Head loss, pipelines

The total annual cost of a pipeline consists of a capital charge plus the running costs. The chief element of the running cost will be the power required to overcome the head loss which is given by equation 3,20 ... 

Pumps are devices for supplying energy or head to a flowing liquid in order to overcome head losses due to friction and also, if necessary, to raise the liquid to a higher level. The head imparted to a flowing liquid by a pump is known as the total head Ah. If a pump is placed between points 1 and 2 in a pipeline, the heads for steady flow are related by equation 1.14... 

Let us imagine that the six pumps in Fig. 23.1 have not run for a few days. The water level in the sump and the level of Lake Michigan will be the same. I now start all six pumps at the same time. An hour later, the water level in the sump is 12 ft below the water level in the lake. This 12 ft is called feet of head loss. If the pipeline is 3 mi long, we say we have lost 4 ft of head per mile of pipeline. ... 

The additional frictional losses due to pipeline fittings such as elbows may be added to the velocity head loss N = 4fL/DH using the same velocity head loss values as for incompressible flow. This works well for fittings which do not significantly reduce the channel cross-sectional area, but may cause large errors when the flow area is greatly... 

Other energy gradients could be plotted as in Fig. 10.2, showing the head loss just barely above the minimum pipe diameter for a positive minimum flow in the pipeline. 

Horsley, R.R. Reizes, J.A. The Effect of Zeta Potential on the Head Loss Gradient for Slurry Pipelines with Varying Slurry Concentrations, in Proc. 7 Int. Conf. Hydraulic Transport of Solids in Pipes, Stephens, H.S. Gittins, L. (Eds.), BHRA Fliud Engineering Cranford, U.K., 1980, pp. 163-172. 

The first, second, and third terms in Equation 3-2 represent pressure head, velocity head, and static differences respectively. Equation 3-2 is used for investigating energy distributions or determining pressure differentials between any two points in a pipeline. Incorporating the head loss due to friction, hL, with constant pipe diameter, i.e., V, = V2, Equation 3-2 becomes... 

The head loss due to friction has been neglected in the calculations but it is very important for long pipelines and in the case of elbows, valves, tees, and other restrictions. In the case of aqueduct design, restrictions were necessary to control flow rate. In the case of pipe flow, straight lines are prefared and all obstructions and changes in direction should be minimized to minimize pressure drop. 

Babcock, H.A. (1967). Head loss in pipeline transportation of solids. Proc. P World Dredging Conf WODCON evf York 1 261-289. 

Eastwood and Sarginson described the experimental investigation of the effect of transition curves on the head loss in flow through 90° bends in pipelines [41]. They observed that for purely circular bend the loss at the bend could be expressed in terms of the equivalent length (L ) of the straight pipe to cause the same loss. 

Since the friction factor in a horizontal pipeline is related to the friction head loss, hf (units of length), by... 

For a more general case of vertical flow in a pipeline network with varying pipe cross-sectional area and head losses and gains due to pumps (positive head), turbines (negative head), valves and fittings (negative head), the modified Bernoulli equation gives ... 

The head loss due to friction in the pipeline alone is related to the pressure drop between points 3 and 2 ... 

Babcock, H. A. 1967. Head losses in pipeline transportation of solids. Paper presented at First World Dredging Conference, WODCON I, the Netherlands. 

Lokon, H. B., P. W. Johnson, and R. R. Horsley. 1982. A Scale-up Model for Predicting Head Loss Gradients in Iron Ore Slurry Pipelines. Working paper B-2, BHRA Group, Hydrotransport 8. 

This 12 ft is called "feet of head loss." If the pipeline is 3 mi long, we say we have "lost 4 ft of head per mile of pipeline."... 

The required diameter of the pipeline is mainly determined by the pumping capacity of the dredger but may also be influenced by the type of material to be transported, the length of the pipeline, the number of branches, etc If the diameter of the pipeline is too small, friction as a result of high velocities may cause excessive head loss, while a too large diameter may result in deposition of fill material inside the pipeline. 

The loss of 12 ft of head as the water flows through the pipeline is due to friction that is, 12 feet of head is converted to heat. But why do we have a temporary loss of an extra 3 ft The answer lies in the concept of acceleration. 

Assume a pipe of length L, and let the head NX (previously explained as a distance upstream from the pipeline valve) be denoted by h. Consider the friction loss in the pipe to be represented as hf= kVA/2g, where k is assumed to be constant, although actually it may vary with the velocity unless the pipe is very rough. With these assumptions the energy equation written between X and N becomes... 

Ppl - pressure losses in the pipeline connecting compressor outlet with the well head of the injection well, kg/cm ... 

For turbulent flow, losses are proportional to the square of the mean velocity. It is therefore customary to express pipeline losses in terms of velocity heads v /2g. The loss associated with a particular fitting may be wi itten as... 

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