Pipe flow fitting losses

The flow resistance of pipe fittings (elbows, tees, etc) and valves is expressed in terms of either an equivalent length of straight pipe or velocity head loss (head loss = Kv /2g ). Most handbooks and manufacturers pubHcations dealing with fluid flow incorporate either tables of equivalent lengths for fittings and valves or K values for velocity head loss. Inasmuch as the velocity in the equipment is generally much lower than in the pipe, a pressure loss equal to at least one velocity head occurs when the fluid is accelerated to the pipe velocity. 

Hs0 = Head at no flow, or shutoff, ft I4ms = Head of viscous fluid, ft Hw = Water equivalent head, ft hd = Discharge head on a pump, ft of fluid hs = Suction head (or suction lift) on a pump, ft of fluid hSL, hDL = Friction losses in pipe and fittings , subscript SL for suction line and DL for discharge line, ft of fluid hv = Velocity head, ft of fluid L = S = Static head, suction side, ft (Figure 3-38)... 

Fanning (Darcy) friction factor f(f or fD) e, D 2 V2L fo = 4f TW yv2 e, = friction loss (energy/mass) rw = wall stress (Energy dissipated)/ (KE of flow x 4L/D) or (Wall stress)/ (momentum flux) Flow in pipes, channels, fittings, etc. 

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... 

Two-phase flow pressure loss due to pipe-fitting acceleration... 

Anyhow, (1.255) is not properly closed yet as the pressure drop variable is still undetermined. Therefore, before we can apply (1.255) we need to parameterize the losses in terms of known flow parameters in pipes, valves, fittings, and other internal flow devices. Assuming that the viscous stress tensor reduces to a single shear stress component per unit wall surface (e.g., [102] ]185]), Apf per unit cross sectional area can be related directly to the friction drag force on the tube wall surface —Cwt DL. That is, since the friction drag force in a horizontal tube with a constant rate of flow is given by Z p/(- )D, the wall shear stress 3uelds ... 

The loss term, ft-Friction) is commonly correlated with flow parameters in pipes, valves, fittings, and other flow devices. 

A loss coefficient can be defined for any element in which energy is dissipated (pipe, fittings, valves, etc.), although the friction factor is defined only for pipe flow. All that is necessary to describe the pressure-flow relation for pipe flows is Bernoulli s equation and a knowledge of the friction factor, which depends upon flow conditions, pipe size, and fluid properties. 

EFFECT OF FITTINGS AND VALVES. Fittings and valves disturb the normal flow lines and cause friction. In short lines with many fittings, the friction loss from the fittings may be greater than that from the straight pipe. The friction loss hff from fittings is found from an equation similar to Eqs. (5.59) and (5.65) ... 

Gilman, S.F. (1955). Pressure losses of divided-flow fittings. Heating, Piping and Air Conditioning 6 A) 141-147. 

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