Question

Two pipes of diameters $d_1$ and $d_2$ converge to form a pipe of diameter d. If the fluid flows with a velocity of $v_1$ and $v_2$ in the two pipes, what will be the flow velocity in the third pipe ?

• A. $\frac{d_1{v}_1+d_2{v}_2}{d}$
• B. $\frac{d^2(v_1+v_2)}{d}$
• C. $\frac{(d_1+d_2{)}^2(v_1+v_2)}{d^2}$
• D. $\frac{d_1^2{v}_1+d_2^2{v}_2}{d^2}$

Answer 1

The correct option is D $\frac{d_1^2{v}_1+d_2^2{v}_2}{d^2}$

As per continuity equation

$\sum Av=constant$

$A_1{v}_1+A_2{v}_2=Av$

$\frac{\pi }{4}{d}_1^2{v}_1+\frac{\pi }{4}{d}_2^2{v}_2=\frac{\pi }{4}{d}^{2}v$

$v=\frac{d_1^2{v}_1+d_2^2{v}_2}{d^2}$