Calculating Length and Equivalent Length in a Pipe: Screencast

Describes how to calculate an equivalent length for minor losses.

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Important Equations:

\[Re = \frac{\rho \, UD}{\mu} = \frac{UD}{\nu}\]

where \(Re\) = Reynold’s number, \(\rho\) = fluid density, \(U\) = freestream velocity, \(D\) = pipe diameter, \(\mu\) = fluid dynamic viscosity, and \(\nu\) = fluid kinematic viscosity.

\[\frac{P_1}{\gamma} + \frac{V_1 ^2}{2g} + z_1 = \frac{P_2}{\gamma} + \frac{V_2 ^2}{2g} + z_2 + h_L\]

where \(P_1\) and \(P_2\) are the pressures at points 1 and 2, \(\gamma\) = specific weight of fluid, \(V_1\) and \(V_2\) are the velocities at points 1 and 2, \(g\) = gravitational constant (9.81 m/s2), \(z_1\) and \(z_2\) are the relative heights at points 1 and 2, and \(h_L\) = head loss. 

\(h_L\) consists of 2 components: major head loss and minor head loss.

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

where \(f\) = friction factor, and \(L\) = length of pipe.

\[h_{L,minor} = \frac{K_L V^2}{2g} = \frac{f \left( \frac{L_{eq}}{D} \right) V^2}{2g}\]

\[L_{eq} = \frac{K_L D}{f}\]

where \(K_L\) = loss coefficient and \(L_{eq}\) = equivalent length.