Concept explainers
(a)
Find the change in the angular velocity of the turbine disk.
(a)
Answer to Problem 17.24P
The change in angular velocity of the turbine disk is
Explanation of Solution
Given information:
The mass of the turbine disk is
The centroidal radius of gyration of the turbine disk is
The angular velocity of the small blade is
The weight of the small blade is
The centroidal radius of the blade is
The angle the turbine disk rotates is
Position 1:
Find the mass of inertia about point O
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 30 kg for
Find the location of mass center
Position 1
The angular velocity at the position 1 is
Find the total kinetic energy
Substitute
Find the total potential energy
Here, the conditional center of gravity is
In this case, the center of gravity lies at the point O. so,
Substitute 0 for
Position 2
Find the total kinetic energy
Substitute
Find the total potential energy
Here, the conditional center of gravity is
In this case, the center of gravity lies at the point O. so,
Substitute
Substitute 30 kg for
Write the equation of conservation of energy as follows;
Substitute 18.04480 J for
Find the change in angular velocity
Substitute 59.75 rpm for
Therefore, the change in angular velocity of the turbine disk is
(b)
Find the change in the angular velocity of the turbine disk.
(b)
Answer to Problem 17.24P
The change in angular velocity of the turbine disk is
Explanation of Solution
Given information:
The mass of the turbine disk is
The centroidal radius of gyration of the turbine disk is
The angular velocity of the small blade is
The weight of the small blade is
The centroidal radius of the blade is
The angle the turbine disk rotates is
Position 1:
Find the mass of inertia about point O
Here, the acceleration due to gravity is g.
Consider the acceleration due to gravity is
Substitute 30 kg for
Find the location of mass center
Position 1
The angular velocity at the position 1 is
Find the total kinetic energy
Substitute
Find the total potential energy
Here, the conditional center of gravity is
In this case, the center of gravity lies at the point O. so,
Substitute 0 for
Position 3
Find the total kinetic energy
Substitute
Find the total potential energy
Here, the conditional center of gravity is
In this case, the center of gravity lies at the point O. so,
Substitute
Substitute 30 kg for
Write the equation of conservation of energy as follows;
Substitute 18.04480 J for
Find the change in angular velocity
Substitute 60.249 rpm for
Therefore, the change in angular velocity of the turbine disk is
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Chapter 17 Solutions
Connect 2 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
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