Supplementary Material, Appendix G – G.3

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 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 = I_x

I_x = (π/4) r⁴ = 0.25 * π * 0.15⁴ = 0.000398 m⁴

Radius of gyration R_x = (I_x/Area)^0.5

Area = πr² = 0.0707 m², R_x = 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 = I_z

I_z =  2 I_x  = (1/2) πr⁴ = 0.5 * π * 0.15⁴ = 0.000795 m²

Radius of gyration R_z = (I_z/Area)^0.5 = 0.1061m (or r/√2)

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