Roughness of pipe surface

A petroleum fraction is pumped 2 km from a distillation plant to storage tanks through a mild steel pipeline, 150 mm in diameter, at the rate of 0.04 m3/s. What is the pressure drop along the pipe and the power supplied to the pumping unit if it has an efficiency of 50% The pump impeller is eroded and the pressure at its delivery falls to one half. By how much is the flowrate reduced Density of the liquid = 705 kg/m3. Viscosity of the liquid = 0.5 mN s/m2. Roughness of pipe surface = 0.004 mm. 

The estimation of the roughness of the surface of the pipe often presents considerable difficulty. The use of an incorrect value is not usually serious, however, even for turbulent... 

The roughness of the surface of the inside of the pipe can have an important bearing on rates of heat transfer to the fluid, although Cope(i9), using degrees of artificial roughness... 

At higher Reynolds numbers, the friction factor is affected by the roughness of the surface, measured as the ratio e/D of projections on the surface to the diameter of the pipe. Values of e are as follows glass and plastic pipe essentially have e = 0. 

In laminar flow/ = 16/Re, whereas in turbulent flow the dependence of/ on Re is a function of the specific rheological behavior of the fluid and roughness of the walls of the inside of the drill pipe (91). A number of functional relationships between / and Re have been proposed for turbulent flow. Ignoring the effects of the roughness of the surface of the drill pipe, / can be approximately related to Re by a generalized form of the well-known Blasius equation for Newtonian fluids (90, 95)... 

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. 

Amplitude variable in variational analysis Parameter in least squares method minimization statement Ratio of eddy size to the bubble size, e = A/J,- (—) Represent small threshold value in convergence criterion Surface roughness of pipe (m)... 

The friction factor in Equations 2-54 and 2-55 is a function of the surface roughness of the pipe and the Reynold s number. Typical surface roughnesses of new commercial pipes are shown in Table 2-9. Old or corroded pipes may have a significantly higher roughness. 

Region l (Re < 2000) corresponds to streamline motion and a single curve represents all the data, irrespective of the roughness of the pipe surface. The equation of the curve is R/pu2 = 8/Re. 

Now the friction factor R/pu2 is a function of the Reynolds number Re and the relative roughness e/d of the pipe surface which will normally be constant along a given pipe. The Reynolds number is given by ... 

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