Working Principle:
DWT (Dead Weight Tester) is based on the principle of Pascal's law. The law states that in a closed system of incompressible fluid, the pressure applied will exert equal amount of force in all the directions. In DWT system, silicon oil is used within the closed boundaries of the Piston cylinder arrangement, piping, pressurisation chamber and in the head on which the gauge to be tested/ calibrated is fixed. The oil is taken in to the pressurisation chamber from oil bowl and all the air entrapped is vented off. This is because of the reason that air is compressible and hence do not allow pressure to be exerted equally in all the areas and there by create error in the test results. Once the system is full with air free oil, pressure is gradually increased from the pressurization chamber. Oil pressure starts increasing in all the areas including piston cylinder arrangement over which the dead weights are mounted. As the force increases gradually and equals the amount of down ward force being exerted by the dead weights, the total system gains the state of equilibrium and just at that moment, the dead weights starts getting lifted up. At this condition, the amount of force operating in the entire system is same. The sum of pressure values stamped on weights lifted is operating on the pressure gauge element also, which is under test/ to be calibrated. Necessary corrections are made in the zero/ span adjustments in gauges/ Pressure transmitters. Above sequence is repeated for all the values at 0%, 25%,50%,75% and 100% to check for linearity and repeatability. This is how the DWTs are working. 

Formula :
The formula on which the design of a DWT is based basically is expressed as follows :
where :
p 
: 
reference pressure 
F 
: 
force applied on piston 
A 
: 
effective area PCU 
To be able to do accurate measurements, this formula has to be refined. 