Question

What is the pressure exerted in \(\text{kN/m}^2\) at a point \(1070\text{ mm}\) below the free surface of water?

• A. \(10.5 \text{ kN/m}^2\)
• B. \(15 \text{ kN/m}^2\)
• C. \(9 \text{ kN/m}^2\)
• D. \(8 \text{ kN/m}^2\)

Hint:

A useful shortcut: each meter of water depth exerts approximately \(10 \text{ kPa}\) (or \(10 \text{ kN/m}^2\)) of hydrostatic pressure.
For \(1.07 \text{ m}\) of depth:
\[ 1.07 \cdot 10 = 10.7 \text{ kN/m}^2 \approx 10.5 \text{ kN/m}^2 \]

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The hydrostatic pressure exerted by a static fluid at a given depth is directly proportional to the depth, the density of the fluid, and the acceleration due to gravity.
Key Formula or Approach:
The hydrostatic pressure (\(P\)) is given by:
\[ P = \rho \cdot g \cdot h \]
Where:
- \(\rho\) is the density of the fluid (for water, \(\rho \approx 1000 \text{ kg/m}^3\)).
- \(g\) is the acceleration due to gravity (\(g \approx 9.81 \text{ m/s}^2\)).
- \(h\) is the depth below the free surface in meters (\(\text{m}\)).

Step 2: Detailed Explanation:
Let us convert the given values into SI units:
- Depth (\(h\)) = \(1070 \text{ mm} = 1.07 \text{ m}\).
Now, calculate the pressure:
\[ P = 1000 \text{ kg/m}^3 \cdot 9.81 \text{ m/s}^2 \cdot 1.07 \text{ m} \]
\[ P = 10496.7 \text{ kg} \cdot \text{m}^{-1} \cdot \text{s}^{-2} \]
\[ P = 10496.7 \text{ N/m}^2 \]
To convert this value into kilonewtons per square meter (\(\text{kN/m}^2\)), divide by 1000:
\[ P = \frac{10496.7}{1000} \approx 10.5 \text{ kN/m}^2 \]
This matches Option A.

Step 3: Final Answer:
The pressure exerted is \(10.5 \text{ kN/m}^2\).