Complete in Metric Conversions:
The 7 inch diameter drive drum of a belt conveyor is turning at 130 rpm. What is the belt speed (ft/min) if there is no slip between the belt and drum?
To find the belt speed in feet per minute (ft/min), we need to convert the given information into metric units and then convert it back to the desired unit.
Step 1: Convert the diameter from inches to meters.
The diameter of the drive drum is given as 7 inches. To convert it to meters, we need to use the conversion factor 1 inch = 0.0254 meters.
So, the diameter in meters is calculated as follows:
7 inches × 0.0254 meters/inch = 0.1778 meters
Step 2: Calculate the circumference of the drive drum.
The circumference of a circle can be calculated using the formula C = πd, where C is the circumference and d is the diameter.
Using the given diameter of 0.1778 meters, the circumference is:
C = π × 0.1778 meters = 0.5596 meters
Step 3: Find the belt speed in meters per minute (m/min).
The belt speed can be calculated using the formula Speed = Circumference × RPM, where Speed is the belt speed and RPM is the revolutions per minute.
Substituting the given values, we get:
Speed = 0.5596 meters × 130 revolutions/minute = 72.748 meters/minute
Step 4: Convert the belt speed from meters per minute to feet per minute.
To convert meters to feet, we need to use the conversion factor 1 meter = 3.28084 feet.
So, the belt speed in feet per minute (ft/min) is calculated as:
72.748 meters/minute × 3.28084 feet/meter = 238.845 ft/min
Therefore, the belt speed, with no slip between the belt and drum, is 238.845 ft/min.