A siphon is used to transfer liquid from one vessel to another placed at a lower level. Under which condition will the siphon fail to work and the liquid will no longer flow through the tube?

Introduction / Context:

A siphon is a simple device used to transfer liquid from a higher container to a lower container using a bent tube. The working of a siphon often appears almost magical to beginners, but it is based on pressure differences and gravity. This question asks under what condition the siphon action will stop and fail to work.

Given Data / Assumptions:

• A siphon connects two vessels containing the same liquid.
• The outlet of the siphon is initially placed below the level of liquid in the first vessel.
• We consider steady conditions without air leaks into the tube.

Concept / Approach:

A siphon works because the outlet end of the tube is lower than the liquid surface in the source vessel. This creates a difference in hydrostatic pressure and allows gravity to pull the liquid through the tube. The continuous column of liquid in the tube transmits pressure. When the levels become equal, the pressure difference that drives the flow disappears, so the flow stops. Temperature or density equality alone does not destroy the pressure difference created by height, so these factors do not by themselves cause failure of the siphon.

Step-by-Step Solution:

Verification / Alternative check:

You can test this with a simple home experiment using two containers and a tube. Once the levels become equal, you will see the flow cease even though the tube is still filled with liquid. Changing temperature but keeping height difference will not instantly stop the siphon, which confirms that height difference is the controlling factor.

Why Other Options Are Wrong:

Option B: When the temperatures of the liquids are the same does not affect the pressure difference directly, so the siphon can still operate.

Option C: When the densities of the liquids are equal is usually the case anyway, as the siphon typically carries the same liquid; equal density does not stop the flow.

Option D: Unequal limb lengths do not by themselves prevent siphon action, as long as the outlet end is lower than the inlet liquid level and the tube remains filled without air gaps.

Common Pitfalls:

A common misconception is that the shape or length of the tube controls the siphon. In reality, the key factors are the relative heights of the liquid surfaces and the continuity of the liquid column. Students should focus on the pressure difference created by height rather than on geometric details of the tube.

Final Answer:

The siphon will fail when the liquid levels in the two vessels are at the same height.