What equation describes the relation between engine thrust and EPR?
I'm heavily cribbing from Boeing's &quot;Jet Transport Performance Methods&quot; here, so hold on to your seat...

F = m· (V2 – V1)
where m· is the gas flow rate, mass per unit time
V1 is the initial velocity of the gas
V2 is the final velocity of the gas
Let’s re-write equation 3 in a more complete form:
Fnet = [(m·core air + m·fuel) × Vcore exhaust] + (m·fan air × Vfan exhaust) - (m·air × Vairplane)                                       Note that the force is
now called Fnet, for net thrust. What are those terms in
parentheses? The term (m·air × Vairplane)is the momentum per unit
of time of the air being taken into the engine.  The term [(m·core
air + m·fuel) × Vjet exhaust] is the momentum per unit of time of
the gas leaving the core of the engine. Notice that we are now
accounting for the fact that the mass flow of the exhaust is greater
than the mass flow of the inlet, because fuel has been added to the
intake air.  Finally, the term (m·fan air × Vfan exhaust)is the
momentum per unit of time of the air leaving the fan stage of the
engine. The net force, which is the thrust produced by the engine,
is the algebraic sum of these three terms, which is the rate of
change of momentum of the gas as it passes through the engine.
If we considered only the first two terms, the exhaust flow, we would see only the force created at the fan and the exhaust nozzle.
But this is only half of the story, because we must remember that the
flow of the air entering the engine also has momentum and the useful
work that the engine is doing is the difference between the two.

Note that m· is &quot;m-dot.&quot; The dot should be over the letter &quot;m&quot; but didn't copy well from the original pdf. I bold-texted the part about force created at the fan and exhaust nozzle, because I think that's what you're measuring with EPR. Again, from the JTPM textbook:

This stands for engine pressure ratio. It’s the ratio of the gas flow
total pressures measured at two specific points: at the entrance to
the exhaust nozzle (station 7) and at the inlet to the fan and
compressor (station 2). EPR is defined simply as:
EPR = Pt7 / Pt2
where Pt2 is the total pressure measured at station 2 Pt7 is the total
pressure measured at station 7

Hope this helps. Just a little math, but I highly recommend the whole book.