Slack flow

A special condition called slack flow can occur when the gravitational driving force exceeds the full pipe friction loss, such as when a liquid is being pumped up and down over hilly terrain. Consider the situation shown in Fig. 7-5, in which the pump upstream provides the driving force to move the liquid up the hill at a flow rate of Q. Since gravity works against the flow on the uphill side and aids the flow on the downhill side, the job of the pump is to get the fluid to the top of the hill. The minimum pressure is at point 2 at the top of the hill, and the flow rate (Q) is determined by the balance between the pump head (Hp = — w/g) and the frictional and gravitational resistance to flow on the uphill side (i.e., the Bernoulli equation applied from point 1 to point 2)  

The friction loss is determined by the fluid properties, the fluid velocity, and the pipe size. If the pipe is full of liquid, the velocity is determined by the pipe diameter and flow rate (Q), both of which are the same on the downhill side as on the uphill side for a constant area pipe. Since the downhill driving force is mainly gravity, the higher the hill the greater is the driving force relative to the full pipe flow resistance. Thus it is quite feasible that, for a full pipe, the downhill conditions will be such that 

The cross section of the fluid in the partially full pipe will not be circular (see Fig. 7-6), so the methods used for flow in a noncircular conduit are applicable, i.e., the hydraulic diameter applies. Thus, Eq. (7-61) becomes 

In order to find / for a given pipe, fluid, and flow rate, a trial-and-error (iterative) procedure is required  

Calculate, VRe = (D Qp)/A/x, and determine / from the Moody diagram (or Churchill equation). 

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Example 7-2 Slack Flow. A commercial steel pipeline with a 10 in ID carries water over a 300 ft high hill. The actual length of the pipe is 500 ft on the upstream side, and 500 ft on the downstream side of the hill. Find (a) the minimum flow rate at which slack flow will not occur in the pipe and (b) the position of the interface in the pipe when the flow rate is 80% of this value. 

Solution. Slack flow will not occur until the driving force (due to gravity) on the downstream side of the hill (from 2 to 3 in Fig. 7-5) exceeds the friction loss in this part of the pipeline that is, when Eq. (7-63) is no longer satisfied with A = itD1 /4 and Db = D. 

The method just outlined and illustrated is route specific. It is very flexible and simple to use. It can also be easily computerized if the GP data can be fed in as numerical values. Here we have illustrated its use in the context of a cross-country pipeline, such as a crude oil, products, or perhaps slurry pipeline, which might be commonly encountered by chemical engineers. The method is completely adaptable to any hydraulic flow problem and could be used equally well for a short in-plant pumping system analysis. It can help the designer of flow systems to avoid sometimes subtle traps for slack flow and siphons that might not be immediately obvious if the mechanical energy equation is applied only once between the initial and final points of the flow system. 

The words flume, launder, open channel, and slack flow are often used to express the same thing. In the following discussion, these words will be used interchangeably. Even though launders are crucial to mining, very little research on the subject has been published. Despite the lack of reference material on launders for slurries, it is important to start from basic principles. The analysis will focus initially on water flows. The reader will then be introduced to the complexity of slurry flows. The reader should appreciate that an upper practical limit on these flows is a 65% concentration of solids by weight. 

Two positive displacement WUson-Snyder pumps were installed at the main pump station. These were Mven by 746 kW (1000 hp) direct current motors. The booster station is connected to a water pond and draws water on demand to avoid slack flow by providing additional back pressure in low flow conditions. Choke stations are also provided for additional back pressure. According to Weston and Worthen, the pipeline used high-yield-strength steel rated at 413 MPa (60,000 psi). An allowance of 2.5 mm (0.1 in) for corrosion/erosion over a lifetime of 25 years was factored into the design. The thickness of the pipeline varied between 6.4-12.7 mm (0.25-0.5 in). 

Feed capacity is limited by putting a given amount of feed (RHS) in a feed capacity tank. The other type of limit is that necessary to keep flows from accumulating or stacking in the middle of the plant in one of the intermediate tanks (rows). To inhibit this stacking, high prices are placed on any material accumulation. These are called slack prices (SPRICES). 

There have been several studies in which the flow patterns within the body of the cyclone separator have been modelled using a Computational Fluid Dynamics (CFD) technique. A recent example is that of Slack et a/. 54 in which the computed three-dimensional flow fields have been plotted and compared with the results of experimental studies in which a backscatter laser Doppler anemometry system was used to measure flowfields. Agreement between the computed and experimental results was very good. When using very fine grid meshes, the existence of time-dependent vortices was identified. These had the potentiality of adversely affecting the separation efficiency, as well as leading to increased erosion at the walls. 

At this period the practice is to throw a little slack Into the furnace, with tho view of assisting in the reduction of tho oxidised compounds of lead whiuh may still exist, as well as to prevent the oxidation of the metal. This is the period of the fourth firing, and lasts forty minutes so that its effect takes place in about four houfs forty minutes from the hour of charging, Now the doors are opened, the smcltor pierces the tap-hole, and slows the reduced metal to flow out into the basin Sunk in the floor outside, Quicklims is thrown upon the slags which remain, in order to dry them he then pushes them towards the back, wheneo the assistant draws them out at the back doors. 

Vector of uncertain variables (supply temperatures, flow rates, and/or heat transfer coefficients) Hyperrectangular uncertainty range A Kuhn-Tucker multiplier (35) f Kuhn-Tucker slack variables (35) aL Load surplus, kW (26) crT surplus, K (25)... 

The theoretical estimate of Slack has predicted k = 1.7 W/(cm K) for room temperature thermal conductivity of GaN [12], The thermal conductivity of GaN layers grown on sapphire substrates by the HVPE method [23] was measured by Sichel and Pankove using the heat flow method [24], The room temperature thermal conductivity was k = 1.3 W/(cm K). Sichel and Pankove attributed the smaller value to high impurity content, at least 1018 cm 3, and the presence of small angle grain boundaries. 

Slack SM, Cui Y, IXiritto VT. The effects of flow on blood coagulation and thrombosis. Thrombos Haemost 1993 70 129-134. 

At very low temperatures, the thermal conductivity of 6H SiC could have a T 2 or T 3 temperature dependence [1]. For very pure or highly compensated material the temperature dependence is T 3. Slack [3] has shown the T 2 temperature dependence is due to the heat flow associated with phonons. Doping of SiC shifts the thermal conductivity peak toward higher temperatures [1-3]. For the 4H and 6H samples reported the measured conductivity is perpendicular to the C direction. 

Electrokinetic removal of nitrate from saline soil has been reported by several research groups. Application of an electric potential over a saline soil field resulted in increased salt content in drainage water and salt accumulation near the cathode (Gibbs, 1966). In addition, it was found that solute movement increased with greater electrical voltage. Cairo, Larson, and Slack (1996) reported that nitrate concentration increased from anode to cathode in saturated soil as solute flowed toward a horizontal drainage tube located adjacent and parallel to the cathode after application of a direct current (DC) electrical potential in field lysimeter experiments. However, after the soil became unsaturated, continued electrical input resulted in nitrate movement toward the anode. 

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