An ideal gas with k 133 is flowing through a nozzle such th

An ideal gas with k = 1.33 is flowing through a nozzle such that the Mach number is 2.5 where the flow area is 25 cm^2. Assuming the flow to be isentropic, determine the How area at the location where the Mach number is 1.2.

Solution

The area Mach number relation is given by,

A / A* = [ a ^ (- a / k - 1) (1 + k-1 / 2 * M^2) ^a / (k-1) ] / M

where a - (k+1) / 2 and A* is the throat area.

The Mach number 2,5 at A = 25cm2 with k = 1.33 gas, the throat area of the nozzle.

A* = A x M / [ a ^ (- a / k - 1) (1 + k-1 / 2 * M^2) ^a / (k-1) ]

A* = 25 x 2.5 / [1.165 ^ (-1.165 / 0.33) (1 + (0.33/2) x 2.5^2)

A* = 53. 577 cm2

Now, the throat area is found we can determine the area where the mach is 1.2.

A/A* = [ a ^ (- a / k - 1) (1 + k-1 / 2 * M^2) ^a / (k-1) ] / M

A = A* x [1.165 ^ (-1.165 / 0.33) (1 + (0.33/2) x 1.2^2)] / 1.2

A = 53.577 x 0.598 = 32.03 cm2