I was wondering how to calculate the required fan power for the following air pipe network. Other losses besides friction is not calculated for.
Known parameters:
- Fan provided flow, VA = 3000 m3/h
- pressure at inlet to fan and outlets 1,2,3 , 1 bar
- Friction coefficient, f = 0.012
- Lenghts, L1 = 20m, L2 = 5m, L3 = 20m, LA = 50m, LB = 5m
- Density of air, constant at 1.2 kg/m3 (we are assuming incompressible flow)
- Pipe diameter, d = 0.25m (same for all)
- Output flow, $\dot V_1=0.3128$ m3/s, $\dot V_2=0.3470$ m3/s, $\dot V_3=0.1735$ m3/s
- Fan efficency, ${\eta _f} = 0.75$
With the known parameters I could formulate the equation for the fan power: $$\left| {{{\dot E}_f}} \right| = {\dot V_A} \cdot \frac{{\Delta p}}{{{\eta _f}}}$$
I am unsure how to define the pressure increase ${\Delta p}$ from the fan
I have tried defining it as the sum of all pipe's pressure loss using the following: $$\frac{{\Delta {p_{f,i}}}}{\rho } = f \cdot w_i^2 \cdot \frac{{{L_i}}}{d}$$
That however did not yield an appropriate answer.
