Question

Water flows through a horizontal pipe of varying cross-section at the rate of \( \pi \times 10^{-1} \, \text{m}^3/\text{s} \). The velocity of water at a point where the radius of the pipe is 10 cm is \( (\pi = 3.14) \)

• A. 0.1 m/s
• B. 1 m/s
• C. 10 m/s
• D. 100 m/s

Hint:

Use the equation of continuity: the volume flow rate equals area times velocity.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Volume flow rate \(Q = A v\), where \(A\) is the cross-section area at that point.

Step 2: Area at the Point
Radius \(r = 10\) cm \(= 0.1\) m, so \(A = \pi r^2 = \pi \times 10^{-2}\ \text{m}^2\).

Step 3: Calculation
\(v = \dfrac{Q}{A} = \dfrac{\pi \times 10^{-1}}{\pi \times 10^{-2}} = 10\) m/s.

Step 4: Compare the options
The velocity is 10 m/s, the third option.

Final Answer:
The velocity of water at that point is 10 m/s. \[ \boxed{\text{(C) }10\ \text{m/s}} \]