Poiseuille's law [Eq. (9-41)] gives the volume flow rate of a viscous fluid through a pipe. 

(a) Show that Poiseuille's law can be written in the form ΔP = IR, where I = ΔV/Δt represents the volume flow rate and R is a constant of proportionality called the fluid flow resistance. 

(b) Find R in terms of the viscosity of the fluid and the length and radius of the pipe. 

(c) If two or more pipes are connected in series so that the volume flow rate through them is the same, do the resistances of the pipes add as for electrical resistors (R_eq = R₁ + R₂ + ⋯)? Explain. 

(d) If two or more pipes are connected in parallel, so the pressure drop across them is the same, do the reciprocals of the resistances add as for electrical resistors (1/Req = 1/R₁ + 1/R₂ + ⋯)? Explain.

Transcribed Image Text:

(9-41) π ΔΡΙL 8η