Question

The cylindrical tube of a spray pump has radius of $5\text{cm}$, one end of which has $10$ fine holes each of radius $0.1\text{cm}$. If the speed of liquid in the tube is $1\text{m/s}$, the speed of the ejection of the liquid through the holes is

• A. $125\text{m/s}$
• B. $250\text{m/s}$
• C. $450\text{m/s}$
• D. $500\text{m/s}$

Answer 1

The correct option is B $250\text{m/s}$

Given, radius of pipe $R=5\text{cm}$
Area of pipe $A_1=\pi R^2=\pi (5{)}^2\times {10}^{-4}{\text{m}}^2$
Radius of one fine hole $=r=0.1\text{cm}$
Area of $10$ fine holes = $10\times \pi r^2$
$=10\times \pi (0.1{)}^2\times {10}^{-4}{\text{m}}^2$
Speed of liquid in tube $v_1=1\text{m/s}$
Let speed of ejection of liquid through the holes $=v_2$
Using continuity equation,
$A_1{V}_1=A_2{V}_2$
$\pi (5{)}^2\times {10}^{-4}\times (1)=10\times \pi (0.1{)}^2\times {10}^{-4}\times v_2$
$\Rightarrow v_2=250\text{m/s}$