1. Calculate the cross-sectional area of the fan excluding the motor core:

   • The fan's total diameter is cm (0.12 m), and the motor core's diameter is cm (0.05 m).
   • First, calculate the area of the entire fan: $$\text{Area of the entire fan} = \pi \left(\frac0.12{2}\right)^2 = \pi (0.06)^2 = 0.011310 \, \text{m}^2$$
   • Next, calculate the area of the motor core: $$\text{Area of the motor core} = \pi \left(\frac0.05{2}\right)^2 = \pi (0.03)^2 = 0.001963 \, \text{m}^2$$
   • Subtract the motor core area from the total area to get the effective airflow area: $$\text{Effective airflow area} = 0.011310 \, \text{m}^2 - 0.001963 \, \text{m}^2 = 0.009346 \, \text{m}^2$$

2. Calculate the airflow rate in cubic meters per second (m³/s):

   • Multiply the effective area by the average air velocity measured at the fan surface: m/s: $$\text{Airflow rate} = 0.009346 \, \text{m}^2 \times 4.5 \, \text{m/s} = 0.042058 \, \text{m}^3/\text{s}$$

3. Convert the airflow rate to cubic meters per hour (m³/h):

   • There are 3600 seconds in an hour, so: $$\text{Airflow rate} = 0.042058 \, \text{m}^3/\text{s} \times 3600 \, \text{s/h} = 151.409058 \, \text{m}^3/\text{h}$$

4. Calculate the per-fan CADR:

   • CADR is the product of the airflow rate and the filter efficiency.
   • The filter efficiency is %, or 0.98 as a decimal.
   • So, the CADR is: $$\text{CADR} = 151.409058 \, \text{m}^3/\text{h} \times 0.98 = 148.380877 \, \text{m}^3/\text{h}$$

5. Number of identical fans:

   • Number of fans:
   • Total CADR for all fans: $$\text{Total CADR} = 148.38 \, \text{m}^3/\text{h} \times 4 = 593.52 \, \text{m}^3/\text{h}$$

In summary, after taking the motor core into account, the total Clean Air Delivery Rate (CADR) for 4 fan(s) at 4.5 m/s through a 98% efficient filter is approximately 593.52 cubic meters per hour or 349.33 cubic feet per minute (cfm).