Question

For flowing through the same discharge, the diameters of a pipe at section 1 and section 2 are 50 mm and 100 mm respectively. If the velocity of fluid at section 1 is 8 m/s, then the velocity at section 2 is

• A. 8 m/s
• B. 6 m/s
• C. 4 m/s
• D. 2 m/s

Hint:

From the continuity equation, velocity is inversely proportional to the square of the diameter ($v \propto 1/D^2$).
If you double the diameter, you increase the area by a factor of 4, so the velocity must decrease by a factor of 4.
In this problem, $D_2 = 2D_1$, so $v_2 = v_1/4 = 8/4 = 2$ m/s.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Pipe diameter changes 50mm to 100mm. v₁=8m/s. Find v₂.

Step 2: Key Formula (Alternate):
A₁v₁=A₂v₂. Since A∝D²: D₁²v₁=D₂²v₂. v₂=v₁(D₁/D₂)².

Step 3: Detailed Explanation:
v₂=8×(50/100)²=8×(1/2)²=8×1/4=2m/s. Larger area → lower velocity to maintain constant Q=Av.

Step 4: Final Answer:
2 m/s.