A small fan moves air at a mass flowrate of \(0.004 \mathrm{lbm} / \mathrm{s}\). Upstream of the fan, the pipe diameter is 2.5 in., the flow is laminar, the velocity distribution is parabolic, and the kinetic energy coefficient, \(\alpha_{1}\), is equal to 2.0. Downstream of the fan, the pipe diameter is 1 in., the flow is turbulent, the velocity profile is quite flat, and the kinetic energy coefficient, \(\alpha_{2}\), is equal to 1.08. If the rise in static pressure across the fan is \(0.015 \mathrm{psi}\) and the fan shaft draws \(0.00024 \mathrm{hp}\), compare the value of loss calculated:

(a) assuming uniform velocity distributions,

(b) considering actual velocity distributions.