## Velocity Head

The determination of pressure losses at compressor nozzles and other peripheral points must be made when performing an analysis of the system. It is common in the compressor industry to state the losses as a function of velocity head. An expression for velocity head may be derived from Equation 2.39 and the following: (1) Assume flow is incompressible, which is reasonable since the change in density is negligible; therefore, V] = v2, (2) because there is no heat added or work done, u, W, 0- - 0. When these assumptions are factored into Equation 2.39, vP, =

Equation 2.79 contains two pairs of head terms, the Pv head terms and the V2/2g or velocity head terms. When a flow stream passes through a nozzle, the flow is accelerated. This flow phenomenon can be further examined by regrouping Equation 2.79.

2g yL 2g

The left term of Equation 2.80 represents a head drop required to accelerate the flow from an initial velocity to the final velocity V2. If the initial velocity is low it can be assumed negligible and if density p = 1/v is substituted into Equation 2.80, it can be written as

When gas flows through pipe, casing openings, valves, or fittings, a pressure drop is experienced. This pressure drop can be defined in terms of an equivalent velocity head. The velocity head is, therefore, the pressure drop necessary to produce a velocity equal to the flowing stream velocity. The term K will be used to describe the pressure dropping potential of various restrictive elements, regardless of density or velocity. The term K is a multiplier equal to one at a value of one velocity head and can be greater than or less than one. Typical values of K are presented in Table 2-2. By substituting AP = Pj - P2 and dropping the subscript on the velocity term, the working equation to use in the calculation of pressure drop for K velocity heads is

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