LearnChemE

#### Calculating Velocity in Pipe Flow: Screencast

Presents the problems involved in calculating velocity in a pipe and demonstrates methods to solve for it.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

The value of 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.

$\frac{p_1}{\gamma} + \frac{V_1^2}{2g} + z_1 = \frac{p_2}{\gamma} + \frac{V_2^2}{2g} + z_2 + h_L$

where $$p$$ = pressure, $$V$$ = velocity, $$g$$ = gravitational constant, $$\gamma$$ = specific weight, $$z$$ = 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 friction factor.

$\frac{1}{\sqrt{f}} = -2.0log\left( \frac{\frac{\epsilon}{D}}{3.7} + \frac{2.51}{Re \sqrt{f}} \right)\,\,\,\, or\,\,\,\, f = \left( -2.0 log\left( \frac{\frac{\epsilon}{D}}{3.7} + \frac{2.51}{Re \sqrt{f}} \right) \right)^{-2}$

where $$\epsilon$$ = roughness factor.