Solved Problems

Example

Problem: Calculate the absolute pressure at a depth of 15 m in seawater (SG=1.03SG = 1.03). Assume Patm=101.3 kPaP_{atm} = 101.3 \text{ kPa}.

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Example

Problem: A differential manometer connects pipe A (Water) and pipe B (Oil, SG=0.8SG=0.8). The mercury (SG=13.6SG=13.6) level in the U-tube is 0.2 m higher on the B side. The level of water in A is 0.5 m below the mercury interface on the left. The level of oil in B is 0.3 m above the mercury interface on the right. Find the pressure difference PAPBP_A - P_B.

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Example

Problem: An inclined manometer is used to measure small pressure differences. The tube is inclined at 3030^\circ to the horizontal. If the reading along the incline is L=0.4 mL = 0.4 \text{ m}, what is the vertical pressure head difference?

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Example

Problem 4: Absolute vs Gauge Pressure A tire pressure gauge reads 210 kPa210 \text{ kPa}. The atmospheric pressure is 101.325 kPa101.325 \text{ kPa}. What is the absolute pressure inside the tire?

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Example

Problem 5: Pressure at Depth with SG Calculate the pressure at a depth of 5 m5 \text{ m} in a tank filled with oil having a specific gravity of 0.850.85.

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Case Study 1: Dams and Hydrostatic Pressure

Context: The design of dams fundamentally revolves around hydrostatic pressure.
Application: As depth increases, hydrostatic pressure increases linearly. This is why dams are typically much wider at their base than at their crest. Gravity dams use their immense weight to counteract the overturning moment generated by the hydrostatic pressure force acting horizontally on their upstream face. Analyzing the pressure distribution is critical to ensure the dam's structural integrity and prevent sliding or overturning.

Case Study 2: Scuba Diving and Barotrauma

Context: Hydrostatic pressure has significant physiological impacts on humans.
Application: For every 10 meters a scuba diver descends, the pressure increases by approximately 1 atmosphere. This rapid increase in pressure affects air-filled spaces in the body, such as the lungs, ears, and sinuses. According to Boyle's Law, as pressure increases, the volume of these air spaces decreases. Divers must equalize pressure during descent to avoid barotrauma. Similarly, during ascent, if a diver holds their breath, the expanding air can cause lung overexpansion injuries due to decreasing ambient pressure.