As shown, a microchannel is being designed to transfer fluid in a MEMS (micro electrical mechanical system)

Question:

As shown, a microchannel is being designed to transfer fluid in a MEMS (micro electrical mechanical system) application. The channel is 240 micrometers in diameter and is 8 cm long. Ethyl alcohol is driven through the system at the rate of 0.1 microliters/s (μL/s) with a syringe pump, which is essentially a moving piston. The pressure at the exit of the channel is atmospheric. The flow is laminar, so α = 2. The head loss in the channel is given byWhere L is the channel length, D the diameter, V the mean velocity, μ the viscosity of the fluid, and γ the specific weight of the fluid. Find the pressure in the syringe pump. The velocity head associated with the motion of the piston in the syringe pump is negligible.