Question

Water flows through a hose (pipe), whose internal diameter is 2.0 cm at a speed of 1.0 ms${}^{-1}$. What should be diameter of the nozzle, if the water is to emerge at a speed of 4.0 m s${}^{-1}$?

• A. $1$ m
• B. $1$ cm
• C. $0.005$ m
• D. $0.5$ m

Answer 1

The correct option is B $1$ cm

From Continuity equation: $A_1{V}_1=A_2{V}_2$

$\Rightarrow \pi (1{)}^2\times 1=4\times \pi r^2$

$\Rightarrow \frac{1}{4}=r^2\Rightarrow r=\frac{1}{2}cm$

So, Diameter of the nozzle $=\frac{1}{2}\times 2cm=1cm$