Expansion and Exit Losses

Expansion and Exit Losses For ducts of any cross section, the frictional loss for a sudden enlargement (Fig. 6-13c) with turbulent flow is given by the Borda-Carnot equation ... 

For individually finned tubes as shown in Fig. 17.14a, flow expansion and contraction take place along each tube row, and the magnitude is of the same order as that at the entrance and exit. Hence, the entrance and exit losses are generally lumped into the core friction factor. Equation 17.65 for individually finned tubes then reduces to... 

Equation (6-95) is valid for incompressible flow. For compressible flows, see Benedict, Wyler, Dudek, and Gleed (J. E/ig. Power, 98, 327-334 [1976]). For an infinite expansion, A1/A2 = 0, Eq. (6-95) shows that the exit loss from a pipe is 1 velocity head. This result is easily deduced from the mechanic energy balance Eq. (6-90), noting that Pi =pg. This exit loss is due to the dissipation of the discharged jet there is no pressure drop at the exit. 

The discharge head of a pump is the head measured at the discharge nozzle (gauge or absolute), and is composed of the same basic factors previously summarized 1. static head 2. friction losses through pipe, fittings, contractions, expansions, entrances and exits 3. terminal system pressure. 

Water flows through a 45° expansion pipe bend at a rate of 200 gpm, exiting into the atmosphere. The inlet to the bend is 2 in. ID, the exit is 3 in. ID, and the loss coefficient for the bend is 0.3 based on the inlet velocity. Calculate the force (magnitude and direction) exerted by the fluid on the bend relative to the direction of the entering stream. 

Pipe entrance and exit pressure losses should also be calculated and added to obtain the overall pressure drop. The loss in pressure due to sudden expansion from a diameter dtl to a larger diameter dl2 is given by the equation... 

Derivation of Head Loss in a Sudden Expansion. This example illustrates the use of all three conservation equations to derive an expression for the head loss through a sudden expansion in a pipe or as a pipe enters a large vessel, an exit loss, and is illustrated in Figure 6. 

The pressure drop of particulate filters is composed of five primary contributions, shown in Fig. 20.7. The inlet and outlet effects, shown as (1) and (5) in Fig. 20.7, are due to the contraction and acceleration as the gas enters the inlet channels and the expansion and deceleration of the gas as it exits the channels, respectively. Compared to flow-through substrates where inlet and outlet effects typically are less than 10 % of the total pressure loss, these pressure losses are larger in case of filters since only one half of the channels is open on each end. In addition, the open frontal area of filter honeycombs is often lower. For clean filters inlet and outlet effects can contribute as much as 30-40 % of the total pressime drop, especially at high flow rates. The turbulent entrance effects as result of the developing flow inside channels is typically lumped into these contributions. The inlet and outlet contributions are described by terms proportional to the kinetic energy, with the proportionality constant Cj. 

The additional pressure losses between (A) and (B) include the friction losses and pressure losses in all the pipe fittings such as valves, elbows, expansions, contraction branches, and bypasses. Pressure is also lost at entry and exit as well. Such pressure losses are expressed in terms of the Darcy-Weisbach equation and in terms of pressure loss factors for each fitting. 

This problem can also be solved using the 2-K method in conjunction with Eq. (2.19). For a hole, the fiictional losses are only due to riie entrance and exit effects. Thus, 0.5 + 1.0 = 1.5. Fori = 1.2, firom Figure 2.3 (or equations in Table 2.7) (P, -P j/Pj = 0.536 and it follows thatPj = 2.32 bar. Since the ambient pressure is well below this value, the flow will be choked. From Figure 2.4 (or equation in Table 2.7), the expansion factor, Y, is 0.614. The upstream gas density is... 

Further reductions in reservoir pressure move the shock front downstream until it reaches the outlet of the no22le E. If the reservoir pressure is reduced further, the shock front is displaced to the end of the tube, and is replaced by an obflque shock, F, no pressure change, G, or an expansion fan, H, at the tube exit. Flow is now thermodynamically reversible all the way to the tube exit and is supersonic in the tube. In practice, frictional losses limit the length of the tube in which supersonic flow can be obtained to no more than 100 pipe diameters. 

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