Propeller blade in aeroplane is 2m long if propeller rotates 1800rev/min compute tangential velocity.
radius= 2m
Frequency= 1800 rev/min =30 Hz
Angular velocity=
2πn= 2 × 3.14 ×30
Velocity=radius×angular velocity
V=2×(2×3.14)=376.8 m/s
V=?
Given:
N=1800rev/min,. 1st we need to convert this in rev/sec
Therefore n=30rev/sec
Radius=2m
We know that,
V=r2πn
=2×2×3.14×30
=376.8m/s
Circumference=pi*2r = 3.14 * 4m=12.57 m.
V = 1800rev/min * 12.57m/rev * 1min/60s=
377 m/s.
r=2m
V=rw
= r2πn
= 2×2×3.14×30
v=376.8 m/s
To compute the tangential velocity of a propeller blade in an airplane, we need to use the formula:
Tangential velocity = 2π * Radius * Rotational speed
Given:
- Propeller blade length: 2m
- Rotational speed: 1800 rev/min
First, we need to convert the rotational speed from rev/min to radians/second. Since there are 60 seconds in a minute and 2π radians in a revolution, we can use the following conversion:
Rotational speed in radians/second = (Rotational speed in rev/min) * (2π radians/1 rev) * (1 min/60 seconds)
Rotational speed in radians/second = (1800 rev/min) * (2π radians/1 rev) * (1/60)
Rotational speed in radians/second = 188.5 radians/second (rounded to one decimal place)
Next, we calculate the radius of the propeller blade. We know that the propeller blade length is 2m, but this length represents the diameter, not the radius. The radius is half of the diameter, so:
Radius = 2m / 2
Radius = 1m
Finally, we apply the formula to calculate the tangential velocity:
Tangential velocity = 2π * Radius * Rotational speed
Tangential velocity = 2π * 1m * 188.5 radians/second
Tangential velocity = 1179.8 meters/second (rounded to one decimal place)
Therefore, the tangential velocity of the propeller blade in the airplane is approximately 1179.8 meters/second.