Concept explainers
The swirl angles
Whether the turbine have forward or swirl flow.
The power output in
The net head in
Answer to Problem 86EP
The swirl angles
The turbine will have a forward swirl.
The power output is
The net head is
Explanation of Solution
Given information:
The gross head is
Write the expression for the angular velocity of turbine.
Here, the speed of the runner is
Write the expression for the normal component of velocity at the inlet.
Here, the volume flow rate of water is
Write the expression for the tangential velocity component at inlet.
Here, the radius at the inlet is
Write the expression for the angle for tangential velocity component at inlet.
Write the expression for the normal component of velocity at the outlet.
Write the expression for the tangential velocity component at outlet.
Here, the radius at the outlet is
Here, the volume flow rate of water is
Write the expression for angle of the tangential velocity component at outlet.
Write the expression for the shaft output power.
Here, the density of water is
Write the expression for the net head.
Calculation:
Substitute
Substitute
Substitute
Substitute
Therefore, the runner leading angle at the inlet is
Substitute
Substitute
Substitute
Therefore, the runner leading angle at the outlet is
Refer to Table A-3E, “Properties of saturated water” to obtain the value of density
Substitute
Therefore, the power output is
Substitute
Therefore, the net head is
Conclusion:
Therefore, the swirl angles
The turbine will have a forward swirl.
The power output is
Want to see more full solutions like this?
Chapter 14 Solutions
FLUID MECHANICS:FUND.+APPL.(LL)>CUSTOM<
- A Francis radial-flow hydroturbine is being designed with the following dimensions: r2 = 2.00 m, r1 = 1.42 m, b2 = 0.731 m, and b1 = 2.20 m. The runner rotates at n. = 180 rpm. The wicket gates turn the flow by angle ?2 = 30° from radial at the runner inlet, and the flow at the runner outlet is at angle ?1 = 10° from radial. The volume flow rate at design conditions is 340 m3 /s, and the gross head provided by the dam is Hgross = 90.0 m. For the preliminary design, irreversible losses are neglected. Calculate the turbine specific speed of the turbine. Provide answers in both dimensionless form and in customary U.S. units. Is it in the normal range for a Francis turbine? If not, what type of turbine would be more appropriate?arrow_forwardA Francis radial-flow hydroturbine is being designed with the following dimensions: r2 = 2.00 m, r1 = 1.42 m, b2 = 0.731 m, and b1 = 2.20 m. The runner rotates at n. = 180 rpm. The wicket gates turn the flow by angle ?2 = 30° from radial at the runner inlet, and the flow at the runner outlet is at angle ?1 = 10° from radial. The volume flow rate at design conditions is 340 m3 /s, and the gross head provided by the dam is Hgross = 90.0 m. For the preliminary design, irreversible losses are neglected. Calculate the inlet and outlet runner blade angles ?2 and ?1, respectively, and predict the power output (MW) and required net head (m). Is the design feasible?arrow_forwardA Kaplan turbine has the following specifications: H =25 ft., N=400 rpm; power = 650 hp. If the efficiency of the unit is 90%, estimate (a) the flow rate, (b) approxi-mate diameter of the runner, (c) turbine setting to avoid cavitation if the location is at sea level, and (d) turbine setting to avoid cavitation if the location of the unitis at an elevation of 5000 ft. The local temperature is 60°F.Ans: (a) Q=254 cfs; (c) Hs=5.8 ft.; (d) 0.12 ft.arrow_forward
- An electric utility decides to add 50 MW of wind generation to its system. If the individual units are to be rated at 2 MW in a 13-m/s wind at standard conditions and have efficiencies Cp = 0.32, ηm = 0.94, and ηg = 0.96, what is the required swept area of each rotor?arrow_forwardWater of density ? =998.2kg/m3 flows through a fireman’s nozzle—a converging section of pipe that accelerates the flow. The inlet diameter is d1 = 0.100 m, and the outlet diameter is d2 = 0.050 m. The average velocity, momentum flux correction factor, and gage pressure are known at the inlet (1) and outlet (2). (a) Write an expression for the horizontal force Fx of the fluid on the walls of the nozzle in terms of the given variables. (b) Verify your expression by plugging in the following values: ?1 = 1.03, ?2 = 1.02, V1 = 3 m/s, P1,gage = 137,000 Pa, and P2,gage = 0 Pa.arrow_forwardAt a hydraulic plant the propeller type turbine are rated at 48,000 HP at 82 rpm under a 14 meters head, the diameter is 7 meters, for a geometrical similar turbine to develop 36,000 HP under a 11 meters head. After resolving the percentage change in probable flow, determine the following: (A) What diameter, in meter, of the impeller to be used? (B) What is the speed, in RPM, should be used?arrow_forward
- 1) Interpret solar power in the context of environmental impact.2. What is the rigid dichotomy between windmill and diesel-driven pumps?3. For a normal windmill-driven pump at 3 m/s wind speed, the yield at a 10 m Head is typically 0.12 liters/s per m2 of rotor area, value windmills in the context of yield.arrow_forwardIn a certain hydraulic turbomachine, the following data apply:Inlet blade velocity is 20 m/s. Vu1=21 m/s; Vr1=10 m/s.At the exit, V2 is purely axial and has a value of 14 m/s, and blade speed is9 m/s. Is this power absorbing or power producing? Find E and the changes instatic and stagnation pressures. Would this machine be classified as a purelyradial, purely axial, or mixed flow type?Ans: E=420 J/kg; Δpstag=420 kPa; Δpstat=247.4 kPaarrow_forwardA 1:10 model of a Francis turbine developed 0.5 kW under a head of 2.5 m at 480 rpm. The physical data are r1=1.5m, r2 = 0.4m, α1=15°, β2=135°. Find the speed of the prototype at a head of 20m.arrow_forward
- Two pumps (Pump A and B) have performance curves which can be approximated by the following equations: H_A = 340 - (1.2(Q^2)), in feet H_B = 360 - (2.5(Q^2)), in feet where Q is in ft^3/s. If pumps A and B were to operate in parallel as depicted in the figure below, at what head (in ft.) should either pump be operated?arrow_forwardA certain centrifugal pump was tested and its performance curves can be approximated as follows: H = 340 - 1.2(Q2), in feet BP = (0.0521Q3) + (1.25Q2) + (11.042Q) + 134.5, in horsepower where Q is in ft3/s. If two of this pump is connected in series to deliver water to a system whose head requirement is 615 ft, what will be the operating discharge rate in ft3/s of either pumps? Assuming the head is equally divided between the two pumps, what is the efficiency of either pumps (in %)? Take the specific weight of water to be 62.4 lbf/ft3.arrow_forwardLook up the word affinity in a dictionary. Why do you suppose some engineers refer to the turbomachinery scaling laws as affinity laws?arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY