Problem

One method of driving flow and mixing two streams of fluid is shown below $($all pipes shown here are cylindrical$).$ The jet pump injects water at $\backslash (\backslash$mathrm$\{$V$\}\_\{1\}=40\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ through a $7\mathrm{.}6$ cm $($diameter of a cylindrical$)$ pipe and entrains a secondary flow of water $\backslash (\backslash$mathrm$\{$V$\}\_\{2\}=3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ in the annular region around the small pipe. The two flows become fully mixed downstream, where $\backslash (\backslash$mathrm$\{$V$\}\_\{3\}\backslash )$ is approximately constant $($does not vary with position in the larger pipe at position $3).$ For steady, incompressible flow, compute $\backslash (\backslash$mathrm$\{$V$\}\_\{3\}\backslash ).$

Note: all of these conduits are cylindrical $($not rectangular$).$

Step $1$

Write the equation for mass flow rate of fluid coming from the jet pump $($V$\_(1)).$ Keep the solution in symbols

until Step $5.$

Step $2$

Write the equation for mass flow rate of fluid coming from the entrained flow $($V$\_(2)).$ Keep the solution in

symbols until Step $5.$

Step $3$

Write the equation for mass flow rate of fluid after mixing $($V$\_(3)).$ Keep the solution in symbols until Step $5.$

Step $4$

Write the mass balance $($accumulation $=$ in $-$ out $+$ generation $-$ consumption$)$ for this situation. Keep the

solution in symbols until Step $5.$

Step $5$

Solve for the velocity after mixing $($V$\_(3)).$

COMPLETE THIS PROBLEM WITH ALL THE STEPS