Friction of a pipe and the effects on compressed air?

TheDarkChomp

Let's say a receiving device that requires compressed air is 1.5 miles away from the source and demands 600 cubic feet per minute. Let's say the pipes have a diameter of four inches and already contain air at 90psi.

If friction in the pipes would be ignored, it would require the same amount of energy to supply air regardless of pipe distance correct?

SO how would one understand the properties of pipe friction on the compressed air? How would I figure out the energy required to keep pushing the air to meet the demand of 600 cubic feet per minute through 1.5 miles of piping?

Any insight would be appreciated, thanks in advance

Chestermiller

I think what you are asking is, what is the pressure drop in the pipe. To do this problem, you need to know the viscosity of the air at the operating temperature. Do you know the operating temperature?

The first thing to do is to assume that the air is incompressible, so that its density is constant. If the pressure drop you calculate is significant compared to your 90 psi, then you need to get more serious, and to redo the calculation taking into account the compressibility. Use the ideal gas law to calculate the density of the gas. Divide the volumetric throughput rate 600 cfm by the cross sectional area of the pipe to get the velocity of the air in the pipe. Use the velocity, density, viscosity, and pipe diameter to get the Reynolds number. Use the friction factor-Reynolds number relationship to get the friction factor at the wall. Use the calculated wall friction factor, gas density, and gas velocity to get the shear stress at the wall. Use the shear stress at the wall to calculate the pressure drop.

TheDarkChomp

Sorry if I'm not understanding correctly I'm pretty new to this stuff

I'm trying to determine total cost to run a compressor based of the energy required to push compressed air to the receiving device plus the cost of the compressed air being used at the receiver.

The actual of the compression of the air causes the temperature to heat up a lot so air is first compressed to 60 psi, cooled, compressed to 90 psi, cooled, and sent through a dryer and out through the pipes.

(I'm ignoring the dryer because the compressors are being replaced but not the dryers and to simplify the problem slightly)
When the air is first sent through the pipes it is 70 degrees Fahrenheit (dynamic viscosity would be 0.018424 I think) How would this allow me to calculate pressure drop? Would I need the temperature at the end of the pipe also?

Chestermiller

You need the viscosity to calculate the Reynolds number. Is the temperature constant at about 70F over the entire length of the pipe, or does the surrounding environment heat or cool the air from one end of the pipe to the other? If significant heating and cooling are involved, then you also have a coupled heat transfer problem that you are dealing with.

TheDarkChomp

Ok I think I've calculated everything...

Would converting this pressure drop to pounds per square foot then using that in
(pounds per square foot * cfpm)/33000 = theoretical horsepower allow me to quantify the energy needed to compensate for this drop?

TheDarkChomp

Disregard that last post...

I could convert the pressure drop to volume drop, and using the efficiency of the compressor find out how much energy it takes to generate that much volume correct?

Chestermiller

What pressure drop did you calculate?

TheDarkChomp

I found Reynolds number and relative roughness then used the moody diagram to find the friction factor, but not sure how to get to pressure drop from there. Why is shear stress needed?

(Have velocity, distance, diameter, viscosity, flow rate also)

SteamKing

The shear stress is not required. You already have a friction factor from the Moody Diagram.

TheDarkChomp

Ok found the formula Δp = (v² × f × L × ρ)/2D

With the pressure drop how would I convert to volume drop or energy required to accomidate for that pressure drop?

(I tried ideal gas law but that definitely doesn't work)

Chestermiller

I think you're missing a factor of 4 in the equation. What number of psi do you calculate for the pressure drop?

russ_watters

Sorry I missed this thread before, but the discussion is waaaaay too complicated. Engineers don't figure this stuff out from scratch every time they design a system, they use tables and/or specialized calculators or slide rules. Just Google "compressed air pipe friction loss" and pick one.

For the energy, select an air compressor and see how much power it uses at the different pressures.

Travis_King

It's good to understand what's going on and what factors come into play in these things, but I'm with Russ on this one. Pressure losses in pipelines is a pretty well established science.

Here's a calculator on Eng. Toolbox

Chestermiller

This is a great link Travis_King. So what do you get for the pressure drop when you plug the OPs numbers in? I assumed 600 scfm flow rate and a pipe ID of 1 ft, and, using the link, got a pressure drop of <1psi. The OP didn't tell us the pipe ID. What do you get. If the pressure drop truly is < 1psi, then this is what I was initially driving at when I speculated that it might be possible to treat the gas as incompressible. Obviously, if the diameter is a lot less than 1 ft, the pressure drop is going to be higher.

Chet

russ_watters

Dia was four inches.

Travis_King

Yea, Engineering Toolbox is great. And yep, OP said ID was 4 inches, it results in an approximate pressure drop in the viscinity of 5.4 psi. This of course doesn't include the losses from any valves, elbows, tees, flanges, etc.

Compressibility isn't really a huge issue here anyway. The difference in the density of air (at otherwise standard conditions) between 95 psi and 90 psi is only something like .026 lb per cubic foot. It's not going to alter the pressure drop too much, and since these calculations are only good as close approximations anyway, it most likely falls within the margin of error.

Edit:
The one issue I see is that the the airflow the calculator (indeed, most calculations) uses is the airflow at atmospheric conditions. So it really depends on whether the OP meant 600 ACFM or SCFM.
If the OP is expecting 600 ACFM (at the 90 psi condition), then that means that the actual, standard conditions, flow is in the realm of 3600 SCFM, making the pressure drop more significant, probably prohibitively so in a 4" ID pipe.

Chestermiller

Nice analysis. The OP never told us whether the 600 cfm is scfm or acfm. However, for pipelines, throughput rates are usually reported as scfm. That means that your 5 psi would be about right. You gotta figure also that the pipe diameter would have been specified such that not much pressure loss would ensue from the compressor to the delivery point. This would be consistent with 600 scfm rather than 600 acfm (as you alluded to).