Supplementary Material, Appendix G – G.4

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. 

Solution:

I_x = (π /4) (r₂⁴ – r₁⁴)   = 0.25 * π * (0.15⁴ – 0.125⁴)= 0.000206 m²

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

Area = π(r₂² – r₁²)  = 0.0216 m², R_x = 0.0976 m

I_z =  2 I_x  = (1/2) π(r₂⁴ – r₁⁴)

I_z = 0.5 * π * (0.15⁴ – 0.125⁴)= 0.000412 m²

Radius of gyration R_z = (I_z/Area)^0.5= 0.138 m

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