Pipe friction chart

Figure 3.8. Pipe friction chart Re2 versus Re for various values of e/d (also see fold-out in the Appendixi...

For a Newtonian fluid, the data for pressure drop may be represented on a pipe friction chart as a friction factor = (R/pu2) expressed as a function of Reynolds number Re = (udp/n). The friction factor is independent of the rheological properties of the fluid, but the Reynolds number involves the viscosity which, for a non-Newtonian fluid, is... 

Thus, the pipe friction chart for a Newtonian fluid (Figure 3.3) may be used for shearthinning power-law fluids if Remit is used in place of Re. In the turbulent region, the ordinate is equal to (R/pu2)n 0 fn5. For the streamline region the ordinate remains simply R/pu2, because Reme has been defined so that it shall be so (see equation 3.140). More recently, Irvine(25j has proposed an improved form of the modified Blasius equation which predicts the friction factor for inelastic shear-thinning polymer-solutions to within 7 per cent. 

Oil of density 950 kg/m3 and viscosity 10-2 Ns/m2 is to be pumped 10 km through a pipeline and the pressure drop must not exceed 2 x lt N/m2. What is the minimum diameter of pipe which will be suitable, if a flowrate of 50 tonne/h is to be maintained Assume the pipe wall to be smooth. Use either the pipe friction chart or the Blasius equation (R/pu1 = 0.0396/ -1/4). 

An air stream at approxin tely atmospheric temperature and pressure and containing a low concentration of carbon disulphide vapour is flowing at 38 m/s through a series of 50 mm dimneter tubes. The inside of flie tubes is covered with a thin film of liquid and both heat and mass transfer are taking place between the gas stream and the liquid film. The film heat transfer coefficient is found to be 100 W/m K. Using a pipe friction chart and assuming the tubes to behave as smooth surfaces, calculate ... 

Figure 2-3. Moody or regular Fanning friction factors for any kind and size of pipe. Note the friction factor read from this chart is four times the value of the f factor read from Perry s Handbook, 6th Ed. [5]. Reprinted by permission, Pipe Friction Manual, 1954 by The Hydraulic Institute. Also see Engineering DataBook, 1st Ed., The Hydraulic Institute, 1979 [2]. Data from L. F, Moody, Friction Factors for Pipe Flow by ASME [1].

The left-hand side of equation 10.224 is referred to as the y-factor for heat transfer ( //,). Chilton and Colburn found that a plot of against Re gave approximately the same curve as the friction chart (0 versus Re) for turbulent flow of a fluid in a pipe. 

Figure 11.7. Moody chart for pipe friction with smooth and rough walls (from Moody, 1944).

Determine the kinematic viscosity of the oil Use Fig. 6.1 and Table 6.2 or the Hydraulic Institute—Pipe Friction Manual kinematic viscosity and Reynolds number chart to determine the kinematic viscosity of the liquid. Enter Table 6.2 at kerosene and find the coordinates as X = 10.2, Y = 16.9. Using these coordinates, enter Fig. 6.1 and find the absolute viscosity of kerosene at 65°F as 2.4 cP. Using the method of Example 6.2, the kinematic viscosity, in cSt, equals absolute viscosity, cP/specific gravity of the liquid = 2.4/0.813 = 2.95 cSt. This value agrees closely with that given in the Pipe Friction Manual. 

Determine the Reynolds number of the liquid. The Reynolds number can be found from the Pipe Friction Manual chart mentioned in step 1 or computed from Re =2214 B/dk = 2214(500)/[(6.065)(2.95)] = 61,900. 

To use the Pipe Friction Manual chart, compute the velocity of the liquid in the pipe by converting the flow rate to cubic feet per second. Since there are 42 gal/bbl and 1 gal = 0.13368 ft3, 1 bbl = (42)(0.13368) = 5.6 ft3. With a flow rate of 500 bbl/h, the equivalent flow in ft3 = (500)(5.6) = 2800 ft3/h, or 2800/3600 s/h = 0.778 ft3/s. Since 6-in schedule 40 pipe has a cross-sectional area of 0.2006 ft2 internally, the liquid velocity, in ft/s, equals 0.778/0.2006 = 3.88 ft/s. Then, the product (velocity, ft/s)(internal diameter, in) = (3.88)(6.065) = 23.75. In the Pipe Friction Manual, project horizontally from the kerosene specific-gravity curve to the vd product of 23.75 and read the Reynolds number as 61,900, as before. In general, the Reynolds number can be found faster by computing it using the appropriate relation given in Table 6.1, unless the flow velocity is already known. 

Determine the friction factor of this pipe. Enter Fig. 6.2 at the Reynolds number value of 61,900 and project to the curve 4 as indicated by Table 6.3. Read the friction factor as 0.0212 at the left. Alternatively, the Pipe Friction Manual friction-factor chart could be used, if desired. 

Use this procedure for any fluid—crude oil, kerosene, benzene, gasoline, naptha, fuel oil, Bunker C, diesel oil toluene, etc. The tables and charts presented here and in the Pipe Friction Manual save computation time. 

We now have to thank Stanton and PanneU, and also Moody for their studies of flow using numerous fluids in pipes of various diameters and surface roughness and for the evolution of a very useful chart (see Fig. 48.6). This chart enables us to calculate the frictional pressure loss in a variety of circular cross-section pipes. The chart plots Re)molds numbers (Re), in terms of two more dimensionless groups a friction factor < ), which represents the resistance to flow per unit area of pipe surface with respect to fluid density and velocity and a roughness factor e/ID, which represents the length or height of surface prelections relative to pipe diameter. 

The Lapple charts for compressible fluid flow are a good example for this operation. Assumptions of the gas obeying the ideal gas law, a horizontal pipe, and constant friction factor over the pipe length were used. Compressible flow analysis is normally used where pressure drop produces a change in density of more than 10%. 

The friction factor depends on the Reynolds number and the surface conditions of the pipe. There are numerous charts and equations for determining the relationship between the friction factor and Reynolds number. The friction factor can be calculated by [63]... 

Flashing liquids, 134-146 Flow coefficients, Gv, for valves, 81 Friction loss, 68 Incompressible fluid, 71 Laminar flow, 77, 78, 86 Liquid lines, chart, 92 Long natural gas pipe lines, 120 Non-water liquids, 99 Pipe, 71... 

Note the friction factor used in equation 5.3 is related to the shear stress at the pipe wall, R, by the equation / = (R/pu2). Other workers use different relationships. Their charts for friction factor will give values that are multiples of those given by Figure 5.7. So, it is important to make sure that the pressure drop equation used matches the friction factor chart. 

The friction factor may be calculated from a knowledge of the fluid Reynolds number using the chart shown as Figure 13.2. Table 13.1 indicates the friction factors that correspond to zero and 80% conversion for the three pipe sizes of interest at two temperature levels. Examination... 

This procedure based on the friction factor chart is too stringent for large-diameter vessels, which behave nearly like smooth pipe, requiring inordinately large values of Re. 

The changing character of the flow in the different regions of the turbulent boundary layer explains certain aspects of the friction factor chart. If the absolute roughness of the pipe wall is smaller than the thickness of the viscous sublayer, flow disturbances caused by the roughness will be damped out by viscosity. The wall is subject to a viscous shear stress. Under these conditions, the line on the friction factor chart... 

---