Pipe flow example calculations

Example 9 Pipe Distrihator A 3-in schedule 40 (inside diameter 7.793 cm) pipe is to be used as a distributor for a flow of 0.010 mVs of water (p = 1,000 kg/m, i= 0.001 Pa s). The pipe is 0.7 m long and is to have 10 holes of uniform diameter and spacing along the length of the pipe. The distributor pipe is submerged. Calculate the required hole size to limit maldistribution to 5 percent, and estimate the pressure drop across the distributor. 

Pipecalc 2.0, Gulf Publishing Company, Houston, Texas. Note Pipecalc 2.0 will calculate the compressibility factor, minimum pipe ID, upstream pressure, downstream pressure, and flow rate for Panhandle A, Panhandle B, Weymouth, AGA, and Colebrook-White equations. The flow rates calculated in the above sample calculations will differ slightly from those calculated with Pipecalc 2.0 since the viscosity used in the examples was extracted from Figure 5, p. 147. Pipecalc uses the Dranchuk et al. method for calculating gas compressibility. 

Example calculations are included, and Figure 2-52 illustrates the effect of pipe size on the placement of the flow regime. 

Centrifugal pumps, 181 Discharge systems, 187 Example calculation, 186 Flow friction losses, 185. 186 Friction losses, pipe, see Chapter 2 Friction, 188 Pressure head, 184—186 Static head, 184-186 Suction head, 184, 185 Suction lift, 184, 185 Suction systems, 186 Hvdroclones, 265—267 Application system, 267 Ignition, flammable mixtures, 493 Impellers, centrifugal, reducing diameter, 203 Impellers,... 

Although this is a simple example it serves to illustrate the method of calculating the weighted average strain and this will be utilized in subsequent sections dealing with realistic mixing equipment. It will be clear, however, from this example of pipe flow that it is a straightforward procedure to evaluate the residence times and strains and hence WATS if the velocity profile is known. 

Example 6.1. Light hydrocarbons are often stored in spheres and are transported by pipeline at moderate to high pressures in pipelines to chemical plants. To minimize pressure drop, pipeline diameter may be higher than that at the plant. Smaller pipe diameters are preferred in plants to minimize the cost of instrumentation and process control equipment such as valves and flow meters. Calculate the pressure drop, in mbar, resulting from a reduction of 6" Sch40 pipe to 4" Sch40 pipe transporting 10000 kg of n-butane at 60 °F and 7 atm. 

For two cases of streamline flow (selected from those identified in the above example) calculate the pressure drop per 100 metres of pipe. 

When we substitute q, the viscosity for a Newtonian liquid, by the apparent viscosity for AD pastes, the calculated AP values will be roughly correct. For the above example AP over 20 m pipe length would become with the Poiseuille equation 1.0 x W N/m or 1 Bar. With the more precise relation for pseudoplastic flow the calculated pressure drop would have been 0.7 bar. The Poiseuille equation presents a conservative estimate for pseudoplastic liquids. 

A Example Calculations of Droplet Sizes in Pipe Flow 311... 

As discussed above, the flow curves of polymer fluids can be obtained by Equations 8.18 and 8.38 (or 8.39), and the viscosities of the fluids can be calculated by Equation 8.41. While deriving these equations, one of the assumptions is that the flow pattern is constant along the pipe. However, in a real capillary flow, the polymer fluid exhibits different flow patterns in the entrance and exit regions of the pipe. For example, the pressure drops at the die entrance and exit regions are different from AP/Z. Therefore, corrections, e.g., Bagley correction, are needed to address the entrance and exit effects. Another assumption is that there is no slip at the wall. However, in a real flow, polymer fluid may slip at the wall and this reduces the shear rate near the wall. The Mooney analysis can be used to address the effect of the wall slip. In addition, the velocity profile shown in Figure 8.13 is a parabolic flow. However, the tme flow in the die orifice is not necessarily a simple parabolic flow, and hence Weissenberg-Rabinowitsch correction often is used to correct the shear rate at the wall for the non-parabohc velocity profile. 

Example 20.2-2 Heating a flowing solution A viscous solution in laminar flow is flowing steadily through a narrow pipe. At a known distance along the pipe, the pipe s wall is heated with condensing steam. Find a differential equation from which the temperature distribution in the pipe can be calculated. 

Example 6 Losses with Fittings and Valves It is desired to calculate the liquid level in the vessel shown in Fig. 6-15 required to produce a discharge velocity of 2 m/s. The fluid is water at 20°C with p = 1,000 kg/m and i = 0.001 Pa - s, and the butterfly valve is at 6 = 10°. The pipe is 2-in Schedule 40, with an inner diameter of 0.0525 m. The pipe roughness is 0.046 mm. Assuming the flow is tiirhiilent and taking the velocity profile factor (X = 1, the engineering Bernoulli equation Eq. (6-16), written between surfaces 1 and 2, where the... 

Example 8 Compressible Flow with Friction Losses Calculate the discharge rate of air to the atmosphere from a reservoir at 10 Pa gauge and 20 G through 10 m of straight 2-in Schedule 40 steel pipe (inside diameter = 0.0525 m), and 3 standard radius, flanged 90 elhows. Assume 0.5 velocity heads lost for the elhows. 

Approximate prediction of flow pattern may be quickly done using flow pattern maps, an example of which is shown in Fig. 6-2.5 (Baker, Oil Gas]., 53[12], 185-190, 192-195 [1954]). The Baker chart remains widely used however, for critical calculations the mechanistic model methods referenced previously are generally preferred for their greater accuracy, especially for large pipe diameters and fluids with ysical properties different from air/water at atmospheric pressure. In the chart. 

An important practical question is, what is the representative pipe diameter in loading circuits comprising different sizes of pipe This has a large effect on the values calculated for velocity and velocity-diameter product. As an example, static ignition of ester mist in a rail car (5-1.3.1) involved 1450 gpm through a 6-in. pipe (v = 5 m/s and vd = 0.76 mVs) followed by a short 4-in. dip pipe assembly (y = 11 m/s and vd = 1.15 mVs). Were nonconductive liquid flow rate restrictions applied to the semiconductive ester (time constant —0.01 s) involved in this fire, the flow rate based on the 4-in. pipe would be unacceptably large based either on a 7 m/s maximum velocity or a 0.80 mVs maximum vd product. However, based on the 6-in. pipe upstream the flow velocity is less than 7 m/s and also meets API s vd < 0.80 mVs criterion. 

Pressure drop through line systems containing more than one pipe size can be determined by (a) calculating the pressure drop separately for each section at assumed flows, or (b) determining the R totals iox each pipe size sep>-arately, and then converting to one selected. size and using that for pressure drop calculations. For example, using... 

Example 5 A stainless steel pipe is to be used to convey an aerated reducing acid at high velocity. If the concentration of dissolved Oj is 10 mol dm (10 mol cm ) calculate whether or not the steel will corrode when (a) the acid is static, (b) the acid is moving at high velocity. Assume that the critical current density for passivation of the steel in the acid is 200/iAcm the thickness of the diffusion layer is 0-05 cm when the acid is static and 0-005 cm when the acid flows at a high velocity assume the diffusion coeffi-... 

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