Question

The atmospheric pressure head of water column is ____\.

• A. 760 mm
• B. 9.81 m
• C. 8.5 m
• D. 10.30 m

Hint:

Standard atmospheric pressure ($1.01 \times 10^5$ Pa) can support a water column of approximately 10.3 meters or a mercury column of 760 mm.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Atmospheric pressure is the force per unit area exerted on a surface by the weight of the air above it.
This pressure can be expressed as a equivalent height (head) of a fluid column.
The height of the column is inversely proportional to the density of the fluid used to measure it.
Key Formula or Approach:
The hydrostatic pressure equation is:
\[ P = \rho \cdot g \cdot h \]
To find the equivalent fluid column height ($h$):
\[ h = \frac{P}{\rho \cdot g} \]

Step 2: Detailed Explanation:
Let us identify the standard values for atmospheric pressure and water at standard sea-level conditions:
Standard atmospheric pressure is:
\[ P = 1.01325 \times 10^5 \text{ N/m}^2 \text{ (or Pa)} \]
The density of water is:
\[ \rho = 1000 \text{ kg/m}^3 \]
The acceleration due to gravity is:
\[ g = 9.81 \text{ m/s}^2 \]
Substituting these values into the head equation:
\[ h = \frac{1.01325 \times 10^5}{1000 \cdot 9.81} \]
\[ h = \frac{101325}{9810} \]
\[ h \approx 10.328 \text{ m} \]
This value corresponds to approximately 10.30 meters of water column.
For comparison, if mercury (density $\rho = 13600 \text{ kg/m}^3$) is used, the equivalent atmospheric pressure head is 760 mm of mercury.
Therefore, 10.30 m is the correct water column equivalent.

Step 3: Final Answer
The atmospheric pressure head of a water column is approximately 10.30 m.