The hydrostatic pressure exerted by a static homogeneous liquid of density rho at depth h beneath its free surface is expressed by:
Interpretation, solution and typical proof: Hydrostatic pressure equation: P = rho * g * h, derived from the weight of the fluid column acting per unit area.
2
A diver descends to a depth of 30 meters in seawater (density = 1030 kg/m^3). If atmospheric pressure is 1.013 x 10^5 Pa and g = 9.8 m/s^2, the total absolute pressure experienced by the diver is approximately:
Interpretation, solution and typical proof: P_liquid = 1030 * 9.8 * 30 = 302,820 Pa. Total absolute pressure = 101,300 + 302,820 = 404,120 Pa (~4.0 atm).
3
Pascal's principle states that when pressure is applied to an enclosed, incompressible fluid, it is transmitted:
Interpretation, solution and typical proof: Pascal's principle guarantees that pressure applied to an incompressible confined fluid is transmitted equally in all directions.
4
In a hydraulic press, the ratio of the cross-sectional area of the large piston to that of the small piston is 50. If a force of 100 N is exerted on the small piston, the maximum force exerted by the large piston is:
Interpretation, solution and typical proof: F = f * (A / a) = 100 N * 50 = 5000 N.
5
The mechanical advantage (eta) of an ideal hydraulic press equals all of the following ratios EXCEPT:
Interpretation, solution and typical proof: Conservation of energy dictates that work output cannot exceed work input (W_out / W_in <= 1). Statement A violates thermodynamics.
6
The relative density (specific gravity) of a substance is defined as:
Interpretation, solution and typical proof: Specific gravity is a dimensionless ratio comparing substance density to the reference density of pure water at 4°C.
7
In a U-tube manometer containing two immiscible liquids in equilibrium, the heights of the liquid columns measured above the separating surface are:
Interpretation, solution and typical proof: Equilibrium at the separating surface requires P1 = P2, thus rho1 * g * h1 = rho2 * g * h2 => h1 / h2 = rho2 / rho1.
8
Why are hydroelectric storage dams constructed with a base that is significantly thicker than the crest?
Interpretation, solution and typical proof: Liquid pressure depends solely on depth h; lateral hydrostatic thrust is greatest at the base requiring maximum structural thickness.
9
A metallic cube of side length 10 cm and density 7800 kg/m^3 is completely submerged in water (density 1000 kg/m^3). The buoyant force (upthrust) acting on the cube is (g = 10 m/s^2):
Interpretation, solution and typical proof: Archimedes' principle: F_b = rho_liquid * V_submerged * g = 1000 * (0.1)^3 * 10 = 1000 * 0.001 * 10 = 10 N.
10
Pure water reaches its maximum density (1.000 g/cm^3 or 1000 kg/m^3) at a temperature of:
Interpretation, solution and typical proof: Water anomalous thermal expansion: density peaks at 4°C as hydrogen bonds arrange into open hexagonal ice crystals below 4°C.
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