A 3-m-high tank filled with water has a discharge valve near the bottom and another near the top. (a) If these two valves are opened, will there be any difference between the discharge velocities of the two water streams? (b) If a hose whose discharge end is left open on the ground is first connected to the lower valve and then to the higher valve, will there be any difference between the discharge rates of water for the two cases? Disregard any frictional effects.
> Does it take more, equal, or less power for a helicopter to hover at the top of a high mountain than it does at sea level? Explain.
> Describe in terms of momentum and airflow how a helicopter is able to hover.
> A rocket in space (no friction or resistance to motion) can expel gases relative to itself at some high velocity V. Is V the upper limit to the rocket’s ultimate velocity?
> Two firefighters are fighting a fire with identical water hoses and nozzles, except that one is holding the hose straight so that the water leaves the nozzle in the same direction it comes, while the other holds it backward so that the water makes a U-tu
> Express Newton’s second law of motion for rotating bodies. What can you say about the angular velocity and angular momentum of a rotating nonrigid body of constant mass if the net torque acting on it is zero?
> What is the hydraulic grade line? How does it differ from the energy grade line? Under what conditions do both lines coincide with the free surface of a liquid?
> The power generated by a wind turbine is proportional to the cube of the wind velocity. Inspired by the acceleration of a fluid in a nozzle, someone proposes to install a reducer casing to capture the wind energy from a larger area and accelerate it befo
> In a certain application, a siphon must go over a high wall. Can water or oil with a specific gravity of 0.8 go over a higher wall? Why?
> What is total energy? Identify the different forms of energy that constitute the total energy.
> A pump-storage plant uses a turbine to generate hydropower during the day, letting water from the upper reservoir flow through the turbine into the lower reservoir as sketched. The plant then pumps water back up to the upper reservoir during the night. I
> A wind tunnel draws atmospheric air at 20°C and 101.3 kPa with a large fan located near the exit of the tunnel. If the air velocity in the tunnel is 80 m/s, determine the pressure in the tunnel.
> An oil pump is drawing 18 kW of electric power while pumping oil with ρ = 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 2
> Reconsider Prob. 12–72. In order to drain the tank faster, a pump is installed near the tank exit. Determine the pump head input necessary to establish an average water velocity of 6.5 m/s when the tank is full. Data from Prob. 12-72:
> Reconsider Prob. 12–72. Using appropriate software, investigate the effect of the tank height on the initial discharge velocity of water from the completely filled tank. Let the tank height vary from 2 to 15 m in increments of 1 m, and
> A 3-m-high large tank is initially filled with water. The tank water surface is open to the atmosphere, and a sharp-edged 10-cm-diameter orifice at the bottom drains to the atmosphere through a horizontal 80-m-long pipe. If the total irreversible head lo
> Air flows through a pipe at a rate of 120 L/s. The pipe consists of two sections of diameters 22 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Negle
> Water flows at a rate of 0.011 m3/s in a horizontal pipe whose diameter increases from 6 to 11 cm by an enlargement section. If the head loss across the enlargement section is 0.65 m and the kinetic energy correction factor at both the inlet and the outl
> How is the location of the hydraulic grade line determined for open-channel flow? How is it determined at the outlet of a pipe discharging to the atmosphere?
> Water is flowing through a Venturi meter whose diameter is 7 cm at the entrance part and 4 cm at the throat. The pressure is measured to be 380 kPa at the entrance and 200 kPa at the throat. Neglecting frictional effects, determine the flow rate of water
> What is an adiabatic process? What is an adiabatic system?
> A very large tank contains air at 102 kPa at a location where the atmospheric air is at 100 kPa and 20°C. Now a 2-cm-diameter tap is opened. Determine the maximum flow rate of air through the hole. What would your response be if air is dischar
> A pressurized 2-m-diameter tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level initially is 3 m above the outlet. The tank air pressure above the water level is maintained at 450 kPa absolu
> The water level in a tank is 70 ft above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank is at sea level, and the water surface is open to the atmosphere. In the line leadi
> A fireboat is to fight fires at coastal areas by drawing seawater with a density of 1030 kg/m3 through a 10-cm diameter pipe at a rate of 0.04 m3/s and discharging it through a hose nozzle with an exit diameter of 5 cm. The total irreversible head loss o
> The demand for electric power is usually much higher during the day than it is at night, and utility companies often sell power at night at much lower prices to encourage consumers to use the available power generation capacity and to avoid building new,
> The velocity profile for turbulent flow in a circular pipe is approximated as u(r) = umax(1 − r/R)1/n, where n = 9. Determine the kinetic energy correction factor for this flow.
> Reconsider Prob. 12–61. Determine the flow rate of water and the pressure difference across the pump if the irreversible head loss of the piping system is 4 m. Data from Prob. 12-61: Underground water is to be pumped by a 78-percent ef
> Underground water is to be pumped by a 78-percent efficient 5-kW submerged pump to a pool whose free surface is 30 m above the underground water level. The diameter of the pipe is 7 cm on the intake side and 5 cm on the discharge side. Determine (a) the
> Water in a partially filled large tank is to be supplied to the rooftop, which is 8 m above the water level in the tank, through a 2.5-cm-internal-diameter pipe by maintaining a constant air pressure of 300 kPa (gage) in the tank. If the head loss in the
> Define pressure head, velocity head, and elevation head for a fluid stream and express them for a fluid stream whose pressure is P, velocity is V, and elevation is z.
> In what forms can energy cross the boundaries of a closed system?
> Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 23 kW of useful mechanical power to the water. The free surface of the upper reservoir is 57 m higher than the surface of the lower reservoir. If the flow rate of water
> A 78-percent-efficient 12-hp pump is pumping water from a lake to a nearby pool at a rate of 1.2 ft3/s through a constant-diameter pipe. The free surface of the pool is 32 ft above that of the lake. Determine the irreversible head loss of the piping syst
> Water enters a hydraulic turbine through a 30-cm-diameter pipe at a rate of 0.6 m3/s and exits through a 25-cm-diameter pipe. The pressure drop in the turbine is measured by a mercury manometer to be 1.2 m. For a combined turbine–genera
> A large 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. If the total irreversible head loss in the system is 0.2
> The water level in a tank is 34 ft above the ground. A hose is connected to the bottom of the tank at the ground level, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, but the pressure over the water surface is u
> Water flows at a rate of 20 L/s through a horizontal pipe whose diameter is constant at 3 cm. The pressure drop across a valve in the pipe is measured to be 2 kPa, as shown in Fig. P12–54. Determine the irreversible head loss of the val
> A fan is to be selected to ventilate a bathroom whose dimensions are 2 m × 3 m × 3 m. The air velocity is not to exceed 7 m/s to minimize vibration and noise. The combined efficiency of the fan–motor unit to be
> Reconsider Prob. 12–51E. Determine the flow rate of water if the irreversible head loss of the piping system between the free surfaces of the inlet and the outlet is 36 ft. Data from Prob. 12-51: In a hydroelectric power plant, water flows from an eleva
> In a hydroelectric power plant, water flows from an elevation of 400 ft to a turbine, where electric power is generated. For an overall turbine generator efficiency of 85 percent, determine the minimum flow rate required to generate 100 kW of electricity
> A hydraulic turbine has 50 m of head available at a flow rate of 1.30 m3/s, and its overall turbine–generator efficiency is 78 percent. Determine the electric power output of this turbine.
> What is the caloric theory? When and why was it abandoned?
> What is stagnation pressure? Explain how it can be measured.
> The water level in a tank is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank is at sea level, and the water surface is open to the atmosphere. In the line leadin
> Water flows at a rate of 0.040 m3/s in a horizontal pipe whose diameter is reduced from 15 cm to 8 cm by a reducer. If the pressure at the centerline is measured to be 480 kPa and 440 kPa before and after the reducer, respectively, determine the irrevers
> A 15-hp (shaft) pump is used to raise water to a 45-m higher elevation. If the mechanical efficiency of the pump is 82 percent, determine the maximum volume flow rate of the water.
> Reconsider Prob. 12–45. Using appropriate software, investigate the effect of irreversible head loss on the mechanical efficiency of the pump. Let the head loss vary from 0 to 15 m in increments of 1 m. Plot the results, and discuss them. Data from Prob
> Water is being pumped from a large lake to a reservoir 25 m above at a rate of 25 L/s by a 10-kW (shaft) pump. If the irreversible head loss of the piping system is 5 m, determine the mechanical efficiency of the pump.
> A person is filling a knee-high bucket with water using a garden hose and holding it such that water discharges from the hose at the level of his waist. Someone suggests that the bucket will fill faster if the hose is lowered such that water discharges f
> The water level in a tank is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The water stream from the nozzle is observed to rise 25 m above the ground. Explain what may
> What is the kinetic energy correction factor? Is it significant?
> At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 60-m-diameter blades at that location. Take the air density to be 1.25 kg/m3.
> Consider the steady adiabatic flow of an incompressible fluid. If the temperature of the fluid remains constant during flow, is it accurate to say that the frictional effects are negligible?
> What is streamwise acceleration? How does it differ from normal acceleration? Can a fluid particle accelerate in steady flow?
> Consider the steady adiabatic flow of an incompressible fluid. Can the temperature of the fluid decrease during flow? Explain.
> What is useful pump head? How is it related to the power input to the pump?
> What is irreversible head loss? How is it related to the mechanical energy loss?
> Water enters a tank of diameter DT steadily at a mass flow rate of min.in. An orifice at the bottom with diameter Do allows water to escape. The orifice has a rounded entrance, so the frictional losses are negligible. If the tank is initially empty, (a)
> In cold climates, water pipes may freeze and burst if proper precautions are not taken. In such an occurrence, the exposed part of a pipe on the ground ruptures, and water shoots up to 55 m. Estimate the gage pressure of water in the pipe. State your ass
> The air velocity in a duct is measured by a Pitotstatic probe connected to a differential pressure gage. If the air is at 13.4 psia absolute and 70°F and the reading of the differential pressure gage is 0.15 psi, determine the air velocity.
> The water level in a tank is 20 m above the ground. A hose is connected to the bottom of the tank, and the nozzle at the end of the hose is pointed straight up. The tank cover is airtight, and the air pressure above the water surface is 2 atm gage. The s
> Air is flowing through a venturi meter whose diameter is 2.6 in at the entrance part (location 1) and 1.8 in at the throat (location 2). The gage pressure is measured to be 12.2 psia at the entrance and 11.8 psia at the throat. Neglecting frictional eff
> Consider a river flowing toward a lake at an average velocity of 3 m/s at a rate of 500 m3/s at a location 90 m above the lake surface. Determine the total mechanical energy of the river water per unit mass and the power generation potential of the entir
> Reconsider Prob. 12–30. Using appropriate software, investigate the effect of water height in the tank on the discharge velocity. Let the water height vary from 0 to 5 m in increments of 0.5 m. Tabulate and plot the results. Data from
> A pressurized tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level is 2.5 m above the outlet. The tank air pressure above the water level is 250 kPa (absolute) while the atmospheric pressure
> Define static, dynamic, and hydrostatic pressure. Under what conditions is their sum constant for a flow stream?
> The water pressure in the mains of a city at a particular location is 270 kPa gage. Determine if this main can serve water to neighborhoods that are 25 m above this location.
> Water at 20°C is siphoned from a reservoir as shown in Fig. P12–28. For d = 8 cm and D = 16 cm, determine (a) the minimum flow rate that can be achieved without cavitation occurring in the piping system and (b) the maximum e
> Air at 105 kPa and 37°C flows upward through a 6-cm diameter inclined duct at a rate of 65 L/s. The duct diameter is then reduced to 4 cm through a reducer. The pressure change across the reducer is measured by a water manometer. The elevation
> Reconsider Prob. 12–25. Using appropriate software, investigate the effect of the discharge pipe diameter on the time required to empty the pool completely. Let the diameter vary from 1 to 10 cm in increments of 1 cm. Tabulate and plot the results. Data
> Reconsider Prob. 12–24. Determine how long it will take to empty the swimming pool completely. Data from Prob. 12-24: The water in an 8-m-diameter, 3-m-high above-ground swimming pool is to be emptied by unplugging a 3-cm-diameter, 25-m-long horizontal
> The water in an 8-m-diameter, 3-m-high above-ground swimming pool is to be emptied by unplugging a 3-cm-diameter, 25-m-long horizontal pipe attached to the bottom of the pool. Determine the maximum discharge rate of water through the pipe. Also, explain
> While traveling on a dirt road, the bottom of a car hits a sharp rock and a small hole develops at the bottom of its gas tank. If the height of the gasoline in the tank is 30 cm, determine the initial velocity of the gasoline at the hole. Discuss how the
> A water jet that leaves a nozzle at 60 m/s at a flow rate of 120 kg/s is to be used to generate power by striking the buckets located on the perimeter of a wheel. Determine the power generation potential of this water jet.
> An airplane is flying at an altitude of 10,500 m. Determine the gage pressure at the stagnation point on the nose of the plane if the speed of the plane is 450 km/h. How would you solve this problem if the speed were 1050 km/h? Explain.
> Water flows through a horizontal pipe at a rate of 2.4 gal/s. The pipe consists of two sections of diameters 4 in and 2 in with a smooth reducing section. The pressure difference between the two pipe sections is measured by a mercury manometer. Neglectin
> A siphon pumps water from a large reservoir to a lower tank that is initially empty. The tank also has a rounded orifice 20 ft below the reservoir surface where the water leaves the tank. Both the siphon and the orifice diameters are 2 in. Ignoring frict
> What are the three major assumptions used in the derivation of the Bernoulli equation?
> The diameter of a cylindrical water tank is Do and its height is H. The tank is filled with water, which is open to the atmosphere. An orifice of diameter D with a smooth entrance (i.e., negligible losses) is open at the bottom. Develop a relation for th
> A piezometer and a Pitot tube are tapped into a 4-cm diameter horizontal water pipe, and the heights of the water columns are measured to be 26 cm in the piezometer and 35 cm in the Pitot tube (both measured from the top surface of the pipe). Determine
> The air velocity in the duct of a heating system is to be measured by a Pitot-static probe inserted into the duct parallel to the flow. If the differential height between the water columns connected to the two outlets of the probe is 3.2 cm, determine (a
> A Pitot-static probe is used to measure the speed of an aircraft flying at 3000 m. If the differential pressure reading is 3 kPa, determine the speed of the aircraft.
> In a hydroelectric power plant, water enters the turbine nozzles at 800 kPa absolute with a low velocity. If the nozzle outlets are exposed to atmospheric pressure of 100 kPa, determine the maximum velocity to which water can be accelerated by the nozzl
> A student siphons water over an 8.5-m-high wall at sea level. She then climbs to the summit of Mount Shasta (elevation 4390 m, Patm = 58.5 kPa) and attempts the same experiment. Comment on her prospects for success.
> Determine the specific potential energy, in kJ/kg, of an object 50 m above a datum in a location where g = 9.8 m/s2.
> Explain how and why a siphon works. Someone proposes siphoning cold water over a 7-m-high wall. Is this feasible? Explain.
> The water level of a tank on a building roof is 20 m above the ground. A hose leads from the tank bottom to the ground. The end of the hose has a nozzle, which is pointed straight up. What is the maximum height to which the water could rise? What factors
> The velocity of a fluid flowing in a pipe is to be measured by two different Pitot-type mercury manometers shown in Fig. P12–11C. Would you expect both manometers to predict the same velocity for flowing water? If not, which would be mo
> A glass manometer with oil as the working fluid is connected to an air duct as shown in Fig. P12–10C. Will the oil levels in the manometer be as in Fig. P12–10Ca or b? Explain. What would your response be if the flow d
> Express the Bernoulli equation in three different ways using (a) energies, (b) pressures, and (c) heads.
> A cylindrical tank is fully filled with water (Fig. P11–9). In order to increase the flow from the tank, an additional pressure is applied to the water surface by a compressor. For P0 = 0, P0 = 5 bar, and P0 = 10 bar, calculate the hydr
> Consider a 200-ft-high, 1200-ft-wide dam filled to capacity. Determine (a) the hydrostatic force on the dam and (b) the force per unit area of the dam near the top and near the bottom.
> Consider a circular surface subjected to hydrostatic forces by a constant density liquid. If the magnitudes of the horizontal and vertical components of the resultant hydrostatic force are determined, explain how you would find the line of action of this
> Consider a submerged curved surface. Explain how you would determine the vertical component of the hydrostatic force acting on this surface.
> The volume of a rock is to be determined without using any volume measurement devices. Explain how you would do this with a waterproof spring scale.
> Calculate the total potential energy, in Btu, of an object that is 20 ft below a datum level at a location where g = 31.7 ft/s2 and which has a mass of 100 lbm.
> Repeat Prob. 11–49 for a water height of 0.8 m above the hinge at B. Data from Prob. 11-49: The 280-kg, 6-m-wide rectangular gate shown in Fig. P11–49 is hinged at B and leans against the floor at A, making an angle o
> Consider a submerged curved surface. Explain how you would determine the horizontal component of the hydrostatic force acting on this surface.
> The 280-kg, 6-m-wide rectangular gate shown in Fig. P11–49 is hinged at B and leans against the floor at A, making an angle of 45° with the horizontal. The gate is to be opened from its lower edge by applying a normal force a
> A raft is made using a number of logs 25 cm in diameter and 2 m long, as shown in the figure. It is desired that a maximum 90 percent volume of each log will be submerged when carrying two boys weighing 400 N each. Determine the minimum number of logs th
