I don't know the size of your bullet or where you got 100 Pa for the pressure or the length of your barrel.
Wikipedia has a page on the characteristics of a 9 mm cartridge, which includes a measurement of the exit velocity, which is 350 m/s.
From that page, I got the mass and diameter of the bullet, and the length of the test barrel. Using those numbers, I created a set of equations to calculate the exit velocity assuming a constant average pressure on the back of the bullet for the length of the barrel. In reality, there is a pressure profile over the time the bullet is in the barrel. That Wiki page also lists the maximum pressure of 350 MPa. I typed in numbers for the average pressure until I found that 67.5 MPa delivered the correct exit velocity. At the exit time, there is no pressure to accelerate the bullet anymore. Instead there is a drag force on the bullet that gradually slows it down. You could model this using a 2 step solution where the pressure is 67.5 in step 1 till a time of 6.74e-4 then the pressure becomes some negative value that represents the drag force slowing the velocity down as it travels down range.
Try using these equations with the mass of your bullet, or make a model using the values I used.
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