Flow with Friction Losses

Example 8 Compressible Flow with Friction Losses Calculate the discharge rate of air to the atmosphere from a reservoir at 10 5 Pa gauge and 20°C through 10 m of straight 2-in Schedule 40 steel pipe (inside diameter = 0.0525 m), and 3 standard radius, flanged 90° elbows. Assume 0.5 velocity heads lost for the elbows. 

For commercial steel pipe, with a roughness of 0.046 mm, the friction factor for fully rough flow is about 0.0047, from Eq. (6-38) or Fig. 6-9. It remains to be verified that the Reynolds number is sufficiently large to assume fully rough flow. Assuming an abrupt entrance with 0.5 velocity heads lost, 

Before accepting this solution, the Reynolds number should be checked. At the pipe exit, the temperature is given by Eq. (6-120) since the flow is choked. Thus, T , = T = 244.6 K. The viscosity of air at this temperature is about 1.6 x 10 5 Pa s. Then 

At the beginning of the pipe, the temperature is greater, giving greater viscosity and a Reynolds number of 3.6 x 10. Over the entire pipe length the Reynolds number is very large and the fully rough flow friction factor choice was indeed valid. 

Once the mass flux G has been determined, Fig. 6-21a or 6-21 b can be used to determine the pressure at any point along the pipe, simply by reducing 4fL/DH and computing p2 from the figures, given G, instead of the reverse. Charts for calculation between two points in a pipe with known flow and known pressure at either upstream or downstream locations have been presented by Loeb (Chern. Eng., 76[5], 179-184 [1969]) and for known downstream conditions by Powley (Can. J. Chem. Eng., 36, 241—245 [1958]). 

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Example 8 Compressible Flow with Friction Losses. 6-25... 

This is a statement of Bernoulli s theorem the quantity v2l2+Plp+gh is constant throughout the fluid for steady, irrotational flow. Equation A.33 is the same as equation 1.11. It will be recalled that, for rotational flow with friction, the engineering form of Bernoulli s equation applies only along a streamline and allowance must be made for frictional losses. 

Equation (2.10-15) for laminar flow with a = for a Newtonian fluid gives values reasonably close to those of Eq. (3.5-16) for /i = 1 (Newtonian fluid). For turbulent flow the frictional loss can be approximated by Eq. (2.10-15), with a = 1.0 for non-Newtonian fluids (S2). 

From equation 60 one can obtain a theoretical power requirement of about 900 kWh/SWU for uranium isotope separation assuming a reasonable operating temperature. A comparison of this number with the specific power requirements of the United States (2433 kWh/SWU) or Eurodif plants (2538 kWh/SWU) indicates that real gaseous diffusion plants have an efficiency of about 37%. This represents not only the barrier efficiency, the value of which has not been reported, but also electrical distribution losses, motor and compressor efficiencies, and frictional losses in the process gas flow. 

Eig. 11. Power saving for variable speed drives. Power input for variable speed adjusts with flow to naturally match the frictional losses. FIC = flow... 

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 ... 

Vanes may be used to improve velocity distribution and reduce frictional loss in bends, when the ratio of bend turning radius to pipe diameter is less than 1.0. For a miter bend with low-velocity flows, simple circular arcs (Fig. 6-37) can be used, and with high-velocity flows, vanes of special airfoil shapes are required. For additional details and references, see Ower and Pankhurst The Mea.surement of Air Flow, Pergamon, New York, 1977, p. 102) Pankhurst and Holder Wind-Tunnel Technique, Pitman, London, 1952, pp. 92-93) Rouse Engineering Hydraulics, Wiley, New York, 1950, pp. 399 01) and Joreensen Fan Engineerinp, 7th ed., Buffalo Forge Co., Buffalo, 1970, pp. Ill, 117, 118). 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

Skin friction loss. Skin friction loss is the loss from the shear forces on the impeller wall caused by turbulent friction. This loss is determined by considering the flow as an equivalent circular cross section with a hydraulic diameter. The loss is then computed based on well-known pipe flow pressure loss equations. 

Consider the pressure loss in a duct with straight, uniform cross-sectional area. The pressure loss is caused by friction. When different air sheets move against each other, friction is generated. The velocity and thermodynamic properties of air influence the friction. The duct wall has an overall roughness, which causes vortices to be formed with resulting friction in gas. The velocity has a pronounced effect in flow with low velocity, the vortices are small. Eor a straight duct the pressure loss Ap can be determined from... 

Cross-sectional area There is a direct relationship between flue flow and the cross-sectional area. The draft is unaffected by the cross-sectional area but the frictional losses decrease as the area is increased, resulting in greater flow. Too great an area, however, will lead to a low velocity with its attendant problems of down-wash and possible condensation. 

The property of a fluid that resists any force such as atmospheric or pump pressure, tending to produce flow. Viscosity is a function of the fluids cohesive forces and generally decreases with increase in temperature. Also, friction losses decrease with increase in temperature. 

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