If w is the specific weight of liquid and h the depth of any point from the surface, then pressure intensity at that will be :
Try it first: pick an option, then read the explanation.
Asked in SSC JE 4 MARCH 2017 Morning Shift
Detailed Explanation
The fundamental equation of hydrostatics states that pressure increases linearly with vertical depth in any static, incompressible liquid.
1. Hydrostatic law formulation:
\[ \frac{dp}{dh} = w = \rho g \]
Where \(w\) is the specific weight (weight density) of the liquid and \(h\) is depth below the free surface.
2. Integrating from the free surface (\(h = 0, p = p_0 = 0\) gauge):
\[ \int_0^p dp = \int_0^h w \, dh \]
For an incompressible liquid, \(w\) is constant:
\[ p = w \cdot h \]
Why “w h” Is Correct
By direct integration of the hydrostatic equation, the pressure intensity at vertical depth \(h\) equals the weight density (specific weight \(w\)) multiplied by the depth \(h\), yielding \(w \cdot h\).
Why the Other Options Are Wrong
- A. h: h has dimensions of length [L], whereas pressure has dimensions [M L⁻¹ T⁻²].
- C. w/h: w/h has dimensions of force per unit volume per length [M L⁻² T⁻²], which is not pressure.
- D. h/w: h/w has dimensions of length per specific weight, which is dimensionally incorrect.
Key Point
Hydrostatic pressure intensity: p = w · h = ρ · g · h.
Key Concepts for Students
- Specific weight w = ρg has SI units of N/m³.
- Pressure intensity p = wh has SI units of N/m² (Pascals).
- Surfaces of equal depth below the free surface form horizontal isobaric planes.
Practice more: this is question 11 in Measurement of Pressure MCQs – Part 1. Try the whole set and check every answer instantly.