2. A propeller on a gas turbine rotates 64° every 2.70 minutes. What is the angular velocity in rev/s? What is the linear speed of a point at the tip of the blade if the diameter of the blade is 5.37 ft?
a. 64o/2.70min * 1rev/360o * 1min/60s=
= 1.1 rev/s.
b. C = pi*D = 3.14*5.37=16.9 Ft=5,12 m.
The Circumference.
b. 64o/2.70min * 1rev/360o * 5.12m/rev
* 1min/60s = 5.62 m/s.
To find the angular velocity in rev/s, we need to convert the given information into the appropriate units.
1. First, let's convert the rotation from minutes to seconds. Since there are 60 seconds in a minute, we can multiply the given rotation of 64° by the ratio of seconds to minutes: (64°) * (1 minute / 2.70 minutes) * (60 seconds / 1 minute).
Calculating this expression, we get:
64° * (1 minute / 2.70 minutes) * (60 seconds / 1 minute)
= 64° * (60 seconds / 2.70 minutes)
= 64° * 22.22 seconds
≈ 1422.08°
2. Next, we need to convert the angular rotation to revolutions by dividing by a full circle or 360°:
1422.08° / 360° = 3.95 revolutions
So, the propeller rotates at an angular velocity of approximately 3.95 revolutions every 2.70 minutes.
To find the linear speed of a point at the tip of the blade, we can use the formula:
Linear speed = r * angular velocity,
where r is the radius or half the diameter of the blade. In this case, the radius is 5.37 ft / 2 = 2.685 ft.
3. Now, let's find the linear speed:
Linear speed = 2.685 ft * 3.95 rev / 2.70 minutes
Since we want the result in feet per second, we will convert minutes to seconds: 2.70 minutes * 60 seconds / 1 minute
Linear speed = 2.685 ft * 3.95 rev / (2.70 minutes * 60 seconds / 1 minute)
≈ 2.685 ft * 3.95 rev / 162 seconds
≈ 0.0658 ft/s
Therefore, the linear speed of a point at the tip of the blade is approximately 0.0658 ft/s.