Simple rule can be used to calculate friction loss in piping

Alejandro Anaya Durand
Institute Mexicano del Petróleo
Mexico City

• Equations [44212 bytes]

For determining pressure loss in piping, friction-loss tables are often more convenient than calculating the Reynolds number or finding the friction factor on a Moody chart, then calculating the friction loss by the Darcy or Fanning relationships.

Friction-loss tables can be found in the Crane Technical Paper, Hydraulic Institute Engineering Data Book, and several other references.^1-5 There are occasions, however, when such tables are not readily available to the engineer trying to estimate pressure drop in fluid flowing through pipelines.

Because friction loss is essentially a point function, it is only necessary to determine the pressure drop for a given set of conditions. The author has developed a simple rule for such calculations.

The rule

The Rule of Fours states that: The pressure drop of 400 gpm of water at 60° F. in a 4-in. clean, commercial, schedule-40 steel pipe is almost 4 psi/100 ft.

The accuracy of the rule can be improved considerably by applying another "four"; that is, to change 400 gpm to 400 gpm plus 4% (416 gpm).

This mnemonic statement can be used to calculate pressure drop for other fluids and pipe diameters with simple correction factors. The following sections will trace the development of the rule and correction factors.

Development

The Darcy equation is often used to calculate friction losses in fluid flow through pipes (Equation 1, Equations and Nomenclature). Volumetric flow is defined by Equation 2.

In Equation 2, the pipe area flow (S) can be calculated as a function of pipe diameter (Equation 3). Substituting Equations 2 and 3 into Equation 1 yields Equation 4.

Equation 4 shows that pressure drop varies approximately with the square of the flow and inversely with the fifth power of the diameter. (This is a second mnemonic rule.)

Considering this relationship, the Rule of Four, improved by the 4% correction can be expressed as shown in Equation 5. In Equation 5, DP is the pressure drop, in psi per 100 ft for water at 60° F. at a given flow rate and pipe diameter.

Corrections

The Darcy equation can be expressed for water conditions such as Crane (60° F.) in terms of pressure drop (Equation 6). Equation 7 is often used to calculate the Darcy friction factor for smooth pipes in turbulent flow.

Combining Equations 6 and 7 yields Equation 8, which can be used to obtain the pressure drop for water at 60° F. For liquids other than water at temperatures other than 60° F., Equation 9 can be used.

Dividing Equation 9 by Equation 8 and solving for fluid pressure drop yields Equation 10. It can also be shown that, for laminar flow, the correction factor, Fc, depends only on the ratio of the fluid's viscosity to water's viscosity (Equation 11).

The final, improved Rule of Fours can be expressed, for use with liquids other than water at 60° F., as Equation 12.

Example

The flow of a fluid with a specific gravity of 0.8 and a viscosity of 0.9 cP is 500 gpm in a 6-in. diameter schedule-40 pipeline. To estimate the pressure drop per 100 ft in psi, apply the Rule of Fours (Equation 12):

DP = 4 (500/416)2 (4/6)5 3 (0.8)0.8 (0.9/1.1)0.2 = 0.60 psi

To check this result, the author used the Darcy equation and a Moody chart. The resulting pressure drop was 0.58 psi, which is very close the result obtained using the Rule of Fours.

References

1. "Flow of fluids through valves, fittings, and pipe," Crane Technical Paper No. 410, Crane Co., 1982.

2. The Hydraulic Institute Engineering Data Book, 2nd edition, 1992, Hydraulic Institute, Cleveland.

3. The Cameron Hydraulic Data Book, Ingersoll-Rand, Woodcliff Lake, N.J., 16th edition, 1981.

4. Sandler, H.J., and Luckiewicz, E.T., Practical Process Engineering, McGraw-Hill Inc., 1987.

5. Knodsen and Katz, Fluid Dynamics and Heat Transfer, McGraw-Hill Inc., 1958.

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