocity in the smaller section is 8 m/s and the flow is turbulent. The pressure in the smaller section is P1 = 410 kPa. Taking the kinetic energy correction factor to b
> During a retrofitting project of a fluid flow system to reduce the pumping power, it is proposed to install vanes into the miter elbows or to replace the sharp turns in 90° miter elbows by smooth curved bends. Which approach will result in a greater redu
> A piping system involves sharp turns, and thus large minor head losses. One way of reducing the head loss is to replace the sharp turns with circular elbows. What is another way?
> Which has a greater minor loss coefficient during pipe flow: gradual expansion or gradual contraction? Why?
> The effect of rounding of a pipe exit on the loss coefficient is (a) negligible, (b) somewhat significant, or (c) very significant.
> Show that the Reynolds number for flow in a circular pipe of diameter D can be expressed as Re = 4m/(πDμ).
> Define equivalent length for minor loss in pipe flow. How is it related to the minor loss coefficient?
> What is minor loss in pipe flow? How is the minor loss coefficient KL defined?
> Consider the fully developed flow of glycerin at 40°C through a 70-m-long, 4-cm-diameter, horizontal, circular pipe. If the flow velocity at the centerline is measured to be 6 m/s, determine the velocity profile and the pressure difference acr
> A ski lift has a one-way length of 1 km and a vertical rise of 200 m. The chairs are spaced 20 m apart, and each chair can seat three people. The lift is operating at a steady speed of 10 km/h. Neglecting friction and air drag and assuming that the avera
> Liquid ammonia at −20°C is flowing through a 20-m-long section of a 5-mm-diameter copper tube at a rate of 0.09 kg/s. Determine the pressure drop, the head loss, and the pumping power required to overcome the frictional losses in the tube.
> Reconsider Prob. 14–44. Using appropriate software, investigate the effect of the pipe diameter on the pressure drop for the same constant flow rate. Let the pipe diameter vary from 1 to 10 cm in increments of 1 cm. Tabulate and plot the results, and dra
> Glycerin at 40°C with ρ = 1252 kg/m3 and μ = 0.27 kg/m·s is flowing through a 6-cm-diameter horizontal smooth pipe with an average velocity of 3.5 m/s. Determine the pressure drop per 10 m of the pipe.
> In an air heating system, heated air at 40°C and 105 kPa absolute is distributed through a 0.2 m × 0.3 m rectangular duct made of commercial steel at a rate of 0.5 m3/s. Determine the pressure drop and head loss through a 40-m-long section of the duct.
