Air Pressure, Velocity and Flow

<...What is the effect that elbows cause to blow off the sludge in a pipe by using compress air?...>

The pressure in the pipe has exceeded that which the pipe is able to withstand. On a pipe carrying sludge, the effect will be quite spectacular...

The air density is related to the pressure and the base line is atmospheric pressure so two atmosphere's = twice the density.

Flow is the amount of air you have to move in the time you have to move it and Flow depends on pressure drop ...no pressure drop = no flow.

An elbow is a restriction and a resistance to flow.

C_V = coefficient of velocity
This may help if you should come across a formula containing C_{V .}

Conductance is the inverse of resistance. For electrically inclined people, the unit of electrical resistance is the ohm. The inverse of resistance is measured in the little know unit of the mho. That's ohm spelled backwards.
The mho is directly analogous to C_V. The coefficient for C_V represents the ability of a pneumatic system or component to flow air.

See Boyle's Law and The Ideal Gas Law.

http://www.grc.nasa.gov/WWW/K-12/airplane/isentrop.html

Simple question, complicated answer. Air is a compressible fluid so the flow, velocity, and density vary non-linearly. The first link above is to a NASA webpage showing the pertinent compressible flow equations. For more details and explanation, any book on compressible flows will do. "Modern Compressible Flow" by Anderson is a good book on the topic. Googling would probably yield similar info, eventually.

Specific to pipes, pipes will choke such that the internal mach number is no greater than sonic (Mach = 1.0). Higher pressures above that which is needed to choke the pipe will tend to create shock waves at defects inside the pipe and at the pipe exit.

Blowing sludge out of a pipe using compressed air likely relies on the sludge creating a noticeable pressure restriction such that the pressure load plus air-to-sludge surface shear across the sludge is greater than the sludge's surface adherence to the pipe. In a straight section of pipe, the pressure load acts essentially parallel to the pipe and would tend to strip the sludge from the pipe wall. On the otherhand, pipe elbows would reduce the effectiveness of sludge removal since the air pressure load would tend to push the sludge against the outer elbow. Additionally, the centrifugal acceleration from turning in the elbow would tend to centrifuge the sludge towards the outer elbow surface. Thus turns tend to be spots that accumulate contanimants, and are difficult to clean just using air flow.

What is the diameter and length of the piping that you are trying to clean? How many elbows? Does the sludge need to be completely removed? Or just enough to allow proper flow? What is the sludge composition? If reasonably possible, perhaps some mechanical means of breaking up / loosening the sludge could be done before using the compressed air? Or maybe a small air supply line could be snaked in to locally blast the sludge (same source filling a bigger pipe will reduce the source pressure and air velocity; small local jet will have higher velocity with direct impact). Otherwise, you may need a higher pressure source or some other method of cleaning.

If the sludge is a common problem that is difficult to clean, you may want to consider whether a sink trap or filter could be used to limit future sludge accumulations. Then you would just have one removable location to clean, or a filter to change out.

Vince, At 6 bar (87 psig) the potential force with no flow should be Area in² x pressure. If you have a 1/2" diameter pipe (.7854 x (1/2)² x 87 = 17 lbs_f. With a 2" I.D. pipe the force would be approx. 273 lbs_f.

What does the sludge weigh? My guess is that the compressed air forces past the sludge which spreads along the bottom of a horizontal pipe. If the sludge fills only half of the internal area and air is allowed to pass through the other half with little resistance the pressure will drop drastically with very little force imparted to the sludge. You might try something like the slugs or plugs used to clean the inside of pipe. This plug acts like a dart in a blow gun and prevents blow by.

You can find out what is happening by putting a pressure gauge in the air supply and another on the far side of the sludge. If the pressure is reduced at the supply and negligible past the sludge see the above.

There are systems available that are commonly called "pigs" to clean out pipe and tube. They are urethane wipers that are sent through the line via an air supply that essentially squeegee the pipe walls down. They are much more effective than just normal air.

http://www.csidesigns.com/prs.php