Final answer:
Using the principles of thermodynamics and fluid dynamics, including isentropic flow relations and energy equations, the inlet conditions of velocity, static temperature, and static pressure can be calculated by working backward from the known choked flow conditions.
Step-by-step explanation:
To determine the velocity, static temperature, and static pressure at the duct inlet, we need to apply the principles of thermodynamics and fluid dynamics to the given scenario where the air flow is choked due to the heat addition. When a flow is choked, it means that the flow velocity at the choke point reaches the speed of sound for the gas at that temperature and pressure. To find the inlet conditions, we can use the isentropic flow relations and the energy equation.
The velocity can be determined using the conservation of mass and the condition that at the choke point, the Mach number is one. For the temperature and pressure, we can use the energy equation and isentropic relations, which for an ideal gas give relationships between temperature, pressure, and velocity changes in the flow.
In summary, to find the sought parameters at the duct inlet, we use the given conditions at the choke point and apply the relevant thermodynamic and fluid dynamic equations to backtrack the state of air before it got heated and its flow became choked.