How much thrust is created?

Question

If a turbine is pushing 6,803.3333 cubic feet of air at sea level per minute out a jet nozzle of 14.59 inches diameter how much thrust is created. I am not concerned with feasibility or application i simply wish to check my math. If you need more information to find the answer please ask and I will supply.

I was told that the magic number at sea level was 1.204mg per Cubic Centimeter but I really don't know if that is correct. If that number is correct and my math is correct I have 0.075 Lbs. per Cubic Foot.

Answer 1

Force is the rate of momentum change, in this case the exhaust velocity times the mass rate. Assuming no compression, mass rate is volume rate * density, and velocity is volume rate / area. If you observed all the right units conventions (in ths case, slugs-feet-pounds force) I'm sure you got the math right.
EDIT: If you want to give me the value you are using for air density I'll give you the thrust. For density = 1.168 kg/m^3, I get:
mass rate = 0.25697 slug/sec
velocity = 97.664 ft/sec
thrust = 25.097 lb.
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Let me give you the metric to english constants, since most web sites seem to have air density in kg/m^3 (same as mg/cc).
grav accel = 9.80665 m/sec^2 = 32.17405 ft/sec^2
1 ft = 0.3048 m (exact)
1 kg = 2.204622622 lbmass = 2.204622622/32.17405 slug = 0.0685218 slug
1 kg/m^3 = 0.0685218 * 0.3048^3 = 0.00194032 slug/ft^3
32.17405 lbmass = 1 slug
Now you can use any source you like and get the density in the right units, slug/ft^3.
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So, assuming 0.075 lbmass/ft^3, we get
density = 0.075/32.17405 = 0.00233107 slug/ft^3
vol. rate = 113.389 ft^3/sec
mass rate = 0.264318 slug/sec
velocity = 97.6636 ft/sec
thrust = 25.8142 lb.
Thrust is directly proportional to density so that makes it easy if you decide to use a different density. However, 0.075 lbmass/ft^3 seems to be one of the accepted values (see ref.).