APPENDIX G – Pumps and Turbines
Surge Analysis and the Wave Plan Method
Supplementary Material: Example Problems and Solutions
Appendix G – Problem 3
G.3 Compute the area moment of inertia (I) of a thin circular steel plate of 300 mm diameter with respect to its principal x-axis as well as the centerline z-axis perpendicular to its surface. Compute the radius of gyration of this plate with respect to both x and z axes.
Solution:
Area moment of inertia through principal x-axis = Ix
Ix = (π/4) r4 = 0.25 * π * 0.154 = 0.000398 m4
Radius of gyration Rx = (Ix/Area)0.5
Area = πr2 = 0.0707 m2, Rx = 0.075 m (or r/2)
Area moment of inertia through the centerline axis perpendicular to the surface, also referred to as polar moment of inertia = Iz
Iz = 2 Ix = (1/2) πr4 = 0.5 * π * 0.154 = 0.000795 m2
Radius of gyration Rz = (Iz/Area)0.5 = 0.1061m (or r/√2)

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