Friction loss, absence

The inclusion of significant fitting friction loss in piping systems requires a somewhat different procedure for the solution of flow problems than that which was used in the absence of fitting losses in Chapter 6. We will consider the same classes of problems as before, i.e. unknown driving force, unknown flow rate, and unknown diameter for Newtonian, power law, and Bingham plastics. The governing equation, as before, is the Bernoulli equation, written in the form... 

Water is allowed to enter the foam tank from the main stream with as little friction loss as possible, while pressure in the main stream is dropped about 10% through use of an orifice. Liquid in the tank is metered into the low pressure area by a second orifice. The pressure proportioning system offers the advantages of low pressure drop, automatic proportioning over a range of flows and pressures, freedom from external power and the absence of moving parts. Its disadvantages are that the concentrate cannot be resupplied while the system is in operation, the bladders tend to leak and there is an economic maximum limit on size. 

In the absence of height differences and if frictional losses are ignored, the application of the energy equation (4.55) to the system of Figure 4.4 gives, after adjustment of the station subscripts ... 

When fluid flows around the outside of an object, an additional loss occurs separately from the frictional energy loss. This loss, called form drag, arises from Bernoulli s effect pressure changes across the finite body and would occur even in the absence of viscosity. In the simple case of very slow or creeping flow around a sphere, it is possible to compute this form drag force theoretically. In all other cases of practical interest, however, this is essentially impossible because of the difficulty of the differential equations involved. 

One way out of these difficulties lies in the observation that the static pressure at the wall is close to the cross-sectional mean of the static pressure plus the dynamic pressure stored in the swirl (Hoffmann et al., 1992). Or said in another way the static pressure measured at the wall is close to the static pressure that would be measured after an ideal rectifier (or pressure recovery diffuser ), which would convert all the swirl dynamic pressme into static pressme. We emphasize that this is not necessarily so, it only happens to be so because the static pressure in the vortex finder happens to be very nearly a linear function of the radius. Thus, in the absence of pressme recovery devices, the static pressure measured at the wall of the outlet tube minus the static pressme at the inlet gives the true dissipative loss between inlet and the measurement point in the outlet. One should be aware, though, that further dissipation of dynamic swirl pressure will take place in the downstream piping as the spin decays due to friction with the pipe wall, bends, etc. 

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