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A large hydroelectric power plant is under consideration. Its hydraulic head or water Level difference above and below the dam and its power requirement dictate its water turbine or runner must turn at from 137.00 rpm (14.347 rad/sec). The power required is 60 Hz. Then How many poles must a direct-connected alternator have?

f = (p * n) / 120

where f is the frequency in Hz, p is the number of poles, and n is the rotational speed in revolutions per minute (rpm).

Substituting the given values, we get:

60 = (p * 137) / 120

p = 120 * 60 / 137

p ≈ 52.7

Since the number of poles must be an integer, we round up to the nearest integer, which is 53. Therefore, the direct-connected alternator must have 53 poles to generate the required power at a frequency of 60 Hz.