A purely-converging nozzle is supplied by a reservoir of P0 = 100 bar and T0 = 300K, with the flow through the nozzle being adiabatic, reversible, and choked. Assume a constant 1 bar of back pressure (i.e exhausting into atmosphere). Answer the following questions:If the reservoir P0 is reduced assuming a constant T0, what effect will this have on the nozzle throat velocity AND mass flow rate? Explain why.If the reservoir pressure is allowed to reduce to say 1.2 bar, describe what effect (if any) this will have on the assumptions listed in the first sentence above.
Question
A purely-converging nozzle is supplied by a reservoir of P0 = 100 bar and T0 = 300K, with the flow through the nozzle being adiabatic, reversible, and choked. Assume a constant 1 bar of back pressure (i.e exhausting into atmosphere). Answer the following questions:If the reservoir P0 is reduced assuming a constant T0, what effect will this have on the nozzle throat velocity AND mass flow rate? Explain why.If the reservoir pressure is allowed to reduce to say 1.2 bar, describe what effect (if any) this will have on the assumptions listed in the first sentence above.
Solution
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If the reservoir P0 is reduced assuming a constant T0, the nozzle throat velocity will decrease and the mass flow rate will also decrease. Here's why:
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Nozzle Throat Velocity: The velocity of the gas at the throat of the nozzle is determined by the pressure difference between the reservoir and the throat. If the reservoir pressure decreases, the pressure difference decreases, which results in a lower velocity.
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Mass Flow Rate: The mass flow rate through the nozzle is proportional to the reservoir pressure. If the reservoir pressure decreases, the mass flow rate decreases.
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If the reservoir pressure is allowed to reduce to say 1.2 bar, the flow through the nozzle will no longer be choked. Here's why:
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Choked Flow: Choked flow occurs when the pressure ratio (reservoir pressure to back pressure) is above a certain critical value. For air, this critical value is approximately 1.89. If the reservoir pressure is reduced to 1.2 bar, the pressure ratio becomes 1.2, which is below the critical value. Therefore, the flow is no longer choked.
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Adiabatic, Reversible Flow: The assumptions of adiabatic, reversible flow should still hold as long as no heat is added or removed from the system and no irreversibilities (like friction or turbulence) are introduced. However, the flow characteristics will change because the flow is no longer choked.
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