Question

A diffuser has an inlet area of 60 cm2. Air enters the diffuser with a density of 0.748 kg/m2. The velocity at the inlet is 150 m/sec. It exits with a density of 2.0 kg/m2 at a velocity of 25 m/sec. Determine the area of the outlet.

Answer 1

`A_(out) = 134.64\,cm^(2)`

Step-by-step explanation:

The area of the outlet can be found by means of the Principle of Mass Conservation. A diffuser works usually as a steady state system:

`\dot m_(in) - \dot m_(out) = 0`

`\rho_(in)\cdot A_(in)\cdot v_(in)- \rho_(out)\cdot A_(out)\cdot v_(out) = 0`

The area of the outlet is:

`A_(out) =(\rho_(in)\cdot A_(in)\cdot v_(in))/(\rho_(out)\cdot v_(out))`

`A_(out) = ((0.748\,(kg)/(m^(3)) )\cdot (60\,cm^(2))\cdot (150\,(m)/(s)))/((2\,(kg)/(m^(3)) )\cdot (25\,(m)/(s) ))`

`A_(out) = 134.64\,cm^(2)`