The large tank contains air at an absolute pressure of 600 kPa and temperature of 70^∘ C. The no

step 1 For the area of the exit to a star ratio being 6 .25, the supersonic exit mock is about 3 .41. I

The large tank contains air at an absolute pressure of 600...

The large tank contains air at an absolute pressure of $600 \mathrm{kPa}$ and temperature of $70^{\circ} \mathrm{C}$. The nozzle has a throat diameter of $20 \mathrm{~mm}$ and an exit diameter of $50 \mathrm{~mm}$. Determine the absolute pressure within the connected pipe, and the corresponding mass flow through the pipe, when the nozzle chokes and maintains isentropic supersonic flow within the divergent portion of the nozzle.

Key Concepts

Choked Flow

Choked flow occurs when the flow rate through a restriction, such as a nozzle throat, reaches a maximum limit because the sonic condition (Mach 1) is achieved at the throat. This means that further decreases in downstream pressure will not increase the mass flow rate, and the flow behavior is dominated by local sonic conditions rather than the reservoir conditions.

Isentropic Flow

Isentropic flow refers to a process that is both adiabatic (no heat transfer) and reversible, resulting in constant entropy along the flow path. In the context of compressible flow and nozzle dynamics, the assumption of isentropic flow allows the use of analytical relationships between pressure, temperature, and Mach number to predict flow properties such as density and velocity.

Compressible Flow Dynamics

Compressible flow dynamics deals with the behavior of fluids when density variations cannot be neglected, which is common at high velocities approaching or exceeding the speed of sound. This concept is crucial when analyzing nozzle flows, as variations in pressure and density affect the acceleration of the fluid and the resulting mass flow rate.

Nozzle (De Laval Nozzle) Behavior

A de Laval nozzle is designed with a convergent section leading to a throat and then a divergent section, enabling the acceleration of a compressible fluid to supersonic speeds in the divergent part when properly choked. Understanding the design and performance of such nozzles is essential for calculating pressure changes and mass flow rates in systems where high-speed gas expansion is involved.

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