Question

The specific gravity and height of mercury in a column are 13.6 and 20 cm respectively. For the same maximum pressure at the bottom, the equivalent height of water column is

• A. 27.2 cm
• B. 27.2 m
• C. 272 cm
• D. 272 m

Hint:

For pressure head conversions, use the simple formula $h_1 S_1 = h_2 S_2$, where $S$ is the specific gravity.
Since mercury is 13.6 times denser than water, you need a water column that is 13.6 times taller to produce the same pressure.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Mercury column 20cm, SG=13.6. Equivalent height of water for same pressure?

Step 2: Key Relationship (Alternate):
P = ρgh. h_water = SG_mercury × h_mercury (since ρ_mercury = SG×ρ_water).

Step 3: Detailed Explanation:
h_water = 13.6×20 = 272cm = 2.72m. Mercury is 13.6 times denser, so water column must be 13.6 times taller for same pressure.

Step 4: Final Answer:
272 cm.