I recently witnessed a pressure test followed by the leakage test.  Pressure dropped from 161psi to 159psi for 5,710 ft of 8-inch DI pipe.  Is there a way for me to verify the leakage (7.5 gal) theoretically?  

I'm suspicious of the leakage number because they pulled the suction line out of the water tank used to pump the line up....and I suspect air got in the suction line and messed with the test. Thanks for any help you can provide! 

The pressure test criteria does allow you an allowable which can be calculated in the above formula. At the end of the test you are allowed to pump an additional 4.34 gallons back into the line to bring it back to the test pressure. Typically in the northeastern U.S. I have been required to hold between 150 psi - 200 psi anywhere from 1 hour to 2 hours and everwhere in between. Once completed, if I have dropped below the test pressure, I am allowed to pump in the allowable leakage, calculated above, back into the line to get back to the test pressure. If it does not pump back up, you fail. If you pumped in an additional 7.5 gal then it appears to me that you failed. Keep in mind everywhere I have done a pressure test the rules and regulations have been different! Same basic idea but everyone seems to have there own take.

Additionally be suspicious if the contractor sees an instantaneous jump on the gauge and sucked air as you describe as the system can become air locked and is pointless after that. Contractors try everything from a "secret" buried valve or curbstop to pass if a line has become troublesome. Pay careful attention to the setup and make sure you understand the location of every valve, hydrant, and blowoff.

I fear a reader to this thread might come out of it with some misunderstanding of the specific test it appears was performed, as well as the complexity in general of hydrostatic testing issues.  To begin with my reading of the formula as well as tables of C600 tells me that when make-up water must be pumped back into an 8" ductile iron pipeline 5,710 feet long tested at say 160 psi, the ALLOWABLE "testing allowance" for a two hour test per this standard should not exceed:

L=(2 hrs) (5,710)(8)160^.5/148,000 or 7.81 gallons.  [It appears the contractor in this case for whatever reason pumped only 7.5 gallons back in, that would appear to be a "pass" at least per the AWWA standard .]

With all due respect also to some of the verbiage and terminology in references in this thread, as well as in some of the responses, I feel compelled to make the following additional comments related to the further, original question in general of "calculating leakage".  In my opinion, while it is possible to do all manner of calculations e.g. with "bulk modulus of compressibility" of water and elastic stretching of pipes etc. it is generally not really practical to "calculate leakage" in buried pipeline tests (except maybe in some very HIGHLY controlled test conditions of vessels and limited pipelines).  This is due to the following realities, some that may really be common to installation of pipelines of all materials:

1.  Despite best intentions/design, most rigorous or expensive installation/construction, and inspections etc., pipelines are not necessarily laid precisely with regard to either the horizontal or e.g. vertical lines on plans etc.
2.  Similar to the realities/imperfections of "1.", air valves(Needle Valves) and/or other air release mechanisms etc. are not necessarily always installed precisely at the top or apex of all local, vertical crests that may happen by design, or inadvertently in the installation of pipelines.
3.  Due to the combination of "1." and "2.", some air inevitably becomes trapped in pipelines.
4.  As most venerable standards and specifications also require that pipelines be filled, e.g. in preparation for hydrostatic testing "slowly" [defined in some as at velocities <1 fps (0.3mps)], it is also a reality (at least when high velocity flushing is not accomplished prior to hydrostatic testing) that that any unintentionally trapped and unvented air will simply not be removed (or "scavenged by sufficiently high flow velocity) at the time the (in effect combination air and water containing) pipeline is pressurized in hydrostatic testing.
5.  While trapped air may or admittedly may not cause any sort of noticeable problems in subsequent hydrostatic text results, it is well known that it CAN wreak literal havoc in others.  In other words, pipelines that contain trapped air can appear in various fashions to sometimes fail hydrostatic testing criteria (incidentally either raising or falling in pressure, or requiring excessive make-up water!), even though they really have no leakage!  
6.  For this reason, it is also stated in many long-standing specifications that the installer should remove most or all air (a requirement that appears, at least in many circumstances, sometimes easier said than done and some incongruous with the realities of 1-4!)
7.  Unlike water, that as you note is relatively "incompressible", air is instead highly compressible, and air is also highly volume or pressure (if contained as in a closed hydrostatic test) responsive to changes in temperature in accordance with "Boyle's", "Charles'" and "Gay Lussacs'" et al laws/principles.  Thus if (indeed probably instead "when", in the case of much testing that is of rather long duration) there are any temperature changes this will be accompanied by inevitable changes in pressure etc. and/or disproportionate requirements for make-up water etc., that do not have anything to do with "leakage".
8.  It may be tempting to just assume that pressurized air is just like pressurized water (the old "pressure is pressure" argument), and therefore will not meaningful affect test results.  However, this argument appears to neglect yet another phenomena associated with air/water mixes, that being that when there is no separating membrane air is also somewhat free also go into and out of "solution", and this in turn is probably also influenced by various drivers/variables of pressure and changing temperature etc. (not to mention the locations of at least any large columns of air e.g. from the pressurizing end etc.).   While much at least surface source water is already "saturated" with air, this may not be true of all filling water sources, and also other conditions.  In this regard I saw a writing many years ago (I think from a manufacturer of air valves), "A typical 1-mi (2-km) long pipeline of any diameter that has been supposedly vented of air will, in most instances, still contain enough dissolved air to completely fill over 100 ft (30 m) of the pipe."  Likewise, some water can soak into cement mortar linings of some types of pipe, also over time/pressure.
9.  Lastly, it is also possible that there can be slight movement, settlement, or some extension of pipelines due to installation and/or Bourdon effects etc., again that has nothing necessarily to do with leakage but that would change the test volume and manifest itself in at least some loss of pressure during a long-term test.

I think many of these practical realities were not lost on at least the formulators of venerable standards that have existed for decades, e.g. ANSI/AWWA C600 for the installation and testing of iron pipelines.  In this regard, if after more than 2 hours a particular closed off small diameter pipeline still holds basically a 160 psi level of pressure, while only losing a pound or two of water pressure, I suspect many Owners or installers of pipelines of many materials would probably be pretty happy with such an apparently tight line.  As psnyder notes/quotes above, the C600 standard indeed states, "Testing allowance shall be defined as the maximum quantity of makeup water that is added into a pipeline undergoing hydrostatic pressure testing... IN ORDER TO MAINTAIN PRESSURE within