(Solved): Air lows past an object and exits as a free jet as shown in the figure. Because of the obstruction ...

Air lows past an object and exits as a free jet as shown in the figure. Because of the obstruction, the exit velocity is non-uniform with magnitude of \( 4 \mathrm{~m} / \mathrm{s} \) from \( r=0 \) to \( r=0.5 \mathrm{~m} \) and \( 12 \mathrm{~m} / \mathrm{s} \) from \( r=0.5 \mathrm{~m} / \mathrm{s} \) to \( r=1.0 \mathrm{~m} \). It is initially calculated that the average velocity is \( 10 \mathrm{~m} / \mathrm{s} \), Using a differential area, \( d A=2 \pi r d r \), what is the value of the momentum correction factor, \( \beta \) ?