Rough pipe frictional pressure loss

The friction factor depends on the Reynolds number and duct wall relative roughness e/D, where e is the average height ol the roughness in rhe duct wall. The friction factor is shown in Fig. 9.46. For a Urge Reynolds number, the friction factor / is considered constant for rough pipe surfaces. The friction pressure loss is Ap c. ... 

Frictional Pressure Loss in Rough and Smooth Pipe... 

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. 

We also have the Fanning friction factor,/, which equals 2(j) and the Moody friction factor/, which equals 8(, just as we saw earlier when discussing frictional pressure loss in rough and smooth pipe for Newtonian fluids. 

The Beggs and Brill correlation significantly underpredicts pressure loss (34%) due to the assumption of smooth pipe friction factors. The smooth pipe friction factors in the original correlations were substituted with rough pipe friction factors to produce revised Beggs and Brill correlations. 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

Petrol flows through a horizontal pipe with DN25 (internal diameter dj = 27.2 mm, cross sectional areapR = 5.81 x 10 " m ) and a length of 100 m. At a distance of 1 = 10 m downstream a leak with a cross sectional area of Fl = 7.85 X 10 m opens. Upstream of the leak there is a shut-off valve with a friction coefficient = 0.8. The built-in devices downstream from the leak are represented by the friction coefficient Ca = 3. The roughness of the pipe material is k = 0.4 mm and the coefficient of discharge p = 0.62. The pressure upstream is Pi = 2 bar (it is assumed to be constant despite flow and losses from the leak). The atmospheric pressure is pa = 1 bar. 

The first set of constraints represents the mass conservation law at each node of the water network. The second set describes the energy (head) losses for each pipe in the network to relate the pressure drop (head loss), due to friction, to the pipe flow rate and the diameter, roughness, material of construction, and length of the pipe. In this work, the commonly used Hazen-Williams empirical formula (Alperovits Shamir, 1977 Cunha Sousa, 1999 Coulter Morgan, 1985) is used. The third set of constraints includes bounds on variables such as minimum head or flowrate requirements. This set also includes constraints to ensure that only one diameter can be selected for each pipe (stream), a more realistic representation rather than having a split-pipe design. 

Many are surprised to find that cyclone pressure drop decreases with increasing solid load, wall roughness or cyclone body length. After aU all three give rise to increased wall friction in the cyclone body and, from oiu- experience with pipe flow, we expect this to cause increased frictional loss and, therefore, higher pressure drop. 

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