Question

The cylindrical tube of a spray pump has a cross-section $5{\text{cm}}^2$, one end of which has $50$ fine holes, each of area ${10}^{-8}{\text{m}}^2$. If the liquid flows inside the tube with a speed of $0.3\text{m/min}$, then find the speed with which the liquid is ejected through the holes.

• A. $2\text{m/s}$
• B. $5\text{m/s}$
• C. $10\text{m/s}$
• D. $8\text{m/s}$

Answer 1

The correct option is B $5\text{m/s}$

Given, area of tube $A_1=5{\text{cm}}^2$
Area of one fine hole $={10}^{-8}{\text{m}}^2$
So, area of $50$ holes $A_2=50\times {10}^{-8}{\text{m}}^2$
Speed of liquid inside the tube,
$v_1=0.3\text{m/min}$
$\Rightarrow v_1=\frac{0.3}{60}\text{m/s}$
Let the speed of liquid through the holes $=v_2$
Applying equation of contitnuity,
$A_1{v}_1=A_2{v}_2$
$\Rightarrow (5\times {10}^{-4})\times \frac{0.3}{60}=(50\times {10}^{-8})\times v_2$
$\Rightarrow v_2=5\text{m/s}$