An air flow at 600 kPa, 600 K, M=0.3 flows into a convergent-divergent nozzle with M=1 at the t

An air flow at 600 kPa, 600 K, M=0.3 flows into a...

Key Concepts

Mach Number

The Mach number is a dimensionless parameter defined as the ratio of the flow velocity to the local speed of sound. It characterizes the regime of the flow—subsonic, sonic, or supersonic—and is fundamental in determining the behavior of compressible flows, especially in variable area ducts like nozzles where it directly influences pressure, temperature, and density distributions.

Isentropic Flow Relations

Isentropic flow relations pertain to flows that are both adiabatic and reversible, meaning that the total (or stagnation) properties like pressure and temperature remain constant along a streamline even though the static properties change. These relations allow one to connect the static and total conditions using functions of the Mach number, which is critical when analyzing compressible flows through varying cross-sectional areas.

Convergent?Divergent Nozzle

A convergent?divergent nozzle is used to accelerate a compressible fluid to supersonic speeds; it has a converging section that accelerates the fluid up to Mach 1 (the throat) and a diverging section that further accelerates (or decelerates) the flow. The design principle and area variations in such nozzles are essential in defining the flow regime, including conditions for choked flow and determination of exit conditions.

Choked Flow

Choked flow refers to the condition in which the mass flow rate through a nozzle reaches its maximum possible value due to the flow reaching Mach 1 at the throat. Under choked conditions, further reductions in downstream pressure do not increase the mass flow rate, and the throat becomes a critical condition in the system.

Area-Mach Number Relationship

The area-Mach number relationship in isentropic flow establishes the link between the cross-sectional area of the duct and the Mach number of the fluid at that section. This relationship, derived from the conservation equations and the definition of the Mach number, is pivotal in determining the flow properties at various positions in a nozzle, particularly when the area ratio between the exit and the throat is specified.

Transcript

00:01 The air flow at 600 kiosk 600 calvin temperature and the mac number is 0 .3.

00:10 It is flow in convergent, divergent nozzle.

00:16 So this is convergent divergent nozzle.

00:19 Now the throat, this is the throat where the mac number is 1.

00:25 Now we are assuming the reversible flow with an exit area twice.

00:29 Exit area is twice the throat area so the ratio of area is given now we are calculating in this question the exit pressure exit pressure and temperature exit for subsonic exit flow so here this is subsonic flow so let's find out the stagnation pressure first of all so stagnation pressure is equal to inlet pressure this is the inlet pressure divided by stagnation pressure so so inlet pressure is 600 kilo pascal and this is 0 .9347 so stagnation pressure is 638 0 .66 kilo pascal this ratio at mac number 1 the pressure ratio is 0 .934 similarly temperature ratio from the table that is given 0 .98232.

01:45 So we can calculate the stagnation temperature also.

01:49 So stagnation temperature, inlet temperature, the ratio of temperature.

01:56 So 600 divided by 0 .98232.

02:01 So stagnation temperature is 610 .8.

02:07 Calvin now the ratio of areas are given the exit area to the throat area that is two so using table using table in the last page table a point 1 to a point 12 so exit temperature divided by stagnation temperature is 0 .9812 same the exit pressure stagnation pressure is 0 .9 936.

02:45 So we can calculate in the exit temperature...

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