*By Josh Cosford, Contributing Editor*

In a recent fluid power webinar, while presenting on Selecting & Sizing the Proper Fitting, I was asked a question by an attendee I had no good answer to. Near the latter portion of the webinar, I had been discussing pressure drop through fittings. Ensuring you provide a healthy, unimpeded path for hydraulic fluid to flow saves critical energy for useful work, rather than just pushing molecules. The excessive use of tees, elbows and adapters creates pressure drop, so such fittings should be avoided, if possible.

I had explained the factors for pressure drop through a fitting; diameter, flow rate, radius of bend, surface finish and Reynolds Number. Of course, most of you know there is a direct relationship between conduit diameter, flow rate and pressure drop. The higher the flow rate or smaller the fitting, the higher the pressure drop. It should be noted that pressure drop increases exponentially as diameter decreases … that’s how much fitting size affects energy loss.

Less considered, bend radius is how tightly fluid is forced to change direction in a tube, hose or fitting. In the image, two 90-degree elbows are compared. One fitting’s internals smoothly transition its radius with little drama, ensuring flow is closer to laminar, which prevents excessive backpressure. The other forged and machined elbow fitting more severely alters the fluid path, which creates backpressure as oil loses energy changing direction.

Picture, if you will, the extreme waterslide at your local amusement park … you know, the one with the trap door and fifty-foot plummet? The slide door opens and drops you straight down for ten feet before your posterior contacts the slide to start changing your direction from vertical to horizontal, and with surprising ease and speed, your plummet is managed safely. Now imagine the trap door opens, and you fall twenty feet and land with a thud. In front of you is a dark tunnel. However, you’ve lost all forward momentum, and not until more bodies are dropped to force you down the tunnel, your energy is lost.

My example is extreme, but important nonetheless. It takes energy to turn a 90° corner, and the concept isn’t lost in fluid power. The combination of the bend radius and the smoothness of the walls of the conduit contribute to the Reynolds Number, which is just a dimensionless description dependant on other things like viscosity. The Reynolds Number is defined using the following, which I don’t expect you to calculate or memorize, but have a look at the factors:

*where*

*DH is the hydraulic diameter of the pipe (the inside diameter if the pipe is circular) (m),*

*Q is the volumetric flow rate (m3/s),*

*A is the pipe’s cross-sectional area (m2),*

*u is the mean velocity of the fluid (m/s),*

*μ (mu) is the dynamic viscosity of the fluid*

*ν (nu) is the kinematic viscosity*

*ρ is the density of the fluid (kg/m3)*

I’m only showing you the equation to point out its complication for everyday use in understanding pressure drop through the fittings you choose for your hydraulic system. There must be a better way, and it’s where the attendee I spoke about earlier comes into the picture. They had asked me if manufacturers publish pressure drop for the fittings they sell — and I couldn’t answer that question. I had certainly never seen such pressure drop numbers published in any catalogue, but I said I’d research it.

After extensive research, I came up with … nothing. Well, almost nothing if it weren’t for Gates. Gates has a calculator on their website (found here) that allows you to spell out parameters including flow rate, hose diameter and length, fluid properties and then the number of fittings and adapters. It lets you choose between elbows, adaptors and tees, or even straight couplings. In two tests, I chose ½ in. hose, 12 gpm and standard hydraulic fluid properties. One test had no fittings and the other about a dozen tees and elbows. The second test results in an added 200 psi of pressure drop through my system.

So while not the fitting-by-fitting list of pressure drops which would make it easy and obvious which to choose, it’s a great tool to benchmark your current system and see where you could stand to improve efficiency. Even by playing around with the calculator, you can gauge how dramatic fittings, elbows and tees reduce energy by way of backpressure. There are fluid dynamics modeling software packages available, especially for existing CAD programs, but these are expensive to buy and license. If you want a simple and repeatable way to estimate pressure drop through fittings, the Gates Fluid Flow Pressure Calculator is fantastic.

William K. says

Certainly most suppliers don’t include such pressure drop information, partly because it does depend on both fluid velocity and fluid viscosity.

What I have seen that was truthful was in an ancient text on hot water and steam heating. The pressure drop was expressed in units of Bell and Gosset Elbow equivalents. A rather strange unit, but certainly it could be understood by both an architect and a pipefitter.. And the best part is that the units were equally applicable to water, steam, and heating fuel oil without any complex mathematics.