Thermodynamics

Chapter 7 | 393There are many ways of detecting air leaks in a compressed-air system.Perhaps the simplest way of detecting a large air leak is to listen for it. Thehigh velocity of the air escaping the line produces a hissing sound that is difficultnot to notice except in environments with a high noise level. Anotherway of detecting air leaks, especially small ones, is to test the suspected areawith soap water and to watch for soap bubbles. This method is obviously notpractical for a large system with many connections. A modern way of checkingfor air leaks is to use an acoustic leak detector, which consists of a directionalmicrophone, amplifiers, audio filters, and digital indicators.A practical way of quantifying the air leaks in a production facility in itsentirety is to conduct a pressure drop test. The test is conducted by stoppingall the operations that use compressed air and by shutting down the compressorsand closing the pressure relief valve, which relieves pressure automaticallyif the compressor is equipped with one. This way, any pressure drop inthe compressed-air lines is due to the cumulative effects of air leaks. The dropin pressure in the system with time is observed, and the test is conducted untilthe pressure drops by an amount that can be measured accurately, usually 0.5atm. The time it takes for the pressure to drop by this amount is measured,and the decay of pressure as a function of time is recorded. The total volumeof the compressed-air system, including the compressed-air tanks, the headers,accumulators, and the primary compressed-air lines, is calculated. Ignoringthe small lines will make the job easier and will cause the result to bemore conservative. The rate of air leak can be determined using the ideal gasequation of state.The amount of mechanical energy wasted as a unit mass of air escapesthrough the leaks is equivalent to the actual amount of energy it takes tocompress it, and is determined from Eq. 7–57, modified as (Fig. 7–74)w comp,in w reversible comp,inh comp1n12>nnRT 1h comp 1n 12 caP 2b 1 dP 1(7–89)where n is the polytropic compression exponent (n 1.4 when the compressionis isentropic and 1 n 1.4 when there is intercooling) and h comp isthe compressor efficiency, whose value usually ranges between 0.7 and 0.9.Using compressible-flow theory (see Chap. 17), it can be shown thatwhenever the line pressure is above 2 atm, which is usually the case, thevelocity of air at the leak site must be equal to the local speed of sound.Air inlet1 atmmAir leak (20%)0.2 m24 kWMotor120 kWAirCompressorFIGURE 7–74The energy wasted as compressed airescapes through the leaks is equivalentto the energy it takes to compress it.