Supplementary Material, Appendix G – G.8

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 8

G.8 Compute mass moment of inertia with respect to principal x-axis as well as centerline z-axis of a composite circular steel plate of 300 mm diameter and 5 mm thickness sandwiched between 2 circular steel rings of 300 mm outer diameter, 250 mm inner diameter, and 5 mm thickness. Compute radius of gyration of this plate with respect to both x and z axes. 

Solution:

Mass of annular plates is super imposed on the mass of circular plate.

I_xm  = (I_xm)_circle + 2 * (I_xm)_ring = 0.0316 kg-m² = 0.3096 N-m²

Combined mass = 4.441 kg, R_x = (I_xm/Mass)^0.5 = 0.084m

I_zm =  2 I_xm  = 0.0631 kg-m² = 0.6193 N-m²

R_zm = (I_zm/Mass)^0.5 = 0.1192 m

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