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 the Reynolds Number for this conductor must be at least 25,000 before the inside surface exposes its resistance to fluid flow. To ensure the inside wall of the conductor will be cleaned, the Reynolds number must be greater than 25,000. For flow to be fully in the rough zone of turbulent flow, the Reynolds number must be greater than 3.25 × 107. Using 1.288 × 10-4 ft2/sec (the same fluid kinematic viscosity as in the first example), a Reynolds number of 25,000 corresponds to a fluid velocity of 42.8 fps, or a flow rate of 85 gpm — still easily attainable with conventional hydraulic pumps.

Real-world systems

One argument holds 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. In critical systems, 3- to 25-µm particles can impact system performance significantly. The only way to guarantee that conductor contamination (that can be released at any time during operation) 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 fluid velocities encountered during normal operation can provide fluid velocities higher than flushing at a Reynolds Number of 3,000, the inside wall of the conductors still will not be cleaned.

High-velocity, high-pressure flushing

Flows that produce Reynolds numbers greater than 25,000 ensure exposing conductor walls to turbulent flow. Because system conductors may consist of pipe, tube, hose, and associated fittings, the specification of a contractual Reynolds Number is difficult and still does not guarantee that conductors will be cleaned. The best you can do is establish conditions to maximize the Reynolds number. This is done by using 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.

Safe flushing of a system requires valves actuators to be bypassed so that 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 has the added advantage of expanding and contracting the conductors and fittings as the pressure fluctuates while inducing highly turbulent flow. This optimizes the flushing action.

Equating the pressure drop in a conductor to the maximum pressure rating of that conductor allows calculating the corresponding Reynolds Number and the maximum fluid velocity possible. The temperature of the fluid directly affects its viscosity and is the other variable that can control NR. Flushing pressure also affects viscosity, but this is difficult 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:

hl = fLV2/2D ,

where: hl = head loss,
f = friction factor found in the Moody diagram,
L = conductor length in ft,
V = fluid velocity, and
D = conductor’s ID in inches.

This equation will calculate the maximum velocities and Reynolds Numbers that can be achieved for any given maximum flushing pressure.

Determining the friction factor for pipe flow requires iterative calculations using the Moody diagram. Given the pressure rating, ID, length, and relative roughness of the conductor, assume a friction factor, then calculate the fluid velocity. Next, calculate the Reynolds number and determine a new friction factor from the Moody diagram. Repeat the calculation until the friction factor converges.

The table above contains velocities and Reynolds numbers that have been calculated for 200 ft 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 Reynolds numbers are optimistically high. Also, special fluids with lower viscosities or flushing at higher temperatures to reduce the fluid viscosity can increase the Reynolds number.

The values determined for maximum flushing velocity and flow rate indicate that some of these conditions — mainly for lines with inside diameters smaller than ¾ in. — 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 NRs to properly flush the lines.

Patrick Jones is founder of Consolidated Fluid Power Ltd., Dartmouth, Nova Scotia.