As shown in the illustration, a section of standard weight, seamless steel pipe, has an external diameter of 8.5 inches. When the pipe, is bent into a 90 degree turn, the length of the outside edge of the curve "A-B" will exceed the length of the inside edge of the curve "C-D" by __________. See illustration GS-0108.
• Relationship between arc length, radius, and angle for a circular bend • How the outside radius and inside radius of the pipe relate to the pipe diameter • Conversion of 90° into radians when using the arc-length formula
• Write the arc-length formula for the outside edge and the inside edge separately, then subtract them. What cancels out? • Express the outside radius and inside radius in terms of the unknown bend radius to pipe centerline and the given 8.5-inch diameter. • After simplifying, what single quantity (in inches) is left multiplied by the bend angle (in radians)?
• Use the arc-length formula: s = r × θ (with θ in radians, not degrees). • Remember that R_outside − R_inside = pipe diameter, regardless of the actual bend radius. • Confirm that 90° = π/2 radians before doing your final multiplication.
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