Le/D=4.4*[Re]1/6 —> turbulent Moeckel: Le/D=1.6*[Re]1/4 , Re<107 ***
Le/D=.06*[Re] —>laminar, where Re = DVρ/μ = 4Q/πDν = 4*m_dot/πDμ (pipes);
Re = 4RHVρ/μ (ducts), where Vavg [V = Q/A]; hf = f (L/D)(V2/2g); hL = ΔPL/ρg ; ΔPL = f (L/D)(ρV2/2g)
For laminar flow (Re < 2100): f = 64/Re For smooth pipe turbulent flow: f = 0.316/Re1/4
1&2—>find D
3—>find L
Pg 1-6= nondimensionalization of eqns, params
background; 7-11: (7)Reynolds time averaging;
(8) u’ and u-bar/momentum_x; (9) turb bound
flow; (10-11) u+ vs y+;; 12-15: pi theorem
6.38
6.38,6.48=iteration. [smooth38; rough-48]
PI THEOREM: 6
steps