Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 5, Problem 124P
A hydraulic turbine is used to generate power by using the water in a dam. The elevation difference between the free surfaces upstream and downstream of the dam is 130 m. The water is supplied to the turbine at a rate of 150 kg/s. If the shaft power output from the turbine is 155 kW, the efficiency of the turbine is
(a) 0.79
(b) 0.81
(c) 0.83
(d) 0.85
(e) 0.88
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The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed is increased by a gearbox that has an efficiency of 0.93. In turn, the gearbox output shaft drives an electric generator with an efficiency of 0.95. The cylindrical nacelle, which houses the gearbox, generator, and associated equipment, is of length L = 6 m and diameter D = 3 m. If the turbine produces P = 2.5 MW of electrical power, and the air and surroundings temperatures are T = 25 oC and Tsur = 20 oC, respectively, determine the minimum possible operating temperature inside the nacelle. The emissivity of the nacelle is 0.83, and the convective heat transfer coefficient is h = 35 W/m2 .K. The surface of the nacelle that is adjacent to the blade hub can be considered to be adiabatic, and solar irradiation may be neglected.
Use Fin or N number of fins to reduce the Ts of the nacelle less than 143 oC
The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed
is increased by a gearbox that has an efficiency of 0.93. In turn, the gearbox output shaft
drives an electric generator with an efficiency of 0.95. The cylindrical nacelle, which houses
the gearbox, generator, and associated equipment, is of length L = 6 m and diameter D = 3 m.
If the turbine produces P = 2.5 MW of electrical power, and the air and surroundings
temperatures are T = 25 °C and Tsur = 20 °C, respectively, determine the minimum possible
operating temperature inside the nacelle. The emissivity of the nacelle is 0.83, and the
convective heat transfer coefficient is h = 35 W/m² .K. The surface of the nacelle that is
adjacent to the blade hub can be considered to be adiabatic, and solar irradiation may be
neglected.
Please solve after adding fins and
the number of fins
Air
Tsur -20°C
T-25°C
Hub
h-35 W/m2.K
L-6m
D-3m
T₂,-0.83
Generator, Tigen -0.95
Gearbox,
-0.93
Nacelle
A dam with a hydraulic turbine–generator located 40 m below the water surface has a rate of 4600 kg/s flowing through the penstock. If the electric power generated is measured to be 1400 kW and the generator efficiency is 95%, determine: (a) the overall efficiency of the turbine–generator, (b) the mechanical efficiency of the turbine, (c) the shaft power supplied by the turbine to the generator.
Chapter 5 Solutions
Fluid Mechanics: Fundamentals and Applications
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