Monday, December 17, 2012

Waterjetting 4b - Line losses

High-pressure pumps are, as a general rule, quite efficient at bringing water up to the pressure required for a given task. And yet, time after time, the jet that reaches the target is no longer capable of achieving the work that was promised when the system was designed. More often than not this drop in performance can be traced to the way that the water travels through the delivery system, and out of the nozzle that forms the jet.

The water flows that are used in a broad range of operations are quite low. Ten gallons a minute (gpm) and flows below that volume are mainly used in cutting operations and higher-pressure cleaning. Further, there are few occasions where hand-held operations will use flows much above 20 gpm, because of the thrust levels involved. And low flow rates mean that there is little pressure loss between the pump and the nozzle, right? UM! Well not exactly.

The pressure losses due to overcoming friction in the feed lines (whether hose or tubing) from the pump to the nozzle can make a significant difference in the operation of the system, as I mentioned in one of the early posts of this series. In that post I pointed out that a well-known research team (not us) spent two weeks running a system with 45,000 psi water pressure going into a feed line, but with only around 10,000 psi being usefully available when the flow reached the far end. (And I will freely confess later in this piece to having made a similar mistake myself). So the question naturally arises as to how these losses can be avoided.

In a word – diameter! The smaller the diameter of the feed line through which the water must flow, then the higher the pressure that is required to drive the water through that line, regardless of the nozzle size at the delivery end. The diameter of concern is, further, the inner diameter of the hose or tubing, not the outer diameter (though the combination is important in ensuring that the line can contain the pressure that the water is carrying through the line).

There are concerns over the condition of the line, the fittings that join the different parts together and other factors that I will cover in the posts following this one, but this will deal just with the simple pressure drop that occurs along a tube at different flow volumes. There are formulae that can be used, but a reasonable estimate of the loss can be obtained, either with the design tables that most manufacturers supply with their product, or through a simple nomogram that I will place at the end of this piece.

To begin with consider the basic equations that govern the pressure drop:

Figure 1. The equation relating pressure drop to flow volume and pipe diameter.

Note that in the above equation the pressure drop is related to the fifth power of the diameter of the tube – such is the power that even a small change in flow channel diameter will have on the pressure drop in the line.

When flow begins through a channel it is initially going to occur with the flow being laminar, in other words the water moves in layers. (There is an interesting video of this here and a video of one of the designs used, for example, to give the “solid” jet slugs that you might see jumping around the hedges at one of the Amusement Parks.

Figure 2. The difference between laminar and turbulent flow. (Equipment explained)

As water speed increases, however, the flow will transition from laminar flow into turbulent flow, where the roughness of the flow channel wall becomes more important. The roughness, resulting friction factor and the flow volume all then combine to allow the calculation of the pressure required to overcome the friction in the pipe. This holds true whether the flow is at the one or two gpm used in cutting at high pressure, or the relatively low pressure, high volume flows used in fighting fires.

But (outside of us academics) few actually calculate the numbers. There really is no need, since most of the manufacturers provide the information in their catalogs. There are two ways of presenting the information. The older convention was just to provide a graph, from which one could read off the pressure drop, as a function of the pipe internal diameter, and for a given pipe length.

Figure 3. Pressure drop along a tube, as a function of flow rate and tube internal diameter. Note that the scales are logarithmic.

Charts such as this are a little difficult to read, and being on a log plot small mistakes in reading the value can give significantly wrong estimates so that a more spread-out method is often more helpful. The one that I prefer to use is a nomogram, where it is possible to do comparisons between different options on a single figure with a slightly expanded scale.

Consider, for example, this nomogram from the Parker Catalog which shows the relationship between the volume flowing down through a line, the inner diameter through which it is flowing, and the resulting velocity of the flow.

Figure 4. A nomogram to determine the best pipe diameter, based on the allowable velocity of the flow. (Parker)

While this is not generally a concern in feed lines to nozzles (because of the high levels of filtration of the water) in lines that carry away spent water and debris the velocity can be of concern, and also in abrasive slurry systems, where flow rates above 40 ft/sec can lead to erosion of the line.

The more useful nomogram, however, is one that I have adapted from the U.S. Bureau of Mines (a Government agencies that is now, sadly, defunct).

Figure 5. Nomogram to calculate pressure loss along a 10-ft length of tubing.

Knowing the flow rate through the line, and setting a straight-edge (usually a ruler) to mark the level, the ruler is then positioned so that it also crosses the inner diameter of the tubing. In the example above that would align the ruler along the line shown, that runs from 20 gpm to 0.1875 inch pipe diameter (3/16ths of an inch). The point at which the line crosses the pressure drop gives the friction loss in the line. In this case that reads at 3,600 psi per 10 ft of pipe.

The example was taken from a field trial where we were drilling holes into the side of a rock pillar. We had no problem drilling the first ten feet, but when we added a second length of 10-ft tubing to allow us to drill holes 20-ft deep the drill did not work. It was not until late in the afternoon that we realized that by adding that second length of pipe we had dropped the cutting pressure coming out of the nozzle so that while the gage pressure was 10,000 psi, the initial jet pressure had been only 6,400 psi and when the second pipe length was added, the pressure fell to 2,800 psi. This was below the pressure at which it was possible to effectively cut the rock. And so we learned!