Reference no: EM13974398
Problem- The resistance to flow through pipes and tubes is parameterized by a dimensionless number called the friction factor (denoted as f, ranging from about 0.008 to 0.08), which can estimated using
1/ √f = -20.log10(ε/3.7D + 2.51/Re √f)
where ε = the roughness (m), D = diameter (m), and Re = the Reynolds number defined as
Re = ΡVD/ μ
With Ρ = the fluid's density (kg/m3), V = the fluid's velocity, and μ = dynamic viscosity (N·s/m2).
Assume Ρ = 1.23 kg/m3, μ = 1.79×10-5 N·s/m2, D = 0.005 m, V = 40 m/s, and ε = 1.5×10-6 m.
Part I: By-hand
(a) Determine the friction factor f of the system using the Secant method. Start with initial guesses f = 0.01 and 0.02, and perform two iterations.
Part II: Matlab: Find the friction factor f by performing iterations until the approximate relative error
εa = |fi+1-fi/fi| · 100 % falls below 2 %
(b) Use the Newton's method with initial guess f = 0.01;
(c) Use the Secant method with initial guesses f = 0.01 and 0.02.
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