APPENDIX G – Pumps and Turbines
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Surge Analysis and the Wave Plan Method
Supplementary Material: Example Problems and Solutions
Appendix G – Problem 4
G.4 Compute the area moment of inertia of a thin circular steel annular plate of 300 mm outer diameter and 250 mm inner diameter with respect to its principal x-axis as well as its centerline z-axis. Compute radius of gyration of this plate with respect to both x and z axes.
I x = (π /4) (r 2 4 – r 1 4 ) = 0.25 * π * (0.15 4 – 0.125 4 )= 0.000206 m 2
Radius of gyration R x = (I x /Area) 0.5
Area = π(r 2 2 – r 1 2 ) = 0.0216 m 2 , R x = 0.0976 m
I z = 2 I x = (1/2) π(r 2 4 – r 1 4 )
I z = 0.5 * π * (0.15 4 – 0.125 4 )= 0.000412 m 2
Radius of gyration R z = (I z /Area) 0.5 = 0.138 m
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