Given that I require 100lbs of thrust in a water jet, what is the
formula for calculating pump capacity?    Is the nozzel size, shape or
other characteristics a factor, and if so, how is the optimum
determined?

Hi.

I'm in the firm belief that those links will help You.
Its contain a lot about your question.
Note. Be carefull, cause the type of the examined jets
can be different of yours. 

http://www.wjta.org/Book%202/3_4a_wolgamott_and_zink.pdf
http://www.wrd.state.or.us/waterrights/cwre/ratecalc-pump.xls
http://manuals.dot.state.tx.us/dynaweb/colbridg/hyd/@Generic__BookTextView/48477;cs=default;ts=default

Regards.

pl. give reasons,eg.  domestic utility or only theoretical
knowledge.because  any pump capacity needs pressure(lbs) and
quantity(gallons) both.Only domestic use system can calculated on some
practical assumtions. th. u.

The equation you are looking for is:

Force (newtons) = Mass flow rate (kg/sec) * Avg Velocity of stream (meter/sec)

so for example 
100 pounds of force = 444.82 Newtons
so if we choose an avg velocity of 10 mph = 4.4704 meters/sec we'd
need a flow rate of 99.5 kg/sec. Since water weighs 1000 kg/m^3 that
equates to a flow rate of .0995 m^3/sec or 26.2 gals/second. This is a
high flow rate so you may wish to choose a much faster exit velocity.

To find a pump, you need to determine the pressure required to get
that velocity. Here I will assume you are pumping the water through a
round tube, and the governing model is called Poiseuille flow.
The equation is Q = Flow rate = PI*Pressure*radius of pipe^4 / (8 *
viscocity * length of pipe.)

I wrote a quick spreadsheet that does all these calculations for you but if you
use the 2 equations above and two more: 
Avg velocity in the pipe = Pressure*radius^2/(8 * viscocity * length of pipe.)
Power required by pump = mass flow rate *Velocity^2/2 
you have all the equations you need. (viscocity of water at room temp
= .00145 kg/m/s) You can see that the most efficent pumps (less power)
use lower velocities but many times this is not practical.

For your problem, a pump with a flow rate of 120 gals/min and a output
pressure at this flow rate of 2.5 psi will do the job. Using a 0.5 in
diameter pipe, this will create the required thrust of 100lbf. It will
require 17 hp (theoretical) so you should be size the motor typically
twice that size...
Other combinatations are easily possible.  For more info contact me at
kbreinlinger@netzero.net.  One more comment, more efficency can be had
by minimizing the number of bends from the pump to the outlet and
using smoothed transitions (rather than sharp ones)

PS - The equations I gave for Poiseuille flow are only valid for low
speed (laminar) flow rates (Reynolds number less than 2300).  Since I
am not a Google Researcher, I can't get paid, but I can give you the
spreadsheet that deals with low (laminar) and high speed (turbulent)
flows for the $50 you offer.