Fluid Mechanics Problem A fan is to produce a constant mean

Fluid Mechanics Problem...

A fan is to produce a constant mean air speed V throughout a pipe loop as shown. The pipes are smooth and have diameter D, and each of the 90 degree bends has a loss coefficient K. Determine the pressure raise across the fan.

Solution

Loss coeffecient for 4 bends = 4*K

Total pipe length = 2*L1 + 2*L2

Reynolds number Re = V*D / neu.........where neu = kinematic viscosity of air

For smooth pipe, friction factor f is given by the relationship

1 / f^0.5 = 0.86*ln(Re*f^0.5) - 0.8

Using this we calculate f.

Pressure rise across the fan = (f*L/D + 4K) *(1/2)*rho*V² ..............where rho is the density of air

= (f*2*(L₁ + L₂)/D + 4K) *(1/2)*rho*V²