The pressure gradient for laminar flow through a constant radius tube is given by

where p = pressure (N/m²), x = distance along the tube’s centerline (m), μ = dynamic viscosity (N ∙ s/m²), Q = flow (m³/s), and r = radius (m).

(a) Determine the pressure drop for a l0-cm length tube for a viscous liquid (μ = 0.005 N ∙ s/m², density = p = 1 x 10³ kg/m³) with a flow of 10 x l0⁶ m³/s and the following varying radii along its length.

(b) Compare your result with the pressure drop that would have occurred if the tube had a constant radius equal to the average radius

(c) Determine the average Reynolds number for the tube to verity that flow is truly laminar (Re = pυD/μ < 2100 where υ = velocity).

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