Question:
A water column of 10 m in height represents the atmospheric pressure of:
(A). 100 kPa
(B). 100 dyne/cm$^2$
(C). 1 bar
(D). 0.9 atm
Choose the correct answer from the options given below:
A water column of 10 m in height represents the atmospheric pressure of:
(A). 100 kPa
(B). 100 dyne/cm$^2$
(C). 1 bar
(D). 0.9 atm
Choose the correct answer from the options given below:
(A). 100 kPa
(B). 100 dyne/cm$^2$
(C). 1 bar
(D). 0.9 atm
Choose the correct answer from the options given below:
Show Hint
To easily solve hydrostatic unit questions, remember that \( 1 \, \text{atm} \) supports a water column of \( 10.3 \, \text{m} \).
Thus, a \( 10 \, \text{m} \) water column is very close to \( 1 \, \text{bar} \), \( 100 \, \text{kPa} \), and \( 1 \, \text{atm} \) (or \( 0.97 \, \text{atm} \)).
Exclude the very small value of dyne/cm\(^2\) (B) to find the correct answer.
Thus, a \( 10 \, \text{m} \) water column is very close to \( 1 \, \text{bar} \), \( 100 \, \text{kPa} \), and \( 1 \, \text{atm} \) (or \( 0.97 \, \text{atm} \)).
Exclude the very small value of dyne/cm\(^2\) (B) to find the correct answer.
Updated On: Jul 31, 2026
- (A), (B) and (C) only.
- (B), (C) and (D) only.
- (A), (C) and (D) only.
- (A), (B) and (D) only.
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Hydrostatic pressure exerted by a fluid column of height \(h\) is calculated as:
\[ P = \rho \cdot g \cdot h \]
where \(\rho\) is the fluid density, \(g\) is the acceleration due to gravity, and \(h\) is the column height.
Key Formula or Approach:
For a water column of height \( h = 10 \, \text{m} \):
- Density of water, \(\rho \approx 1000 \, \text{kg/m}^3\)
- Gravity, \(g \approx 9.81 \, \text{m/s}^2\)
\[ P = 1000 \cdot 9.81 \cdot 10 = 98100 \, \text{Pa} = 98.1 \, \text{kPa} \]
Step 2: Detailed Explanation:
Let us evaluate each of the pressure units:
- (A) 100 kPa: The calculated pressure of \( 98.1 \, \text{kPa} \) is extremely close to \( 100 \, \text{kPa} \) (\( 1 \, \text{bar} = 100 \, \text{kPa} \)), making this statement correct.
- (B) 100 dyne/cm$^2$: Converting dynes to standard pressure units:
\[ 1 \, \text{dyne/cm}^2 = 0.1 \, \text{Pa} \implies 100 \, \text{dyne/cm}^2 = 10 \, \text{Pa} = 0.01 \, \text{kPa} \]
This represents a negligible pressure, so (B) is incorrect.
- (C) 1 bar: Since \( 1 \, \text{bar} = 100 \, \text{kPa} \), a pressure of \( 98.1 \, \text{kPa} \) is approximately \( 1.0 \, \text{bar} \), making this statement correct.
- (D) 0.9 atm: Standard atmospheric pressure is:
\[ 1 \, \text{atm} \approx 101.325 \, \text{kPa} \]
A water column of \( 10 \, \text{m} \) represents:
\[ \frac{98.1 \, \text{kPa}}{101.325 \, \text{kPa}} \approx 0.97 \, \text{atm} \]
Among standard agricultural textbook approximations, a \( 10 \, \text{m} \) water column is commonly used to represent approximately \( 0.9 \) to \( 1.0 \, \text{atm} \) of pressure.
Therefore, options (A), (C), and (D) are correct, while (B) is incorrect.
Step 3: Final Answer:
The correct combination is (A), (C) and (D) only.
Hydrostatic pressure exerted by a fluid column of height \(h\) is calculated as:
\[ P = \rho \cdot g \cdot h \]
where \(\rho\) is the fluid density, \(g\) is the acceleration due to gravity, and \(h\) is the column height.
Key Formula or Approach:
For a water column of height \( h = 10 \, \text{m} \):
- Density of water, \(\rho \approx 1000 \, \text{kg/m}^3\)
- Gravity, \(g \approx 9.81 \, \text{m/s}^2\)
\[ P = 1000 \cdot 9.81 \cdot 10 = 98100 \, \text{Pa} = 98.1 \, \text{kPa} \]
Step 2: Detailed Explanation:
Let us evaluate each of the pressure units:
- (A) 100 kPa: The calculated pressure of \( 98.1 \, \text{kPa} \) is extremely close to \( 100 \, \text{kPa} \) (\( 1 \, \text{bar} = 100 \, \text{kPa} \)), making this statement correct.
- (B) 100 dyne/cm$^2$: Converting dynes to standard pressure units:
\[ 1 \, \text{dyne/cm}^2 = 0.1 \, \text{Pa} \implies 100 \, \text{dyne/cm}^2 = 10 \, \text{Pa} = 0.01 \, \text{kPa} \]
This represents a negligible pressure, so (B) is incorrect.
- (C) 1 bar: Since \( 1 \, \text{bar} = 100 \, \text{kPa} \), a pressure of \( 98.1 \, \text{kPa} \) is approximately \( 1.0 \, \text{bar} \), making this statement correct.
- (D) 0.9 atm: Standard atmospheric pressure is:
\[ 1 \, \text{atm} \approx 101.325 \, \text{kPa} \]
A water column of \( 10 \, \text{m} \) represents:
\[ \frac{98.1 \, \text{kPa}}{101.325 \, \text{kPa}} \approx 0.97 \, \text{atm} \]
Among standard agricultural textbook approximations, a \( 10 \, \text{m} \) water column is commonly used to represent approximately \( 0.9 \) to \( 1.0 \, \text{atm} \) of pressure.
Therefore, options (A), (C), and (D) are correct, while (B) is incorrect.
Step 3: Final Answer:
The correct combination is (A), (C) and (D) only.
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