Friction Loss Calculation

Because the influence of gravitation pgh is negligible for horizontal (distribution) systems, this term is ignored in the equations. 

A is friction factor, dimensionless L is length, m d is internal diameter, m p is density, kg 

For turbulent flow the empirical formula of Colebrook-White applies  

This expression is difficult to use, as iteration is required. A simplified expression can be used with sufficient accuracy  

The formulas are represented in the Moody diagram, which allows a quick solution. 

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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. 

Note For quick estimates not as accurate as friction loss calculations... 

Hydraulic properties, that is, friction-loss calculations of proppant-laden fluids or slurries, are very important not only in the design of any hydraulic fracturing treatment but also in real-time monitoring of fracturing treatments. Recent advances (27, 28) in real-time fracture analysis have necessitated an accurate knowledge of bottomhole treating pressure (BHTP). To estimate BHTP, an accurate prediction of friction pressures of fluids in the flow conduit is required. It is possible to obtain the BHTP from the surface pressure with the following equation ... 

EXAMPLE 2.7-6. Rate of Flow from Pressure Measurements A liquid with a constant density p kg/m is flowing at an unknown velocity u, m/s through a horizontal pipe of cross-sectional area >4, m at a pressure Pi N/m, and then it passes to a section of the pipe in which the area is reduced gradually to A2 m and the pressure is P2. Assuming no friction losses, calculate the velocity u, and 02 if the pressure difference (p, — P2) is measured. 

In a vertical flow, it would not be possible to develop dunes, a bed, or saltation. There is no concentration gradient and the flow may be treated as pseudohomogeneous for friction loss calculations, as discussed in Section 4-4-3. 

In Chapter 4, it was clearly explained that the difference in density (or specific gravity) between the carried solids and the carrier liquid was an important parameter in friction loss calculations. This is, in basic terms, the concept of using a heavy medium (water and magnetite) as a carrier for coarse solids. 

In Eigure 4, the pressure drop per unit length (bar/m) due to friction losses calculated with the Friedel model is reported against the experimental values relative to the same pipe sections. In order to check the possible influence of some other parameters involved in the flow, the vapor quality at the entrance of each section has been classified in a discrete number of intervals, and the measurements belonging to each class have been reported with different marks in the figure (see attached key). It can be seen that no significant effect is associated with the vapor quality. 

Common cehter-to-center spacings for tubes and the approximate equivalent lengths of bends (for friction-loss calculations) are indiicated in Table 18-2. 

Tube-side Pressure Drop. Friction loss inside tubes can be computed from the general formulations given in Chap. 13, but the losses caused by enlargements, contractions, and turns must be included in the calculations. In order to account for nonisothermal flow, Sieder and Tate recommend multiplying the friction loss calculated by isothermal formulations such as F.q. (13-1), p. 395, b the dimensionless ratio for turbulent... 

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