Pipe flow economic velocities

Economic velocities for turbulent flow (the most common industrially), taking into account piping capital costs (piping, fittings, pumps, etc.) and running costs (pressure drops), are primarily a function of fluid density [A/ fT oc pu2]. Details are given in the literature.4 Order of magnitude economic velocities are ... 

This equation says that for a given set of cost data the economic velocity is independent of the mass flow handled and dependent on only the. fluid density and the friction factor. More thorough analyses and far more complicated cost equations lead to substantially the same conclusion. For example, for schedule 40 carbon-steel pipe, Boucher and Alves [16] give the data shown in Table 6.4. 

Why does App. A.4 show the velocity in feet per second for all the water flows given Fromj Table 6.4 and Fig. 6.21 we can see that for water (which is almost always in turbulent flow in industrial equipment) an economic velocity is almost always about 6ft/s. Thus, working engineers often simply select pipe sizes for water or similar fluids by looking at App. A.4 for the pipe size which gives a velocity ofj about 6ft/s (2m/s). 

The economic size for a pipe is the size with the lowest sum of annual charges for thle purchased cost of the pipe and pump and the annual power cost of running the pump or compressor needed to overcome friction. For turbulent flow, this results in an economic velocity which is practically independent jof everything but fluid density it is about 6ft/s for most liquids and about 40ft/s for air under normal conditions. 

To determine the fluid velocity in a pipe, the rule-of-thumb economic velocity for turbulent flow is used, as given next ... 

Piping systems should be designed for an economic flow velocity. For relatively clean fluids, a recommended velocity range where minimum corrosion can be expected is 2 to 10 fps. If piping bores exist, maximum fluid velocities may have a mean velocity of 3 fps for a 3/8-in. bore to 10 fps for an 8-in.-diameter bore. Higher flow velocities are not uncommon in situations that require uniform, constant oxygen supply to form protective films on active/passive metals. 

The bend radii of pipes should be designed to be as large as possible. A minimum of three times the pipe diameter is recommended to maintain safe, economic flow velocities. 

We have seen how heat transfer and thus dry deposition of SO2 is reduced on large surfaces, due to the buildup of boundary layer thickness (which reduces the local gradients). However, there are economically important structural objects composed of many elements of small dimension which show the opposite effect. These include fence wire and fittings, towers made of structural shapes (pipe, angle iron, etc.), flagpoles, columns and the like. Haynie (11) considered different damage functions for different structural elements such as these, but only from the standpoint of their effect on the potential flow in the atmospheric boundary layer. The influence of shape and size act in addition to these effects, and could also change the velocity coefficients developed by Haynie (11), which were for turbulent flow. Fence wire, for example, as shown below, is more likely to have a laminar boundary layer. 

Such pipe flocculators tend to create rather high velocity gradients at practical flow rates and need to be very long to give the required detention times. Therefore it may be useful to utilize an existing pipe as a flocculator, but it is not economic to build one for the purpose, as a concrete channel with baffles would be more compact and cost less. 

The minimum average liquid velocity which causes the motion of capsule under the drag produced by liquid in pipe is defined as threshold velocity, Vm When the drag exceeds friction between pipe and capsule, the capsule will start to move along a pipe bottom. Because the contact friction between pipe and capsule influences a capsule velocity and hydraulic gradient of capsule flow, which can be different from the values determined for a straight pipe, it is necessary to take it into account for design of commercial pipelines to ensure safe and economical operation. 

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