To calculate the polar moment of inertia of a fan

[siddarthan]

1.The motors driving the fans of a large cooling tower must be represented in a dynamic
simulation of a power plant auxiliary system.
Each fan can be described as follows:
Fan diameter = 4.5 meter
No of blades/fan = 6
Fan RPM = 90
The fan blades have a tapering cross section.
The fan cross section may be taken to taper linearly from root to tip.
The mass-per-length of each blade may be taken to vary from 8 Kg/m at the root to 3Kg/m
at the tip.
The root diameter of the fan disc is 1m.
The tip diameter of the fan disc is 4.5m.
Estimate the polar moment of inertia of the fan in Kg-m^2
2. unable to figure out

3. unable to figure out

 

[OldEngr63]

This is not a hard problem; it simply has several parts to be worked out.

First, the fan hub is a disk, so look up the formula for the mass moment of inertia (MMOI) for a disk and apply the given data for the fan hub to geet that part.

Secondly, you are told how the mass per length varies, and you know both the rood radius and the tip radius, so you can perform the following integral for one blade:

MMOI_blade = ∫_r1^r₂ r² (mass/length) dr

Use these two results, with appropriate multipliers, to build the required final result.