The T-shaped construct of tubes has already been configured such that its global flow resistance is minimum subject to fixed total flow volume (V) and fixed rectangular area (A) occupied by the T...

The T-shaped construct of tubes has already been configured such that its global flow resistance is minimum subject to fixed total flow volume (V) and fixed rectangular area (A) occupied by the T (Fig. P13.18). The flow regime is laminar and fully developed (Poiseuille) and all the tubes are sufficiently slender such that the junction pressure drop is negligible.

(a) What are the aspect ratios D₁∕D₂
and L₁∕L₂?

(b) In addition to the above aspect ratios, assume that L₁
= 1 m and D₁
= 1 cm. Calculate A and V and report the slenderness of the drawing, Sv = A^1∕2∕V^1∕3.

(c) If L₁
remains the same and D₁
decreases, will Sv increase or decrease? Will the overall flow resistance of the T construct increase or decrease? Explain why.