When fluid flows through a pipe, the reynolds number will output whether the flow is laminar (smooth, re < 2100), transitional, or turbulent (re > 4000). the reynolds number is expressed as re = rhov d µ where rho is the density, v is the flow velocity and d is the pipe diameter, and µ is the fluid (dynamic) viscosity with units [µ] = kg/(m · s). (a) verify that the reynolds number is dimensionless using si units.

(b) if water at room temperature (20oc) flows through a pipe with a diameter of 10 cm at a speed 1 cm/s, is the flow laminar, transitioning, or turbulent? you should use rho = 998.2 kg/m3 and µ = 1.002 × 10−3 kg/(m · s). show your work.

(c) the flow in part (3b) is maintained by a pump which produces a constant volumetric flow rate q = v · a = 7.854 × 10−5 m3/s, where a = πd2/4 is the pipe’s cross-section area. derive a reynolds number involving q rather than v .

(d) if the flow in parts (3b) and (3c) suddenly transitions from a 10 cm diameter pipe to one with diameter 2 cm. what behavior do you expect in the narrower pipe?