Simple Momentum Theory
Turning to the math, the thrust F generated by the Fart is equal to the pressure jump delta p times the Fart area A:
F = delta p * A
A units check shows that:
force = (force/area) * area
We can use Bernoulli's equation to relate the pressure and velocity ahead of and behind the Fart, but not through the disk. Ahead of the disk the total pressure pt0 equals the static pressure p0 plus the dynamic pressure .5 * r * V0 ^2.
pt0 = p0 + .5 * r * V0 ^2
where r is the air density and V0 is the velocity of the Fart. Downstream of the butt,
pte = p0 + .5 * r * Ve ^2
where pte is the downstream total pressure and Ve is the exit velocity. At the butt itself the pressure jumps
delta p = pte - pt0
Therefore, at the butt,
delta p = .5 * r * [Ve ^2 - V0 ^2]
Substituting the values given by Bernoulli's equation into the thrust equation, we obtain
F = .5 * r * A * [Ve ^2 - V0 ^2]
We still must determine the magnitude of the exit velocity. A Fart based on the momentum equation provides this value.
Turning to the math, the thrust F generated by the Fart is equal to the pressure jump delta p times the Fart area A:
F = delta p * A
A units check shows that:
force = (force/area) * area
We can use Bernoulli's equation to relate the pressure and velocity ahead of and behind the Fart, but not through the disk. Ahead of the disk the total pressure pt0 equals the static pressure p0 plus the dynamic pressure .5 * r * V0 ^2.
pt0 = p0 + .5 * r * V0 ^2
where r is the air density and V0 is the velocity of the Fart. Downstream of the butt,
pte = p0 + .5 * r * Ve ^2
where pte is the downstream total pressure and Ve is the exit velocity. At the butt itself the pressure jumps
delta p = pte - pt0
Therefore, at the butt,
delta p = .5 * r * [Ve ^2 - V0 ^2]
Substituting the values given by Bernoulli's equation into the thrust equation, we obtain
F = .5 * r * A * [Ve ^2 - V0 ^2]
We still must determine the magnitude of the exit velocity. A Fart based on the momentum equation provides this value.
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