I suggest you get a copy of Schaum's Outline Series, Engineering Mechanics,
McLean and Nelson. In
the Second Edition, Chapter 19, page 298, problem 24, describes a water jet.
The formulae are
there, just change the mass from that of water to air. Watch your units!
Jim Y

Unless you're planning on a pretty short test, I have my doubts about trying
to make a treadmill work--you're well in excess of the design load of the
machine, and the belt friction is only one area of concern.
There are SAE papers available that publish a "standard" design for test
machinery of this sort... a trip to a decent engineering library would be
time well spent.

Here is the problem from the both the second and fourth edition, chapter 20
Impulse and Momentum,
page 417:
See several example problems dealing with this situation in the chapter.
Values are based on Standard Temperature and Pressure (STP)
water = 62.428 lb.cu ft
gravity = 32.174 ft/s/s
diameter of stream of water = 2 inches
velocity of water = 80 ft/sec
delts t = time interval of particles of water (Note: delta t cancels out, but
required in formula)
mass = (area of stream in sq ft) (velocity of stream in ft/s) ( density of water
in slug/(cu ft)
mass = (.25 x PI x (2/12) x (2/12)) x (80 x (delta t)) x (62.428 / 32.174)
mass = 3.3865(delta t) slugs Note: delta t cancels out below
---------------
Sum of the forces = mass(v" - v')
P(delta t) = 3.3865(delta t) x ( 0 - 80) = -270.92 lb
P = -271 lb
Force of water on the plate is +271 lb to the right.
The density of air at standard conditions (STP) is 0.074 lb/cu. ft. (Marks
Handbook)
Using the above with the density of air, the mass = 0.004(delta t) slugs and P 0.32 lb.
And 1000 lb / .32 lb = 3125 nozzles. You may modify your velocity and nozzle
diameter..
Jim Y

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