Final answer:
To determine the final velocity of the steam out of the nozzle, we can use the principle of conservation of energy. By calculating the change in specific enthalpy and using the conservation of energy equation, we can find that the final velocity is approximately 648.5 ft/s.
Step-by-step explanation:
To determine the final velocity of the steam out of the nozzle, we can use the principle of conservation of energy. In adiabatic expansion, there is no heat transfer and no work done by or on the system, so the change in energy is equal to the change in internal energy. The initial energy of the steam is given by the enthalpy at 800 psia and 800°F, and the final energy is given by the enthalpy at the final state of saturated steam at 50 psia.
Using steam tables or charts, we can find the enthalpy values at the given states. The specific enthalpy (h) of the steam at the initial state is 1472.4 Btu/lb, and the specific enthalpy at the final state is 1202.1 Btu/lb. The change in specific enthalpy (∆h) is then (1472.4 - 1202.1) Btu/lb.
Now, we can use the conservation of energy equation to find the final velocity (v₂):
∆h = (v₂² - v₁²) / 2
As the initial velocity (v₁) is negligible, we can ignore it in this equation. Rearranging the equation, we get:
v₂² = 2∆h
Plugging in the values, we have:
v₂² = 2 * (1472.4 - 1202.1) Btu/lb
v₂² = 540.6 Btu/lb
Finally, we convert Btu/lb to ft²/s² by multiplying by the conversion factor, 778.17 ft²/s²/Btu/lb:
v₂² = 540.6 Btu/lb * 778.17 ft²/s²/Btu/lb
v₂² = 420,951.6 ft²/s²
Taking the square root of both sides, we find:
v₂ = √(420,951.6) ft/s
v₂ ≈ 648.5 ft/s