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:
The question asks to find the height of a water column that would exert the same pressure as a given height of a mercury column.

Step 2: Key Formula or Approach:
The pressure ($P$) exerted by a column of liquid is given by $P = \rho g h$. Since the pressure is the same for both columns, we can write:
\[ P = \rho_{mercury} g h_{mercury} = \rho_{water} g h_{water} \] The specific gravity (SG) of a substance is the ratio of its density to the density of water: $SG_{mercury} = \rho_{mercury} / \rho_{water}$.
So, $\rho_{mercury} = SG_{mercury} \times \rho_{water}$.
Substituting this into the pressure equation and canceling $g$ and $\rho_{water}$ gives the relationship:
\[ h_{water} = SG_{mercury} \times h_{mercury} \]

Step 3: Detailed Explanation:
We are given:
- Specific gravity of mercury ($SG_{mercury}$) = 13.6
- Height of mercury column ($h_{mercury}$) = 20 cm
Now, calculate the equivalent height of the water column:
\[ h_{water} = 13.6 \times 20 \text{ cm} \] \[ h_{water} = 272 \text{ cm} \] This is also equal to 2.72 m. Comparing with the options, 272 cm is available.

Step 4: Final Answer:
The equivalent height of the water column is 272 cm.