## Fig. 1. Simplified sketch of experiment that Reynolds used to study and define the three regimes of fluid flow. |

Tolerances that exist in today's high-pressure hydraulic systems demand tight control of system contamination. Contamination that is built into systems during manufacture and assembly must be removed before start-up to insure proper and predictable system performance throughout its service life.

A new or rebuilt hydraulic system should be flushed before it becomes operational. The concept of flushing involves loosening and removing contamination particles inside the system by forcing flushing fluid through it at high velocity. In theory, this leaves the inside walls of the fluid conductors at the same cleanliness level as the fluid. Then, during normal operation, the system will experience only externally and internally generated contamination — controllable with appropriate filtration.

Typical instructions state that flushing must be accomplished at normal system fluid velocities for a certain period of time with a certain level of filtration. More stringent specifications may call for a particular fluid contamination level and require documentation by fluidcontamination analysis.

One shortcoming of all these flushing methods is that they are based on procedures to clean the fluid, but ignore the interior cleanliness of the system. Even if the tubing and conductors have been installed with the greatest of visual care, the human eye can only see particles that are larger than 40 µm. That degree of cleanliness is well below the needs of even the crudest and most elementary hydraulic system.

**How high a velocity?**The critical variable in flushing to achieve acceptable fluid and conductor cleanliness is fluid velocity. Traditional flushing methods usually establish this velocity in one of two ways:

- the velocity must be high enough to achieve a Reynolds Number (NR) of 3000 or more, or
- the velocity must meet or exceed the system fluid's normal operating velocity as designed.

Experience has shown that neither of these flushing velocities is sufficient to assure the cleanliness of the ID of the system's conductors. A short review of basic fluid dynamics explains why.

Dimensionless N_{R}s are used (along with other factors) to classify fluid flow as either *laminar* , *turbulent* , or somewhere in between, Figure 1. N_{R} depends on the fluid's viscosity and velocity and the ID of the pipe. The flow condition that exists when N_{R} is less than 2000 is termed laminar, signifying orderly flow with parallel streamlines. When N_{R} is greater than 3000, the flow becomes turbulent, defined as the condition when fluid streamlines are no longer orderly. Between Reynolds Numbers of 2000 and 3000, flow exists in transition. This sometimes is called the critical zone.

Fortunately, the hydraulic fluid velocity required to achieve the textbook definition of turbulent flow is well within the recommended fluid velocity guidelines for hydraulic fluid conductors. This equation reinforces that statement:

N_{R} = VD/*v*

where: *V * is the fluid velocity in ft/sec, *D * is the ID of the fluid conductor in ft, and *v* is the fluid kinematic viscosity in ft^{2}/sec.

**First example**Suppose that the N

_{R}is 3000, the conductor is a 1-in. tube with a wall thickness of 0.049 in., and

*v*is 1.28831024 ft

^{2}/sec. Calculated fluid velocity then is 5.14 ft/sec, which corresponds to a flow rate of 10.24 gpm.

Note that the viscosity of a typical hydraulic fluid is influenced by temperature and pressure. That is, the hotter the oil, the higher the N_{R} for the same fluid velocity and pressure. The higher the pressure, the lower the N_{R} for the same fluid velocity and temperature. Thus, specifying that N_{R} should be 3000 is not a stringent requirement, but is well within the normal operating fluid velocities of a system. By definition, turbulent flow has been created because the fluid streamlines are no longer parallel, but sufficient fluid motion to clean the inside walls of the conductors has not been generated.

Even at the recommended maximum fluid velocities and N_{R}s for hydraulic-system working conductors, fluid flow still is not turbulent enough to greatly affect contamination on conductor walls. Boundary-layer fluid at the interior surfaces of the fluid conductor remains undisturbed.

**Second example**The N

_{R }for flow at normal system velocities next can be calculated using the same conductor size and kinematic viscosity as in the first example, but with the velocity increased to 20 ft/sec. This higher velocity results in a Reynolds Number of 11,671, which corresponds to a flow rate of 39.8 gpm.

As N_{R }increases, flow conditions go from laminar, through the critical zone, to turbulent. It has been proven empirically that once N_{R} exceeds 3000, resistance to fluid flow is a combination of the effects of turbulence and of viscous drag at the conductor wall. (This region of viscous drag at the conductor wall is known as the *viscous sub-layer.) * There is a transition zone within the turbulent flow range where flow resistance goes from being governed by turbulence effects to being governed by the roughness of the inside wall of the conductor.

This is apparent on the Moody diagram, Figure 2, which graphically demonstrates the relationship between Reynolds Number N_{R} , friction factor *f* , and *e* , the roughness of the conductor's inside surface. Resistance to flow through a fluid conductor — as represented by friction factor *f * — is only affected by the surface roughness of the fluid conductor when N_{R} is above 4000. This means that the majority of the resistance to flow is created by turbulence effects. Only when N_{R} is high enough so that surface projections of the conductor walls extend beyond the viscous sublayer does the surface come in contact with the turbulent flow and affect the pressure drop in the conductor.

**Surface roughness**For drawn tubing, average surface roughness

*e*is 0.000005 ft. If the conductor is the same 1-in. tubing with 0.049-in. wall thickness, ratio

*e*/D will be 0.000067. The Moody diagram indicates that for this conductor, N

_{R}must be at least 25,000 before the inside surface exposes its resistance to fluid flow. Therefore, to ensure the inside wall of the conductor will be cleaned, N

_{R}must be 25,000. For flow to be fully in the rough zone of turbulent flow, N

_{R}must be greater than 3.25 x 10

^{7}. Using 1.288 x 10

^{-4 }ft

^{2}/sec, the same fluid kinematic viscosity as in the first example, a N

^{R}of 25,000 corresponds to a fluid velocity of 42.8 ft/sec, or a flow rate of 85 gpm — still easily attainable with conventional hydraulic pumps.

**Real-world systems**It can be argued that if the walls of a conductor are not greatly affected by

*normal*system fluid velocities, contaminants lodged there will have little chance of entering the fluid stream. This may be partially true, but the argument applies only to smooth, straight conductors at steady flows and pressures. It is not representative of normal installations that combine straight runs, bends, and numerous fittings where flow patterns are only predictable empirically, and where pressure fluctuations and spikes are commonplace.

Depending on the severity of service that the system will experience, pressure spikes will dislodge contaminants held in the walls of the conductors and between fitting interfaces. Remember that in critical systems, 3- to 25-µm particles can impact system performance significantly. The only way to guarantee that conductor contamination does not affect system performance is to protect each component with a filter, an option so costly that it would not be used in most systems. Although flushing hydraulic system conductors at the normal system operating-fluid velocities can provide fluid velocities higher than flushing at a N^{R} of 3000, the inside wall of the conductors still will not be cleaned.

**High-velocity/pressure flushing**Flows that produce N

_{R}s > 25,000 are needed to ensure that conductor walls are exposed to turbulent flow. Because system conductors may consist of pipe, tube, and/or hose and associated fittings, the specification of a contractual number for N

_{R}is difficult and still does not guarantee that conductors will be cleaned. The best one can do is establish conditions that will maximize N

_{R}. These conditions are:

*the highest possible velocity at the lowest possible fluid viscosity*. Limiting factors are the conductor's pressure rating and the fluid's maximum operating temperature.

When flushing a system, the valving and actuators must be " jumpered" for safety reasons so the only resistance to fluid flow is the pressure drop in the conductors and fittings. When flow becomes turbulent, the pressure drop is proportional to the square of the velocity. Extrapolating this relationship to its maximum, the highest possible velocity occurs when the pressure drop in the conductor generated by fluid flow is equal to the maximum test pressure of the conductor. Flushing a system at these high flows and pressures expands and contracts the conductors and fittings as the pressure fluctuates while inducing highly turbulent flow. This optimizes the flushing action.

By equating the pressure drop in a conductor to the maximum pressure rating of that conductor, the maximum fluid velocity possible, along with the corresponding N_{R} , can be calculated. The temperature of the fluid directly affects its viscosity and is the other variable that can control N_{R} . Flushing pressure also affects viscosity, but this is hard to quantify because pressure in the pipe being flushed will vary from maximum at the pumping source to atmospheric at the conductor outlet.

The equation used to calculate head loss in the turbulent zone is:

h_{l} = fLV^{2}/2D,

where: *h _{l}* stands for head loss,

*f*is the friction factor found in the Moody diagram,

*L*is the conductor length in ft,

*V*is the fluid velocity, and

*D*is the conductor's ID in in.

This equation will calculate the maximum velocities and *NR* s that can be achieved for any given maximum flushing pressure.

Determining *f * for pipe flow requires iterative calculations using the Moody diagram. Given the pressure rating, ID, length, and relative roughness of the conductor, assume an *f * and then calculate the fluid velocity. Next, calculate N_{R} and determine a new *f * from the Moody diagram. Repeat the calculation until *f * converges.

The table above contains velocities and N_{R}s that have been calculated for 200 feet of Schedule-80 pipe using the maximum test pressure for the pipe and a surface roughness of 0.00015 ft ( for wrought iron pipe). These calculations did not take into account the pressure drop produced by the various fittings normally used, so the values for the attainable fluid velocities and N_{R}s are optimistically high. Also, special fluids with lower viscosities or flushing at higher temperatures to reduce the fluid viscosity can increase N_{R} .

The values determined for maximum flushing velocity and flow rate indicate that some of these conditions — mainly for lines with IDs smaller than 3/4in. — can be satisfied using conventional high-pressure pumps of appropriate flow capacity, although it may be difficult to induce the pressure fluctuations needed to dislodge contaminants. For systems with larger conductors, special methods must be used to achieve the necessary pressures, fluid velocities, and *NR* s to properly flush the lines.

**Calculated flushing velocities and N _{R}s for 200 ft of Schedule-80 pipe**

Pipe size —in. | D | Test pressure— psi |
| MaximumVelocity—fps | Flushingflow-rate—gpm | N_{R} |

1/2 | 0.546 | 3500 | 0.0033 | 65 | 48 | 23,000 |

3/4 | 0.742 | 2900 | 0.0024 | 74 | 100 | 35,000 |

1 | 0.957 | 2700 | 0.0019 | 84 | 188 | 52,000 |

1 1/2 | 1.500 | 2100 | 0.0012 | 96 | 528 | 93,131 |

2 | 1.939 | 1830 | 0.0009 | 117 | 1077 | 146,722 |