LearnChemE

#### Calculating Diameter in Pipe Flow: Screencast

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##### Important Equations:

The value of the Reynold’s number, RE, determines the flow regime in a pipe.

$Re = \frac{\rho VD}{\mu} = \frac{VD}{\nu}$

where $$\rho$$ = density of the fluid, $$V$$ = average velocity, $$D$$ = diameter of the pipe, $$\mu$$ = dynamic viscosity, and $$\nu$$ = kinematic viscosity.

The energy equation is the governing equation for viscous pipe flow.

$\frac{p_1}{\gamma} + \frac{V^2_1}{2g} + z_1 = \frac{p_2}{\gamma} + \frac{V^2_2}{2g} + z_2 + h_L$

where $$p$$ = pressure, $$V$$ = velocity, $$g$$ = gravity, $$z$$ = height measured from some origin, and $$h_L$$ = head loss, which consists of:

$h_{L,major} = f \frac{L}{D} \frac{V^2}{2g}$

$h_{L,minor} = \frac{\Sigma K_L V^2}{2g}$

where $$f$$ = friction factor and $$K_L$$ = loss coefficient.

The Colebrook equation is a method to solve for the friction factor.

$\frac{1}{\sqrt{f}} = -2.0 log \left( \frac{\frac{\epsilon}{D}}{3.7} + \frac{2.51}{Re \sqrt{f}} \right)$

where $$\epsilon$$ = surface roughness