Question

An incompressible liquid flows through a horizontal tube as shown in the figure. Then the velocity $v$ of the liquid coming out of the tube of area $1.5A$ is:

• A. $3.0\text{m/s}$
• B. $1.5\text{m/s}$
• C. $1.0\text{m/s}$
• D. $2.25\text{m/s}$

Answer 1

The correct option is C $1.0\text{m/s}$

If the liquid is incompressible, then mass of the liquid entering through the left end should be equal to the total mass of the liquid coming out from the right end.

Applying equation of continuity at the junction of three tubes,
$A_1{v}_1=A_2{v}_2+A_3{v}_3...\left(i\right)$
where, $A_1=A,A_2=A,A_3=1.5A\&v_1=3\text{m/s},v_2=1.5\text{m/s},v_3=v$
Substituting in Eq.$\left(i\right)$,
$A{v}_1=A{v}_2+1.5Av$
Or,$A\times 3=(A\times 1.5)+\left(1.5Av\right)$
$\therefore v=1\text{m/s}$