Question

A liquid is flowing through a tube of diameter 9 mm with a speed of \(10\,cm\,s^{-1}\). If this tube is connected to a narrow tube in which the liquid flows with a speed of \(90\,cm\,s^{-1}\), then the diameter of the narrow tube is:

• A. 9 mm
• B. 1 mm
• C. 3 mm
• D. 10 mm

Hint:

In continuity equation problems, always remember \(A \propto d^2\), not \(d\).

Answer 1

The Correct Option is C

Step 1: Continuity principle.
For incompressible flow, A₁ v₁ = A₂ v₂, and since area ∝ diameter², d₁² v₁ = d₂² v₂.

Step 2: Inserting data.
(9)² × 10 = d₂² × 90.

Step 3: Simplifying.
81 × 10 = 90 d₂² → 810 = 90 d₂².

Step 4: Solving for diameter.
d₂² = 9 → d₂ = 3 mm.

Step 5: Conclusion.
The narrow tube's diameter is 3 mm.