Question

A liquid with speed $v$ through a horizontal pipe of cross sectional area $A$ enters into another pipe of double the area of cross-section. The speed of the liquid in the second pipe will be

• A. $v$
• B. $2v$
• C. $\frac{v}{2}$
• D. $\frac{v}{4}$

Answer 1

The correct option is C $\frac{v}{2}$

Initial area, $A_1=A$
Initial velocity of liquid, $v_1=v$
Let final velocity of liquid, $v_2$
Given final area, $A_2=2A$
By continuity equaiton.
$A_1{v}_1=A_2{v}_2$
$\Rightarrow A\times v=\left(2A\right)\times v_2$
$\Rightarrow v_2=\frac{v}{2}$