Question #$4$

A circular pipe made from new cast iron is used to convey water at a volume flow rate of

$Q=0\mathrm{.}3\frac{m^3}{s}.$ Assume that the flow is steady and fully developed and the water is

incompressible. The head loss, friction, and diameter are related by the Darcy$-$Weisbach

equation,

$h_L=f(\frac{L{V}^2}{D2g})$

where $f$ is the friction factor $($dimensionless$),L$ is the length $(m),D$ is the pipe inner diameter

$(m),V$ is the velocity $(\frac{m}{s}),$ and $g$ is the gravitational acceleration $(=9\mathrm{.}81\frac{m}{s^2}).$ The

velocity can be related to the flow by$,$

$Q=A_{c}V$

Where $A_c$ is the pipe's cross$-$sectional area $(=\frac{}{4}{D}^2{m}^2)$ and the friction factor can be

determined by the Colebrook equation,

$\frac{1}{\sqrt[\phantom{2}]{f}}=-2lo{g}_{10}(\frac{}{3\mathrm{.}7D}+\frac{2\mathrm{.}51}{Re\sqrt[\phantom{2}]{f}})$

Where $Re$ is the Rynold's number, $Re=\frac{VD}{v}$

If you want the head loss to be less than $0\mathrm{.}006$ m per meter of the pipe, develop a

MATLAB function to determine the smallest diameter pipe to achieve this objective.

Hint: you can use the fzero function.

Use the following parameter values: kinematic viscosity, $v=1\mathrm{.}16{10}^{-6}\frac{m^2}{s}$ and

roughness, $=0\mathrm{.}4mm$ Plzz write a proper smooth matlab code thankyou.