What is the equivalent head (cm) of the kerosene (specific gravity = 0.8), if the head of water is 500 cm ?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 25-01-2018 (Evening Shift)
Detailed Explanation
The hydrostatic pressure exerted by a fluid column can be converted to an equivalent column height of another fluid by equating their pressure intensities.
1. Given parameters:
- Water column head \(h_w = 500\text{ cm}\)
- Specific gravity of water \(S_w = 1.0\)
- Specific gravity of kerosene \(S_k = 0.8\)
2. Equate the hydrostatic pressure developed by both liquids:
\[ p = \rho_w g h_w = \rho_k g h_k \]
3. Express in terms of specific gravities (\(S = \rho / \rho_w\)):
\[ h_w \cdot S_w = h_k \cdot S_k \]
\[ h_k = \frac{h_w \cdot S_w}{S_k} = \frac{500\text{ cm} \times 1.0}{0.8} = \frac{5000}{8} = 625\text{ cm} \]
Why “625” Is Correct
Because kerosene has a specific gravity of \(0.8\) (making it \(20\%\) lighter than water), a kerosene column must be \(1 / 0.8 = 1.25\) times taller than a water column to produce the identical base pressure: \(500 \times 1.25 = 625\text{ cm}\).
Why the Other Options Are Wrong
- A. 100: 100 cm results from subtracting 400 or arbitrary division.
- B. 150: 150 cm results from subtracting 500 − (500 × 0.8) = 100 cm and adding arbitrary offsets.
- C. 550: 550 cm results from adding 50 cm rather than applying the proportional density ratio.
Key Point
Equivalent head formula: h_kerosene = h_water / S_kerosene = 500 / 0.8 = 625 cm.
Key Concepts for Students
- Lighter liquids require proportionally taller column heights: h ∝ 1/S.
- Specific gravity of kerosene typically ranges between 0.80 and 0.82.
- Pressure head represents energy per unit weight and is expressed in units of length.
Practice more: this is question 15 in Measurement of Pressure MCQs – Part 1. Try the whole set and check every answer instantly.