Question

Water flows through a horizontal pipe of diameter \(2\) cm at speed of \(3\ \text{cm s}^{-1}\). The pipe has a nozzle of diameter \(0.5\) cm at its end. The speed of water emerging from the nozzle is

• A. \(6\ \text{cm s}^{-1}\)
• B. \(48\ \text{cm s}^{-1}\)
• C. \(16\ \text{cm s}^{-1}\)
• D. \(12\ \text{cm s}^{-1}\)
• E. \(36\ \text{cm s}^{-1}\)

Hint:

In fluid flow, \[ A_1v_1=A_2v_2 \] and for circular pipes, area varies as diameter squared.

Answer 1

The Correct Option is B

Using equation of continuity: \[ A_1v_1=A_2v_2 \] Since area is proportional to square of diameter, \[ \frac{A_1}{A_2}=\left(\frac{2}{0.5}\right)^2=16 \] So, \[ v_2=16\times 3=48\ \text{cm s}^{-1} \] Hence, \[ \boxed{(B)\ 48\ \text{cm s}^{-1}} \]