I didn't include the answer to that last calculation:
311*9.81ln(1 + 375/(13 + 6.7)) = 9,145 m/s.
Dr. John Schilling has produced a payload estimation program:
Launch Vehicle Performance Calculator.
http://www.silverbirdastronautics.com/LVperform.html
It gives a range of likely values of the payload. I've found the midpoint of the range it specifies is a reasonably accurate estimate to the actual payload for known rockets.
Input the vacuum values for the thrust in kilonewtons and Isp in seconds. The program takes into account the sea level loss. SpaceX gives the Merlin 1D vacuum thrust as 161,000 lbs and vacuum Isp as 311 s:
FALCON 9 OVERVIEW.
http://www.spacex.com/falcon9.php
For the 9 Merlins this is a thrust of 9*161,000*4.46 = 6,460 kN. Use the default altitude of 185 km and the Cape Canaveral launch site, and a 28.5 degree orbital inclination, to match the Cape's latitude.
Input the dry mass of 13,000 kg and propellant mass of 375,000 kg. Then it gives an estimated 7,564 kg payload mass:
Launch Vehicle: User-Defined Launch Vehicle
Launch Site: Cape Canaveral / KSC
Destination Orbit: 185 x 185 km, 28 deg
Estimated Payload: 7564 kg
95% Confidence Interval: 3766 - 12191 kg
This may be enough to launch the Dragon capsule, depending on the mass of the Launch Abort System(LAS).
Bob Clark
