# Interdisciplinary Applied Mathematics

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An alternative expression for the thrust is given by

Ft = M ■ Isp ■ go,

where

sp

Ksxit

go

defines the intrinsic specific impulse (secs), and g0 = 9.80 m/sec2 is the gravitational acceleration at sea level. Isp is the primary performance indicator of the micronozzle; as Isp increases, less propellant is required to achieve a given    thrust.    The thrust    Ft    can be    computed    at    the    exit    (e)    of

the nozzle from

Ft = f (PeUe + Pe)dA.

Another measure of efficiency is the discharge mass efficiency, CD, which is the ratio of the actual mass to the ideal mass discharged assuming inviscid state, i.e., no losses.

An interesting limit of the specific impulse is obtained if we consider the free-molecular flow (Kn ^ ж), as in the work of Ketsdever et al. (1998). In free-molecular flow, the thrust is obtained from

(-Pt)FM =

поквТо

2

At,

where n0 is the stagnation number density, T0 is the stagnation temperature, and At is the nozzle area at the throat. The corresponding free-molecular mass flow rate through the nozzle is

(M) fm

no v

to-

4

###### At

where v is the average thermal speed of the propellant molecules, and m is the mass of the propellant molecule. We then obtain the specific impulse in the limit of free-molecular flow as

We can compare this value to the maximum possible value of Isp by considering the limit in equilibrium expansion, i.e.,

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