Conduits, pressure losses

The frictional pressure loss in the stack must be added to the loss in the heater when estimating the stack draft required. This can be calculated using the usual methods for pressure loss in circular conduits, see Section 12.8. The mass velocity in the stack will be around 1.5 to 2 kg/m2. These values can be used to determine the cross-section needed. 

Euler number Eu A p pV2 frictional pressure loss 2 x velocity head Fluid friction in conduits... 

CW = the pressure losses due to conduits and fittings between the tank (A) and the pump, including entry loss... 

Other Pressure Losses. Losses due to increaidng or decreaang the cross-sectional area of a conduit suddenly are sometimes relatively large. The loss due to a sudden enlargement of the cross i ction may be expressed approximately as follows ... 

Example 5-6 Friction Loss in a Sudden Expansion. Figure 5-7 shows the flow in a sudden expansion from a small conduit to a larger one. We assume that the conditions upstream of the expansion (point 1) are known, as well as the areas A and A2. We desire to find the velocity and pressure downstream of the expansion (V2 and P2) and the loss coefficient, Kt. As before, V2 is determined from the mass balance (continuity equation) applied to the system (the fluid in the shaded area). Assuming constant density,... 

The flow of fluids is most commonly measured using head flowmeters. The operation of these flowmeters is based on the Bernoulli equation. A constriction in the flow path is used to increase the flow velocity. This is accompanied by a decrease in pressure head and since the resultant pressure drop is a function of the flow rate of fluid, the latter can be evaluated. The flowmeters for closed conduits can be used for both gases and liquids. The flowmeters for open conduits can only be used for liquids. Head flowmeters include orifice and venturi meters, flow nozzles, Pitot tubes and weirs. They consist of a primary element which causes the pressure or head loss and a secondary element which measures it. The primary element does not contain any moving parts. The most common secondary elements for closed conduit flowmeters are U-tube manometers and differential pressure transducers. 

In the case of a siphon, such as a pipe connecting two tanks that rises above the tanks, there is a vacuum at its summit, and if the siphon is to operate, the absolute pressure at the summit should equal or exceed the vapor pressure. An exact solution should consider the friction losses in the lengths of conduit involved, but we shall here confine ourselves to... 

SEPARATION FROM VELOCITY DECREASE Boundary-layer separation can occur even where there is no sudden change in cross section if the cross section is continuously enlarged. For example, consider the flow of a fluid stream through the trumpet-shaped expander shown in Fig. 5.16. Because of the increase of cross section in the direction of flow, the velocity of the fluid decreases, and by the Bernoulli equation, the pressure must increase. Consider two stream filaments, one, aa, very near the wall, and the other, bb, a short distance from the wall. The pressure increase over a definite length of conduit is the same for both filaments, because the pressure throughout any single cross section is uniform. The loss in velocity head is, then, the same for both filaments. The initial velocity head of filament aa is less than that of filament bb, however, because filament aa is nearer... 

From the reservoir the gas is assumed to flow, without friction loss at the entrance, into and through a conduit. The gas leaves the conduit at definite temperature, velocity, and pressure and goes into an exhaust receiver, in which the pressure may be independently controlled at a constant value less than the reservoir pressure. 

Hydraulic properties, that is, friction-loss calculations of proppant-laden fluids or slurries, are very important not only in the design of any hydraulic fracturing treatment but also in real-time monitoring of fracturing treatments. Recent advances (27, 28) in real-time fracture analysis have necessitated an accurate knowledge of bottomhole treating pressure (BHTP). To estimate BHTP, an accurate prediction of friction pressures of fluids in the flow conduit is required. It is possible to obtain the BHTP from the surface pressure with the following equation ... 

We are no more able to calculate the pressure drop in steady, turbulent flow in a noncircular conduit than we are in a circular one. However, it seems reasonable to expect that we could use the friction-loss results for circular pipes to estimate the results for other shapes. Let us assume that the shear stress at the wall of any conduit is the same for a given average fluid flow velocity independent of the shape of the conduit. Then, from a force balance on a horizontal section like that leading to Eq. 6.3, we conclude that in steady flow... 

As above noted, in a breeder system the neutron losses must be reduced to a minimum and it has been found that a substantial portion of these losses is due to neutron absorption in gaseous fission products such as xenon formed within the reactive solution 10. These fission products escape within the high pressure chamber 24 and are swept therefrom by an inert gas such as helium pumped through inlet and outlet conduits 35 and 36. Additional gaseous fission products are released within the low pres-... 

Membrane module geometry - Can the membrane formed be incorporated into a module geometry that accommodates conduits for feed and product gases, optimum driving force for the separation, efficient membrane area density, and with minimal pressure head loss (energy) ... 

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