- #1

evan-e-cent

- 15

- 10

http://drevanlewis.com/Hero-Steam-engine.jpg

I have calculated the thrust produced by the jets of steam and the power output compared with the energy required to produce the steam which gives a thermal efficiency of about 1-3%. depending mainly on RPM.

This calculation assumes that the steam nozzles are choked. That occurs when a standing wave forms in the nozzle and prevents the velocity of steam from increasing beyond the speed of sound locally within the steam i.e. mach 1.

This occurs when the pressure difference across the nozzle exceeds a certain critical value.

From EngineeringToolbox.com

The ratio between the critical pressure and the inlet pressure for a nozzle can be expressed as

pc / p1 = ( 2 / (n + 1) )n / (n - 1) (1)

where

pc = critical pressure (Pa)

p1 = inlet pressure (Pa)

n = index of isentropic expansion or compression - or polytropic constant

(For a perfect gas undergoing an adiabatic process the index - n - is the ratio of specific heat of the gas at constant pressure divided by the specific heat at constant volume. k = cp / cv. )

The values for n in steam where most of the process occurs in the wet region is n = 1.135. (In superheated steam it increases to n = 1.30 and some sources say 1.33 and for air is 1.4. ) We will use:

n=1.135

**pc / p1 = ( 2 / (n + 1) )n / (n - 1)**

pc / p1 = ( 2 / 2.135) ** (1.135 / (0.135) = 0.9368 ** 8.407 = 0.577

**pc / p1 = 0.577**

pa is atmospheric pressure or 1 atm (outlet pressure)

pt is absolute pressure in the tank (inlet pressure)

At the critical point

pa / pt = 0.577

pt = pa / 0.577

pt = 1 / 0.577 = 1.7331 atm absolute pressure

Subtract 1 atm = 0.7331 atm = 10.77 psi by gauge.

Any tank pressure greater than 10.77 psi will produce a sonic choke with velocity limited to mach 1 ! There is little to be gained by higher pressures.

I came across a comment in Physics Forums discussing air escaping from a car tyre, which said that for air the critical pressure is 65 psi. Repeating the above calculations for air gives a similar result of 13 psi. I am surprised that this would occur at such a low pressure of 10-13 psi. Is there something wrong with my calculation?

Any positive or negative comment would be helpful.