Long-pipe approximation

Here fipa is the generalized, long-pipe approximation function ... 

The example calculated in Section 6.7 will be recalculated using the explicit, long-pipe approximation. All the same physical data will be used. 

An approximate meth, the Average Specific Volume Approximation Method (ASVAM), is also presented, based on the Long-Pipe Approximation described in Chapter 6. This approximate method retains much of the accuracy of the SVHIM, but has the advantage of yielding a direct estimate of flow. 

We shall use the long-pipe approximation to the compressible flow equation (cf. equation (6.65)) in order to calculate the flow before sonic conditions are reached in the valve ... 

The long-pipe approximation for gas flow is given by equation (6.60), which may be tailored to the notation of Figure 18.1 as ... 

A2.4 Developing a long-pipe approximation to the full compressible flow equations... 

To enable us to compare the long-pipe approximation with the exact solution valid for a horizontal pipe, we substitute equation (A2.29) into (A2.13) with the additional condition that zi = Zs. i-e. ... 

As we would expect from the assumptions made in the derivation of the long-pipe approximation, bo is close to unity when the change in pressure with distance, dp/dx, is relatively low, namely when the pipe is long and/or the pressure drop small. The contours show how bo increases towards unity as pn/p 1.0 and Kt - 00. In fact at Kr = 128 and Pa/P = 0.95, bo is already greater than 0.99. But the deviations from unity grow when dp/dx is large, namely when the pipe is short, or the pressure ratio is small. 

Hgure A2.2 Plot of long-pipe approximation parameter, bo, against frictional pressure loss in veiocity heads, Kt. and pressure... 

Universal Gas Sizing Equation generalized mass-flow function kg/s fhpr high-pressure-ratio function ftpa long-pipe approximation flow function... 

A gas black apparatus consists of a burner pipe approximately 5 m long, which carries 30-50 diffusion burners. The flames burn in contact with a water-cooled drum, where about half of the carbon black formed is deposited. This black is scraped off and transported by a screw to a pneumatic conveying system. The gas black apparatus is surrounded by a steel box open at the bottom. At the top of it, fans suck the off-gas into filters, which collect the carbon black suspended in the gas. 

A pipe approximately 3 feet long, 1 inch in diameter filled with 1/2 lb of molecular sieve is preferable to a shorter, fatter device as the contact time will be greater in the longer tube. 

Iron pipe approximately 3 ft. l meter) long and 2 in. to 4 in. <5 to vancing troops. 

Cartridge water pipe approximately 4 ft (1 meter) long and 2 to 4 in. (5 to... 

To derive an approximation to the compressible flow equations for a long pipe, we may take as our starting point the incompressible flow equation (4.81), revised so that the outlet is taken as the point Just inside the pipe outlet in Figure 6.1 ... 

Iron pipe approximately 3 feet (1 meter) long and 2 inches to 4 inches (5 to 10 cm) in diameter and... 

Smoke pipe, approximately 4 feet long x 12 inches in diameter, 1/16 inch thick Hardware store... 

While plug flow is an idealization, fluid flow through long pipes, gas flow through packed beds under certain conditions, and some transfer line reactors may be regarded as plug flow systems as a reasonable approximation. 

Fig. 1. Pressure required for propagation of decomposition flame through commercially pure acetylene free of solvent and water vapor in long horizontal pipes. Gas initially at room temperature ignition by thermal nonshock sources. Curve shows approximate least pressure for propagation (0), detonation,...

It is neeessary to understand the TDH and it s eomponents in order to make eorreet deeisions when parts of the system are changed, replaced, or modified (valves, heat exchangers, elbows, pipe diameter, probes, filters, strainers, ete.) It s neces.sary to know these TDH values at the moment of specifying the new pump, or to analyze a problem with an existing pump. In order to have proper pump operation with low maintenance over the long haul, the BF P of the pump must be approximately equal to the TDH of the system. 

PLATE 6. Approximately l-m-long spontaneous PBD on plastic pipe. 

---