Two streams of the same fluid $($gasoline$)$ enter a pipe. Stream $1$ enters through a cross$-$sectional

area of $A_1$ and Stream $2$ enters as a smaller, faster jet with a cross$-$sectional area of $A_2.$ The jet

velocity is $v_2.$ These two fluid streams leave the pipe thoroughly mixed with a velocity $v_3$

through the same cross$-$sectional area as Stream $1.$

$($a$)$ Sketch a figure of this problem, label the corresponding areas and velocities, and draw a

control volume.

$($b$)$ State your assumptions for this problem and write the form$/$version of the continuity

equation you will use for part $($c$).$

$($c$)$ Next, derive an algebraic expression for the velocity of Stream $1(v_1)$ in terms of

$A_1,A_2,v_2,$ and $v_3.$ If $A_1=0\mathrm{.}06m^2,A_2=0\mathrm{.}013m^2,v_2=25\frac{m}{s},$ and $v_3=8\frac{m}{s},$ what is $v_1$ in

$\frac{m}{s}?$

$($d$)$ Determine the weight flowrate of Stream $1$ if the gasoline has a specific gravity of $0\mathrm{.}68$Two streams of the same fluid $($gasoline$)$ enter a pipe. Stream $1$ enters through a cross$-$sectional area of A$\_1$ and Stream $2$ enters as a smaller, faster jet with a cross$-$sectional area of A$\_2.$ The jet velocity is v$\_2.$ These two fluid streams leave the pipe thoroughly mixed with a velocity v$\_3$ through the same cross$-$sectional area as Stream $1.$

Sketch a figure of this problem, label the corresponding areas and velocities, and draw a control volume.

State your assumptions for this problem and write the form$/$version of the continuity equation you will use for part $($c$).$

Next, derive an algebraic expression for the velocity of Stream $1($v$\_1)$ in terms of A$\_1,$A$\_2,$v$\_2,$and v$\_3.$ If A$\_1=0\mathrm{.}06$ m$2,$ A$\_2=0\mathrm{.}013$ m$2,$ v$\_2=25$ m$/$s$,$ and v$\_3=8$ m$/$s$,$ what is v$\_1$ in m$/$s$?$

Determine the weight flowrate of Stream $1$ if the gasoline has a specific gravity of $0\mathrm{.}68$