Equivalent Length and Velocity Head Methods

The other method is the velocity head method. The term V2/2g has dimensions of length and is commonly called a velocity head. Application of the Bernoulli equation to the problem of frictionless discharge at velocity V through a nozzle at the bottom of a column of liquid of height H shows that H = V2/2g. Thus II is the liquid head corresponding to the velocity V. Use of the velocity head to scale pressure drops has wide application in fluid mechanics. Examination of the Navier-Stokes equations suggests that when the inertial terms dominate the viscous terms, pressure gradients are expected to be proportional to pV2 where V is a characteristic velocity of the flow. 

In the velocity head method, the losses are reported as a number of velocity heads K. Then, the engineering Bernoulli equation for an incompressible fluid can be written 

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In the velocity head method of accounting for fitting losses, a multiplicative coefficient is found empirically by which the velocity head term (v)2/2g is multiplied to obtain the fitting loss. This term is then added to the regular velocity head losses in Eq. (63). Extensive tables and charts of both equivalent lengths and loss coefficients and formulas for the effect of flow rate on loss coefficients... 

There is no entirely satisfactory method for estimating these losses. Kern (1950) suggests adding four velocity heads per pass. Frank (1978) considers this to be too high, and recommends 2.5 velocity heads. Butterworth (1978) suggests 1.8. Lord et al. (1970) take the loss per pass as equivalent to a length of tube equal to 300 tube diameters for straight tubes, and 200 for U-tubes whereas Evans (1980) appears to add only 67 tube diameters per pass. 

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