GATE 2023 CE (CE2) – Question 33
The pressure in a pipe at X is to be measured by an open manometer as shown in figure. Fluid A is oil with a specific gravity of 0.8 and Fluid B is mercury with a specific gravity of 13.6. The absolute pressure at X is ______ kN/m$^2$ (round off to one decimal place). [Assume density of water as 1000 kg/m$^3$ and acceleration due to gravity as 9.81 m/s$^2$ and atmospheric pressure as 101.3 kN/m$^2$]. [Note: Figure is not to scale]
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Correct answer: 139.80 to 141.20
Explanation
The manometer is open to the atmosphere, so use gauge pressure in the liquid columns and add atmospheric pressure at the end. Moving **down** in a fluid raises the pressure by $\gamma h$; moving **up** lowers it.
Following the heights given in the figure, starting at the open mercury surface (at atmospheric pressure):
1. From the open mercury surface down 25 cm through mercury ($S=13.6$) to the oil-mercury interface:
$$\Delta p_1=13.6\times9.81\times0.25=33.35\text{ kPa}.$$
2. From the interface through oil ($S=0.8$) over 75 cm to point X:
$$\Delta p_2=0.8\times9.81\times0.75=5.89\text{ kPa}.$$
**Gauge pressure at X** $=33.35+5.89=39.24$ kPa.
**Absolute pressure:**
$$p_X=101.3+39.24=\mathbf{140.5\ kN/m^2}.$$