Question

An incompressible liquid is flowing through the horizontal pipe as shown in the figure. Pipe $1$ is connected to the pipe $2$ and pipe $3$. The flow of liquid through the pipe $1$, pipe $2$ and pipe $3$ are $8\text{m/s},6\text{m/s}$ and $1.1\text{m/s}$ respectively. If cross-section area of pipe $1$ and pipe $2$ are $1{\text{m}}^2$ and $0.8{\text{m}}^2$, find the area of cross-section of pipe $3$.

• A. $5.8{\text{m}}^2$
• B. $4.6{\text{m}}^2$
• C. $16.5{\text{m}}^2$
• D. $2.9{\text{m}}^2$

Answer 1

The correct option is D $2.9{\text{m}}^2$

Given, speed of liquid through pipe
$v_1=8\text{m/s},v_2=6\text{m/s},v_3=1.1\text{m/s}$.
Area of cross-section of pipe 1 and 2 are
$A_1=1{\text{m}}^2,A_2=0.8{\text{m}}^2$
Let area of cross-section of pipe $3$ is $A_3$
By the equation of continuity,
$A_1{v}_1=A_2{v}_2+A_3{v}_3$
$\Rightarrow 1\times 8=0.8\times 6+A_3\times 1.1$
$\Rightarrow A_3=2.9{\text{m}}^2$