In industrial settings, having a single air nozzle or other blowoff product is often not the scenario that is seen. Many applications require multiple points of blowoff, even if not in the same direction or for the same position within the machine. In the scenario where multiple nozzles are used, sound levels can get tricky to calculate and is often thought of as a mystery. If you follow our blog then you may have seen this excellent blog that shows all the math behind calculating the total decibels when multiple sources of noise will be present. The video below gives a demonstration of utilizing two of the EXAIR model 1100 – 1/4″ FNPT Super Air Nozzle.

In the video you see a model 1100 being operated and producing a sound level of 74 dBA from 3′ away from the nozzle point. When the second nozzle is turned on (also producing 74 dBA individually), the pressure is adjusted back up to the same input pressure and the sound level meter registers 78 dBA from 3′ away. Following the math laid out in the “excellent blog” link above, the sound level calculated comes out to be the same 78 dBA that is shown in the video using EXAIR’s Digital Sound Level Meter.

If you would like help determining the sound levels within your facility, check out the EXAIR Digital Sound Level Meter as well as reach out to an Application Engineer.

EXAIR has been manufacturing Intelligent Compressed Air Products since 1983. They are engineered with the highest of quality, efficiency, safety, and effectiveness in mind. Since compressed air is the source for operation, the limitations can be defined by its supply. With EXAIR products and pneumatic equipment, you will need a way to transfer the compressed air from the air compressor. There are three main ways; pipes, hoses and tubes. In this blog, I will compare the difference between compressed air hoses and compressed air tubes.

The basic difference between a compressed air hose and a compressed air tube is the way the diameter is defined. A hose is measured by the inner diameter while a tube is measured by the outer diameter. As an example, a 3/8” compressed air hose has an inner diameter of 3/8”. While a 3/8” compressed air tube has an outer diameter that measures 3/8”. Thus, for the same dimensional reference, the inner diameter for the tube will be smaller than the hose.

Why do I bring this up? Pressure drop… Pressure Drop is a waste of energy, and it reduces the ability of your compressed air system to do work. To reduce waste, we need to reduce pressure drop. If we look at the equation for pressure drop, DP, we can find the factors that play an important role. Equation 1 shows a reference equation for pressure drop.

Equation 1:

DP = S_{x} * f * Q^{1.85 }* L / (ID^{5} * P)

DP – Pressure Drop

S_{x} – Scalar value

f – friction factor

Q – Flow at standard conditions

L – Length of pipe

ID – Inside Diameter

P – Absolute Pressure

From Equation 1, differential pressure is controlled by the friction of the wall surface, the flow of compressed air, the length of the pipe, the diameter of the pipe, and the inlet pressure. As you can see, the pressure drop, DP, is inversely affected by the inner diameter to the fifth power. So, if the inner diameter of the pipe is twice as small, the pressure drop will increase by 2^{5}, or 32 times.

Let’s revisit the 3/8” hose and 3/8” tube. The 3/8” hose has an inner diameter of 0.375”, and the 3/8” tube has an inner diameter of 0.25”. In keeping the same variables except for the diameter, we can make a pressure drop comparison. In Equation 2, I will use DP_{t} and DP_{h} for the pressure drop within the tube and hose respectively.

As you can see, by using a 3/8” tube in the process instead of the 3/8” hose, the pressure drop will be 7.6 times higher.

At EXAIR, we want to make sure that our customers are able to get the most from our products. To do this, we need to properly size the compressed air lines. Within our installation sheets for our Super Air Knives, we recommend the infeed pipe sizes for each air knife at different lengths.

There is also an excerpt about replacing schedule 40 pipe with a compressed air hose. We state; “If compressed air hose is used, always go one size larger than the recommended pipe size due to the smaller I.D. of hose”. Here is the reason. The 1/4” NPT Schedule 40 pipe has an inner diameter of 0.364” (9.2mm). Since the 3/8” compressed air hose has an inner diameter of 0.375” (9.5mm), the diameter will not create any additional pressure drop. Some industrial facilities like to use compressed air tubing instead of hoses. This is fine as long as the inner diameters match appropriately with the recommended pipe in the installation sheets. Then you can reduce any waste from pressure drop and get the most from the EXAIR products.

With the diameter being such a significant role in creating pressure drop, it is very important to understand the type of connections to your pneumatic devices; i.e. hoses, pipes, or tubes. In most cases, this is the reason for pneumatic products to underperform, as well as wasting energy within your compressed air system. If you would like to discuss further the ways to save energy and reduce pressure drop, an Application Engineer at EXAIR will be happy to assist you.

John Ball
Application Engineer
Email: johnball@exair.com
Twitter: @EXAIR_jb

The below video shows how to calculate the air consumption when operating at any pressure.

If you want to discuss efficient compressed air use or any of EXAIR’s engineered compressed air products, give us a call or email. We would enjoy hearing from you!

Daniel Bernoulli was born in Groningen, Netherlands on February 8, 1700 and was part of a large family heritage of famous mathematicians – His father Johann Bernoulli, one of the first founders of calculus, his uncle Jacob Bernoulli and his older brother Nicolous. When he was only 7 years old, Daniel began to take an interest in mathematics but his father convinced him that there was no financial gain to be had in mathematics and recommended he focus his studies in business instead. Reluctant at first, Daniel would take his father’s advice under the one condition, that his father would tutor him in calculus and his theories of kinetic energy.

At 13 years old, Daniel attended Basel University where he studied logic and philosophy completing his bachelor’s degree by the age of 15 and earning his master’s degree just 1 year later. Over the years, Daniel’s relationship with his father was strained as a result of him plagiarizing his father’s findings. Eventually, his father passed without reconciling with Daniel. At 24, Daniel became a Professor of Mathematics at a University in Venice but resigned from the position just 9 years later in 1733.

His most recognized mathematical contribution, Bernoulli’s principle, came in 1938 while performing energy conservation experiments, and he published the results in his book entitled Hydrodynamica. He discovered that when fluid travels through a wide pipe into a smaller, more narrow pipe, the fluid begins to move faster. He determined that the volume or amount of fluid moving through the pipe remains unchanged but will conform to the shape of the pipe or container as it flows. He concluded that the higher the pressure, the slower the flow of the liquid and the lower the pressure, the faster the liquid flow.

The same principle can be applied to air. As air moves around an obstruction or object, it follows the profile of the part and begins to speed up.

Take for example our Super Air Nozzles. The compressed air exits the nozzle through a series of jets which induces a low pressure around the profile of the nozzle, drawing in ambient air. This entrainment of air, up to 25 times or more, results in a high outlet flow at minimal compressed air consumption.

Many of the products offered by EXAIR incorporate this science which can lead to a more efficient operation by lowering compressed air demand ultimately reducing operating costs. To see how our products can help you save money while increasing process performance, contact an Application Engineer for assistance.

My previous blog post was about how Vortex Tubes react when there is back pressure due to a restriction on either the hot or cold discharge of the Vortex Tube. In it I mentioned that there is a formula to calculate what the cooling capacity (Btu/Hr) will be if there is no way to avoid operating the Vortex Tube without back pressure on the discharge. That is the calculation focus of this blog – calculating Btu/hr of a Vortex Tube with back pressure.

To continue with the same example, the calculations from the previous blog are shown below. Last time the example Vortex Tube was operating at 100 psig inlet pressure, 50% cold fraction, and 10 psi of back pressure. We will need some additional information to determine the Btu/Hr capacity. The additional information needed is the temperature of the supplied compressed air as well as the ambient air temperature desired to maintain. For the example the inlet compressed air will be 70°F and desired ambient air temperature to maintain will be 90°F.

(100 psig + 14.7 psia) / (10 psig + 14.7 psia) = X / 14.7 psia
4.6437 = X / 14.7
X= 14.7 * 4.6437
X = 68.2628
(Values have been rounded for display purposes)

The calculation above gives the compensated operating pressure (X = 68.2628) which will be needed for the BTU/hr calculation. The rated air consumption value of the Vortex Tube will also need to be known. A 30 SCFM rated generator will be used for this example, the normal BTU capacity of a Vortex Tube with a 30 SCFM generator is 2,000 BTU/hr.

First, determine the new consumption rate by establishing a ratio of the compensated pressure (68.2628 psi) against the rated pressure (100 psi) at absolute conditions (14.7 psia).

Second, the volumetric flow of cold air at the previously mentioned cold fraction (50%) will be calculated. To do this multiply the cold fraction setting (50%) of the Vortex Tube by the compensated input consumption (21.7 SCFM) of the Vortex Tube.

50% cold fraction x 21.7 SCFM input = 10.85 SCFM of cold air flow

Third, the temperature of air that will be produced by the Vortex Tube will need to be calculated. For this consult the Vortex Tube performance chart which is shown below. To simplify the example the compensated operating pressure (68.2628 psi) will be rounded to 70 psig and to obtain the 70 psig value the mean between 80 psig and 60 psig performance from the chart will be used.

For the example: A 70 psig inlet pressure at 50% cold fraction will produce approximately an 88°F drop.
Fourth, subtract the temperature drop (88°F) from the temperature of the supplied compressed air temperature (70°F).

70°F Supply air – 88°F drop = -18°F Output Air Temperature

Fifth, determine the difference between the temperature of the air being produced by the Vortex Tube (-18°F) and the ambient air temperature that is desired (90°F).

90°F ambient – -18°F air generated = 108°F difference.

The sixth and final step in the calculation is to apply the answers obtained above into a refrigeration formula to calculate BTU/hr.

1.0746 (BTU/hr. constant for air) x 10.85 SCFM of cold air flow x 108°F ΔT = 1,259 BTU/hr.

In summary, if a 2,000 BTU/hr. Vortex tube is operated at 100 psig inlet pressure, 50% cold fraction, 70°F inlet air to maintain a 90°F ambient condition with 10 psi of back pressure on the outlets of the Vortex Tube the cooling capacity will be de-rated to 1,259 BTU/hr. That is a 37% reduction in performance. If a back pressure cannot be avoided and the cooling capacity needed is known then it is possible to compensate and ensure the cooling capacity can still be achieved. The ideal scenario for a Vortex Tube to remain at optimal performance is to operate with no back pressure on the cold or hot outlet.

Vortex tubes have been considered a phenomena of Physics and boggled minds for many years. To give a brief run down of how the Vortex Tube works please refer to Figure 1 below.

As seen above, the control valve is determining the amount of air allowed to escape the hot end and sets the cold fraction. A cold fraction is the percentage of air that exits the cold side versus the hot side. The cold fraction and operating pressure sets the temperature drop on the cold end and temperature rise on the hot end, as well as volumetric flow out of both ends. The control valve is not the only variable that can alter the cold fraction of the Vortex Tube though.

In Figure 1 and the performance chart below, there is no restriction on the hot end or the cold end outlets. No restriction means no back pressure and the cold air has the easiest path to the area needing cooling. Back pressure can directly affect the performance of a Vortex Tube. As little as 3 psig of back pressure can begin to alter the temperature drop or rise on the Vortex Tube. This is due to the fact that Vortex Tubes operate off an absolute pressure differential. If the outlets have a restriction on them then they are not discharging at atmospheric pressure, 14.7 psi. What kind of items can cause back pressure and can the performance with a back pressure on the outlet be determined?

Back pressure is created by implementing any form of restriction on the hot or cold outlet. This may be undersized tubing to deliver the cold air or a valve that has been installed to try and control the volume of air being blown onto the process as well as many other possibilities. The best rule of thumb to eliminate back pressure is to keep the tubing on an outlet the same cross sectional dimension as the outlet on the Vortex Tube and try to keep the tubing as short as possible.

If back pressure cannot be prevented, the performance variance of the Vortex Tube can be calculated and possibly compensated for. The variables that are needed to do so are the inlet air pressure of the vortex tube and the amount of back pressure that is being seen on the outlets. If this is different from the hot end to the cold end both will need to be known. If these are not known they can be measure by installing a pipe Tee and a pressure gauge. This may need to be a sensitive pressure gauge that measures even relatively low psig. (1-15 psig)

Once these variables are known, we want to look at an absolute pressure differential versus the back pressure differential. For example, the Vortex Tube is a operating at 100 psig inlet pressure, 50% cold fraction and 10 psi of back pressure. We look at the pressure differentials and can use Algebraic method to determine the inlet pressure supply that the tube will actually perform at.

(100 psig + 14.7 psia) / (10 psig + 14.7 psia) = X / 14.7 psia
4.6437 = X / 14.7
X= 14.7 * 4.6437
X = 68.2628
(Values have been rounded for display purposes)

So if there is a 10 psig back pressure on the outlet of a Vortex tube operating a 100 psig inlet pressure the tube will actually carry performance as if the inlet pressure was ~68 psig. To showcase the alteration in performance we will look at just the temperature drop out of the cold side of the Vortex Tube. (Keep in mind this is a drop from the incoming compressed air temperature.)

As shown in the performance chart above, if the Vortex Tube was operating at 100 psig inlet pressure and 50% cold fraction the temperature drop would be 100°F. By applying a 10 psi back pressure on the outlet of the Vortex Tube the temperature will be decreased to ~87°F temperature drop. This will also decrease the volumetric flow of air exiting the Vortex Tube which can also be calculated in order to determine the cooling capacity of the Vortex Tube at the altered state. Keep an eye out for a follow up blog coming soon to see that calculation.

If you have ever looked through our catalog, website, blog, twitter feeds, or even our Facebook page, you will see that we can almost always put a dollar amount behind the amount of compressed air you saved by installing EXAIR’s Intelligent Compressed Air Products. No matter which platform we use to deliver the message, we use the same value for the cost of compressed air which is $.25 per 1,000 Standard Cubic Feet of compressed air. This value is derived from average commercial and industrial energy costs nationwide, if you are on either coast this value may increase slightly. On the positive side, if your cost for compressed air is a bit more, installing an EXAIR product will increase your savings.

So where does this number come from? I can tell you this much, we didn’t let the marketing department or anyone in Accounting make it up. This is a number that the Engineering department has deemed feasible and is accurate.

To calculate the amount we first look to what the cost per kilowatt hour is you pay for energy. Then we will need to know what the compressor shaft horsepower of the compressor is, plus the run time percentage, the percentage at full-load, and the motor efficiency.

If you don’t have all of these values, no worries. We can get fairly close by using the industry accepted standard mentioned above, or use some other general standards if all you know is the cost of your electricity.

The way to calculate the cost of compressed air is not an intense mathematical equation like you might think. The best part is, you don’t even have to worry about doing any of the math shown below because you can contact us and we can work through it for you.

If you prefer to have us compare your current compressed air blow off or application method to one of our engineered products, we can do that AND provide you a report which includes side by side performance comparisons (volume of flow, noise, force) and dollar savings. This refers to our free Efficiency Lab service.

If you already know how much air you are using, you can use the Air Savings Calculators (USD or Euro) within our website’s knowledge base. Just plug in the numbers (EXAIR product data is found on our website or just contact us) and receive air savings per minute, hour, day and year. We also present a simple ROI payback time in days.

Now, back to the math behind our calculation. Cost ($) =
(bhp) x (0.746) x (#of operating hours) x ($/kWh) x (% time) x ( % full load bhp)
——————————————————————————————————————————
Motor Efficiency

Where:
bhp — Compressor shaft horsepower (generally higher than motor nameplate Hp) 0.746 – conversion between hp and KW Percent Time — percentage of time running at this operating level Percent full-load bhp — bhp as percentage of full load bhp at this operating level Motor Efficiency — motor efficiency at this operating level

For an average facility here in the Midwest $0.25/1,000 SCF of compressed air is accurate. If you would like to attempt the calculation and or share with us your findings, please reach out to us. If you need help, we are happy to assist.