To determine the rotational speed of the propeller, we need to find the tangential velocity of the propeller tip.
Given:
Diameter of the propeller, d = 2.5m
Mach number, M = 0.8
Speed of sound, a = 340.26 m/s
The tangential velocity of the propeller tip, V, can be calculated using the formula:
V = M * a
Substituting the values, we get:
V = 0.8 * 340.26
V = 272.208 m/s
To find the rotational speed, we need to determine the circumference of the propeller and divide the tangential velocity by the circumference.
The circumference of the propeller, C, can be calculated using the formula:
C = π * d
Substituting the values, we get:
C = π * 2.5
C ≈ 7.85 m
The rotational speed of the propeller, ω, can be calculated using the formula:
ω = V / C
Substituting the values, we get:
ω = 272.208 / 7.85
ω ≈ 34.69 rad/s
Therefore, the rotational speed of the propeller is approximately 34.69 radians per second.
The tip of a 2.5m diameter propeller turns with a Mach number of M = 0.8 at sea level, under ISA conditions. Determine the rotational speed of the propeller (in radians per second).
The speed of sound at sea level is: a = 340.26 m/s.
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1 answer