Practice

Fluids

Density, pressure at depth, buoyant force, floating, the continuity equation, Bernoulli’s equation and the speed of fluid leaving a tank.

The skill

Density is mass per volume, $ρ = m / V$ , and pressure is the perpendicular force per area, $P = F_{⟂} / A$ . The buoyant force equals the weight of the fluid an object pushes aside, $F_{b} = ρ V g$ , where $ρ$ is the fluid's density and $V$ is the volume under the surface. For flowing fluid, continuity, $A_{1} v_{1} = A_{2} v_{2}$ , gives the speeds, and Bernoulli's equation turns a speed difference into a pressure difference. The common slip is using the object's density in $F_{b} = ρ V g$ instead of the fluid's.

A worked example

A rectangular block measuring 0.39 m × 0.21 m × 0.20 m is held completely under the surface of vegetable oil (density 920 kg/m³). Use g = 10 m/s².

What is the buoyant force on the block, in newtons? Give your answer to three significant figures.

Solution

The block displaces its own volume, 0.016380 m³.
$F_{b} = ρ V g$ = (920)(0.016380)(10) = 151 N, the weight of the displaced fluid. The block's own material does not matter.

Answer: 151

Fluids

The skill

A worked example

Solution

Your turn

Lessons behind these problems