Question

When water is flowing through a pipe, the sudden increase in diameter results in the loss of head of water. The sudden decrease in diameter would result

• A. Gain in head of water
• B. Loss of head of water
• C. Initially gain then loss of head of water
• D. Initially loss then gain of head of water

Hint:

Minor Pipe Losses: Both Sudden Enlargement AND Sudden Contraction cause turbulent dissipation resulting in a LOSS OF HEAD ($h_c \approx 0.5 v_2^2/2g$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Minor energy losses in pipe networks: both sudden expansion and sudden contraction in pipe diameter generate flow separation, turbulent eddies, and recirculation zones (vena contracta), dissipating mechanical energy and resulting in a Loss of head.
Key Formula or Approach:
\[ h_c = k_c \frac{v_2^2}{2g} = \left( \frac{1}{C_c} - 1 \right)^2 \frac{v_2^2}{2g} \approx 0.5 \frac{v_2^2}{2g} \implies \mathbf{Loss \text{ } of \text{ } Head} \]

Step 2: Detailed Explanation:
In pipe hydraulics and minor head loss fluid dynamics:
- When a fluid flows through closed conduits:
1. Sudden Expansion: Fluid separates from the walls, forming intense turbulent eddies and causing Borda-Carnot expansion loss ($h_e = \frac{(v_1 - v_2)^2}{2g}$).
2. Sudden Contraction (Sudden Decrease in Diameter) (B):
- Fluid cannot round the sharp 90-degree corner smoothly; streamlines converge beyond the constriction to form a contracted narrow jet known as the vena contracta.
- Deceleration from the vena contracta to normal pipe flow creates severe boundary layer separation and turbulent vortex dissipation.
- This results in an irreversible Loss of head of water ($h_c \approx 0.5\frac{v_2^2}{2g}$). Any abrupt geometric disturbance in a pipe always converts available mechanical head into irreversible viscous heat.

Step 3: Final Answer:
Hence, sudden decrease in diameter results in Loss of head of water, matching option (B).