A Micro –Hydro turbine generator is accelerating uniformly from an angular velocity of 610 rpm to its operating angular velocity of 837 rpm.

Question

A Micro –Hydro turbine generator is accelerating uniformly from an angular velocity of 610 rpm to its operating angular velocity of 837 rpm. The radius of the turbine generator is 0.62 m and its rotational acceleration is 5.9 rad/s2 . What is the turbine’s angular displacement (in radians) after 3.2 s?

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Amity 3 years 2021-08-17T06:05:28+00:00 1 Answers 33 views 0

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    2021-08-17T06:06:55+00:00

    Answer:

    Angular displacement of the turbine is 234.62 radian

    Explanation:

    initial angular speed of the turbine is

    \omega_i = 2\pi f_1

    \omega_1 = 2\pi(\frac{610}{60})

    \omega_1 = 63.88 rad/s

    similarly final angular speed is given as

    \omega_f = 2\pi f_2

    \omega_2 = 2\pi(\frac{837}{60})

    \omega_2 = 87.65 rad/s

    angular acceleration of the turbine is given as

    \alpha = 5.9 rad/s^2

    now we have to find the angular displacement is given as

    \theta = \omega t + \frac{1}{2}\alpha t^2

    \theta = (63.88)(3.2) + (\frac{1}{2})(5.9)(3.2^2)

    \theta = 234.62 radian

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