# Pipe Friction Handbook

Calculating the friction loss in a given pipe system includes two things. Calculation of friction loss in straight pipes and calculating the friction loss in pipe fittings e.g. bends, fittings, valves etc. and equipment. The article will describe how to calculate friction loss in straight pipes and fittings including examples at the end.

## Pipe Friction Handbook

The flow regime in the pipe shall be known in order to calculate the friction loss. This is done by calculating the Reynolds number. The dimensionless Reynolds number is the ratio of inertial forces to viscous forces see more on Wikipedia.

The friction coefficient shall be determined in order to calculate the friction loss in the straight pipes. It is a function of surface roughness and flow type. One way to determine it is by using The Moody Diagram. It show the Darcy-Weisbach friction factor as function of roughness and Reynolds number and is a quick way to quickly determine the friction factor.

An alternative way to determine friction loss in straight pipes is to use the Hazen-Williams equation. It has the advantage that the factor C is independent of the Reynolds Number and consequently the cumbersome procedure of determining the friction coefficient is avoided. The disadvantage is that the procedure is only valid for water, at room temperature and at conventional flow velocities.

There are several ways to calculate the friction loss in fittings i.e. bends, valves, size changes, etc. One way is to treat it as added equivalent length to the straight pipe friction loss calculation and another to calculate the friction loss for each fitting. The first approach will be described here.

Step 3 is to determine the friction coefficient by either using the Moody Diagram or by calculating it using the Colebrook equation. Steel pipe with some fouling is used in the example and the roughness is estimated to ks=0.5mm based on table 2.

Step 5 The next thing after having determined the friction loss of the straight pipe is to determine the friction loss in fittings. The 90 bends has a radius of 100mm hence R/D=2 giving a resistance coefficient of λ=0.30 (see table 4). The friction loss for each bend is:

The head loss that occurs in pipes is dependent on the flow velocity, pipe length and diameter, and a friction factor based on the roughness of the pipe and the Reynolds number of the flow. The head loss that occurs in the components of a flow path can be correlated to a piping length that would cause an equivalent head loss.

Head loss is a measure of the reduction in the total head (sum of elevation head, velocity head and pressure head) of the fluid as it moves through a fluid system. Head loss is unavoidable in real fluids. It is present because of: the friction between the fluid and the walls of the pipe; the friction between adjacent fluid particles as they move relative to one another; and the turbulence caused whenever the flow is redirected or affected in any way by such components as piping entrances and exits, pumps, valves, flow reducers, and fittings.

Frictional loss is that part of the total head loss that occurs as the fluid flows through straight pipes. The head loss for fluid flow is directly proportional to the length of pipe, the square of the fluid velocity, and a term accounting for fluid friction called the friction factor. The head loss is inversely proportional to the diameter of the pipe.

The value of the friction factor is usually obtained from the Moody Chart, an example of which is shown below. The Moody Chart can be used to determine the friction factor based on the Reynolds number and the relative roughness.

The frictional head loss can be calculated using a mathematical relationship that is known as Darcy's equation for head loss. The equation takes two distinct forms. The first form of Darcy's equation determines the losses in the system associated with the length of the pipe.

The sequence of steps necessary to solve this problem is first to determine the flow velocity. Second, using the flow velocity and the fluid properties given, calculate the Reynolds number. Third, determine the friction factor from the Reynolds number and the relative roughness. Finally, use Darcy's equation to determine the head loss.

The losses that occur in pipelines due to bends, elbows, joints, valves, etc. are sometimes called minor losses. This is a misnomer because in many cases these losses are more important than the losses due to pipe friction, considered in the preceding section. For all minor losses in turbulent flow, the head loss varies as the square of the velocity. Thus a convenient method of expressing the minor losses in flow is by means of a loss coefficient (k). Values of the loss coefficient (k) for typical situations and fittings is found in standard handbooks. The form of Darcy's equation used to calculate minor losses of individual fluid system components is expressed by Equation 3-15.

Minor losses may be expressed in terms of the equivalent length (Leq) of pipe that would have the same head loss for the same discharge flow rate. This relationship can be found by setting the two forms of Darcy's equation equal to each other.

Typical values of Leq/D for common piping system components are listed in Table 1. The equivalent length of piping that will cause the same head loss as a particular component can be determined by multiplying the value of Leq/D for that component by the diameter of the pipe. The higher the value of Leq/D, the longer the equivalent length of pipe.

This chapter considers friction head loss in closed pipe systems. The work is straightforward once the components are understood and inherent weaknesses in theoretical calculation are overcome by adaptation to each particular water system. In a dynamic system, pressure decreases along the length of the pipeline; the Hydraulic Grade Line slopes downward, designating pressure loss from friction created as the water encounters the sides of the pipe. Friction losses occur with every foot of pipe length, and this must be included in head loss calculations. Normal flow in water pipes is turbulent, and that turbulence increases with pipe roughness; energy is spent, and pressure drops over length. In a large diameter pipe, less of the water is actually touching the sides of the pipe and encountering friction, than in a small diameter pipe. With the Hazen-Williams formula came a new designation of pipe roughness.

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Drainage fixture unit (DFU) values for the major model plumbing codes Typical resistance coefficients for valves and fittings Water supply fixture units (WSFU) Surface roughness coefficient (C) values for various types of pipe Typical hot water temperatures for plumbing fixtures and equipment Building occupant demographic classifications Hot water demand per fixture for various types of buildings Gallons (liters) of water per hour per fixture scfm to acfm conversions Basic vacuum pressure measurements Conversions from torr to various vacuum pressure units IP and SI pressure conversions Barometric pressures corresponding to altitude Factors for flow rate reduction due to altitude Physical and combustion properties of commonly available fuel gases Average physical properties of natural gas and propane Approximate gas demand for common appliances Specific gravity of a variety of gases Fractions, decimal equivalents, and millimeter equivalents Temperature equivalencies

These conditions will be met with water that is not loaded and that is carried through pipes made of plastic, asbestos cement, centrifuged cement or made of any non-corrodible material or having a smooth lining. In practice, k = 0.1 mm will be the applicable roughness in view of the inevitable minimum deterioration that will take place over time, although k = 0.03 mm will be theoretically accepted in new pipes. For all usual materials, roughness k figures are those provided below, applicable to average utilisation conditions, inclusive of joints (table 53).

When such pipes carry relatively aggressive, corrosive, scale-forming or laden water, it is accepted that mean roughness will reach approximately k = 2 mm. In low aggressivity, low scale-forming non-chlorinated raw water, this coefficient becomes k = 1 mm. In lightly laden raw water and filtered water that is neither aggressive nor scale forming and that has undergone anti-algae treatment, k = 0.5 mm is permissible.

Head loss in straight piping is a result of pipe friction, whichis a function of the surface rough-ness of the interior pipe wall,the inside diameter of the pipe and the fluid velocity, density andviscosity.

The head losses due to friction resulting from actual length offlow path are minor com-pared to losses due to changes in directionof flow path, obstructions in flow path, sudden or gradual changesin the cross-section and shape of flow path.

The following tables list K values for each illustrated type ofvalve and fitting. These coefficients are given as the product ofthe friction factor for the desired size of clean commercial steelpipe with flow in the zone of complete turbulence, and a constant,which represents the equivalent length L/D for the valve or fittingin pipe diameters for the same flow conditions.