The Mach number (M) is defined as the ratio of the speed of an object to the speed of sound in the surrounding medium. In this case, the propeller tip is moving at a speed of M = 0.8 times the speed of sound.
Given that the speed of sound at sea level is a = 340.26 m/s, we can find the speed of the propeller tip by multiplying the speed of sound by the Mach number:
v = M * a
v = 0.8 * 340.26
v = 272.21 m/s
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is half the diameter of the propeller, so r = 2.5m/2 = 1.25m. Therefore, the circumference of the propeller tip is:
C = 2π * 1.25
C = 7.85 m
The rotational speed of the propeller can be determined by dividing the speed of the propeller tip by the circumference of the propeller tip:
ω = v / C
ω = 272.21 / 7.85
ω ≈ 34.67 rad/s
Therefore, the rotational speed of the propeller is approximately 34.67 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.
1 answer
1 answer