Pressure, Density and Buoyancy flashcards

$\rho =\frac{m}{V}$ in kg/m³ (water 1,000 kg/m³ = 1 kg/L). Specific gravity = $\frac{{\rho }_{material}}{{\rho }_{water}}$, unitless; below 1 floats in fresh water, above 1 sinks.

$\Delta P=\rho gh$: liquid density (kg/m³) times g (m/s²) times depth (m), in pascals. With g = 10, each meter of fresh water adds about 10 kPa. Doubling depth doubles pressure.

No. Pressure at a depth depends only on liquid density, g and vertical depth, not on container shape, width or total volume. A thin pipe and a pool 3 m deep have equal bottom pressure.

$F_b={\rho }_{fluid}g{V}_{disp}$: equals the weight of fluid displaced. Use the fluid's density, not the object's. A fully submerged 0.05 m³ object in fresh water gets 500 N (g = 10).

$W_{app}=W-F_b$: true weight minus buoyant force is the scale reading. A 54 N aluminum casting with 20 N of buoyancy reads 34 N; its mass is unchanged.

$\frac{V_{sub}}{V}=\frac{{\rho }_{obj}}{{\rho }_{fluid}}$. A 300 kg/m³ foam float is 30% submerged in fresh water; ice (about 917 kg/m³) is about 92% under.

Compare its average density (total mass / outside volume, including sealed air) with the fluid's. Less dense: floats. Denser: sinks. Equal: neutrally buoyant. That is why a steel ship floats.

No. Pressure rises equally on top and bottom, so the difference, and the buoyant force, stays the same. Only squeezable objects (balloons, wetsuits) lose buoyancy as they compress.