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The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy?
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The given figure shown the turning moment diagram of an engine. The me...
Calculation of Coefficient of Fluctuations of Energy
The coefficient of fluctuations of energy is a measure of the extent of fluctuation in the energy output of an engine. It is defined as the ratio of the difference between the maximum and minimum values of the energy output to the average value of the energy output.
Calculation of Average Torque
From the turning moment diagram, the average torque can be calculated as:
$$\text{Average Torque} = \frac{1}{2\pi}\int_0^{2\pi} T(\theta) \, d\theta$$
where T(θ) is the torque at a given angle θ.
Using the trapezoidal rule, we can approximate the integral as:
$$\text{Average Torque} \approx \frac{1}{2\pi}\left[\frac{T_0 + T_1}{2}(\theta_1 - \theta_0) + \frac{T_1 + T_2}{2}(\theta_2 - \theta_1) + \dots + \frac{T_{n-1} + T_n}{2}(\theta_n - \theta_{n-1})\right]$$
where T_0, T_1, T_2, ..., T_n are the torque values at equally spaced angles θ_0 = 0, θ_1, θ_2, ..., θ_n = 2π.
Using the values from the given diagram, we get:
$$\text{Average Torque} \approx \frac{1}{2\pi}\left[\frac{0 + 20}{2}(\pi/6) + \frac{20 + 40}{2}(\pi/3) + \frac{40 + 20}{2}(\pi/6)\right] \approx 18.38 \text{ Nm}$$
Calculation of Maximum and Minimum Torque
From the turning moment diagram, we can see that the maximum torque occurs at θ = π/3 and is equal to 40 Nm. The minimum torque occurs at θ = 0 and θ = 2π/3 and is equal to 0 Nm.
Calculation of Coefficient of Fluctuations of Energy
The coefficient of fluctuations of energy can now be calculated as:
$$\text{Coefficient of Fluctuations of Energy} = \frac{\text{Maximum Torque} - \text{Minimum Torque}}{\text{Average Torque}} = \frac{40 - 0}{18.38} \approx 2.17$$
Therefore, the coefficient of fluctuations of energy for the given engine is approximately 2.17.
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The given figure shown the turning moment diagram of an engine. The me...
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The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy?
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The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy?.
The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The given figure shown the turning moment diagram of an engine. The meppn speed of the prime mover is 2π rad/s and the mass moment of inertia is 0.1 kg-m², then what is the coefficient of fluctuations of energy?.
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