Calculating Aeration Piping Friction Loss

In order to properly identify the performance requirements of a blower it is necessary to identify the inlet and discharge pressures. The friction losses in the inlet and discharge piping must be calculated to determine the total pressure requirement. This article details a simplified procedure for calculating piping losses.

Basics
The factors that affect pressure drop through air piping are largely intuitive. 

• Flow rate (fluid velocity)
• Pipe diameter
• Pipe length and fitting losses
• Pipe interior roughness
• Fluid density
• Fluid viscosity

The influence of these parameters may be obvious, but the mathematical relationships between them are not. The equations for calculating pressure drop can be complex and intimidating. Calculation is further complicated by the need to assume values for several of the parameters. The result is that pressure drop calculations are not precise, and ±10% should be considered reasonable accuracy. In order to accommodate this uncertainty, it is suggested that the design include the means to accommodate pressure excursions above and below the calculated values.

 

Alternate Methods

The classic method for calculating pressure drop is the Darcy-Weisbach equation, which appears in many forms. One common form is:

Where:
    Δpf = pressure drop, lbf/ft2
    f = friction coefficient, dimensionless
    L = length of pipe, ft
    D = pipe diameter (or hydraulic diameter for non-circular ducts), ft
    ρ = fluid density, slugs/ft3 (Note: 1 slug = 1lbm ∙ 32.174)
    V = velocity of fluid, ft/sec

The Darcy-Weisbach equation is taught in most fluid dynamics classes. It has the advantage of being applicable to any fluid and duct material. However, determination of the friction factor, f, can be challenging. It requires calculating the relative roughness (ε/D) and the Reynolds number (Re). These values in turn are used to determine the friction factor, f. This can be obtained graphically by using a Moody diagram or by iterative solution of the Colebrook equation.

Determining pressure drop for air flowing through a steel pipe is a common problem. Using Darcy-Weisbach can be cumbersome and time consuming. The Compressed Air and Gas Institute (CAGI) has presented an empirical equation that can be solved by iteration. (See Chapter 8, Compressed Air & Gas Handbook, https://www.cagi.org/resource-library) This formula can be written using convenient units as:

Where:
    Δpf = pressure drop from friction, psi
    qstd = air flow rate, scfm; scfm defined as air at 68°F, 14.7 psia, 36% Relative Humidity (RH)
    d = pipe diameter, in
    T = absolute air temperature, °R
    L = total length of pipe, feet
    pm = mean system absolute pressure, psia

Note that the impact of relative humidity in these calculations is negligible and is ignored.

To solve for Δpf an initial value is assumed, pm is calculated, and the assumed value used to calculate a new Δpf. The process is repeated until the desired accuracy is achieved. Sufficient convergence usually occurs after two or three iterations.

 

Pipe Fittings

Air distribution systems rarely, if ever, consist of just straight pipe runs. In practice, pipe fittings often create greater pressure losses than the system’s straight pipe. There are multiple ways to account for the effect of the elbows, tees, and other elements in a system. One of the most convenient is to include the effect of fittings by converting them to an equivalent length of straight pipe.

The equivalent lengths of fittings may be defined in terms of length/diameter (L/D). The tabulated value is multiplied by the nominal pipe size in feet to determine the equivalent length in feet.

 

 

The total equivalent length of pipe in a system, or segment of a system, is the sum of the actual pipe length and the total equivalent length of the fittings.

 

Other Considerations

There are often other components in the system that must be accounted for in the calculations. For example, inlet filters can create pressure drops that affect the inlet density and the necessary blower pressure ratio. The pressure loss across a given filter varies with flowrate and also varies with time as the filter accumulates dust. These changes are not readily predictable. Consequently, a fixed value is usually assumed for filter loss, typically corresponding to the Δp at max flow rate and with a dirty filter element. Typical values are 6” to 12” water (0.2 to 0.4 psig).

Valves are used at several locations in most systems. If they are used for isolation, they will be either fully open or completely closed. Valves, chiefly butterfly valves, are also used for throttling blowers and balancing air distribution between multiple processes. The pressure loss across a valve can be readily calculated if the position of the valve is known (See our article “The Basics of Aeration Control Valves-Part 1” for a deep dive on this). The designer has two choices: assume a valve position and calculate the pressure drop at the expected flowrate or assign an arbitrary value for the pressure drop. A common and conservative allowance for valve losses in aeration systems, for example, is 0.5 psi at the maximum flowrate.

Check valves are a special case. They are commonly employed to prevent flow backwards from the system through parallel blowers. Most air systems use a double disc design and not a swing check design. A spring assists the discs in closing to prevent backflow. A minimum pressure, the cracking pressure, is required to begin opening the discs and some pressure differential across the valve is necessary to hold the disc completely open. If better information is not available, the tabulated value may be used. However, it is recommended that the supplier be consulted for specific application guidance.

Silencers are often employed on the inlet and discharge blower piping. The pressure loss for a given airflow through them varies greatly depending on the design and manufacturer. The pressure drops through silencers, similar to losses through an orifice, is essentially proportional to the square of the air velocity.

Many blower applications include a fixed static pressure that must be included in calculating the required blower discharge. A common example of this is aeration. The blower discharge pressure must exceed the static head of water above the air release point before flow can occur.

Many systems include segments with different pipe diameters and air flows. These are handled by calculating the pressure drop in each segment in series and adding them.

It is usually desirable to develop a system curve, which shows the required pressure over a range of flows. To create a system curve, the pressure losses at several flows are added to the static pressure. For components where pressure loss is given at a single flow rate, for example silencers, the equivalent length of pipe can be back calculated and used for additional data points.

 

Example

Consider the piping system in Figure 1. The pressure drop between the blower and the vendor-supplied equipment must be determined at maximum airflow rate. The supplier requires 8.5 psi at the connection to their equipment. Ambient conditions are given in the figure.

 

Figure 1: Example Blower Piping System.

  

First, the equivalent length of pipe for the silencer must be calculated. The supplier specifies the pressure loss as 0.25 psi for a flow of 3,000 scfm at 14.7 psia and 68 °F. The equivalent length of pipe can be calculated by rearranging the formula for pressure loss given above.

Then the total equivalent length of pipe is calculated:

 

The first iteration of the pressure loss is calculated using an initial assumed value of 0.25 for the pressure loss.

The friction loss is recalculated using the value of Δp from the first estimate:

The difference between the results of the first and second estimates is negligible, indicating the solution has achieved sufficient convergence.

The required discharge pressure at the blower can be calculated:

 

Summary

There are many ways to estimate the pressure losses from friction for air flowing through pipes. The method presented here provides accuracy comparable to other methods with less effort. The method has the further advantage of eliminating the need for graphical information such as the Moody diagram. This enables it to be implemented in spreadsheets or similar software.

 

About the Author

Tom Jenkins has over forty years’ experience in blowers and blower applications. As an inventor and entrepreneur, he has pioneered many innovations in aeration and blower control. He is an Adjunct Professor at the University of Wisconsin, Madison and a WEF Fellow. Tom is the current Chair of the ASME PTC 13 Committee. For more information, visit www.jentechinc.com.

Originally published in the May 2024 issue of Blower & Vacuum Best Practices Magazine.

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