Mechanical Properties of Fluids

A container of liquid accelerates horizontally at 10 m/s². Find the angle its free surface makes with the horizontal. (g = 10 m/s²)

A container of liquid (density 800 kg/m³) accelerates horizontally at 4 m/s². Find the pressure difference between two points 3 m apart along the direction of acceleration.

Water flows through a horizontal pipe with a pressure drop of 8000 Pa between a wide section (negligible speed) and a narrow section. Find the speed at the narrow section. (ρ = 1000 kg/m³)

A 3 mm radius ball (density difference from fluid = 6000 kg/m³) falls through a fluid of viscosity 0.2 Pa·s. Find its terminal velocity. (g = 10 m/s²)

Find the excess pressure inside a soap bubble of radius 2 mm, formed from a solution of surface tension 0.04 N/m.

Find the capillary rise of water (T = 0.05 N/m) in a tube of radius 0.5 mm, assuming complete wetting. (ρ = 1000 kg/m³, g = 10 m/s²)

Find the buoyant force on an object of volume 2×10⁻³ m³ fully submerged in water. (ρ_water = 1000 kg/m³, g = 10 m/s²)

Water flows through a pipe of area 4×10⁻⁴ m² at 2 m/s, into a narrower section of area 1×10⁻⁴ m². Find the speed in the narrow section.

A lift accelerates upward at 2 m/s². Find the pressure at a depth of 2 m in a tank of water (density 1000 kg/m³) inside the lift. (g = 10 m/s²)

Water (density 1000 kg/m³, viscosity 0.001 Pa·s) flows through a 0.02 m diameter pipe at 2 m/s. Find the Reynolds number.

Using Poiseuille's formula, find the rate of flow of a fluid (viscosity 0.001 Pa·s) through a tube of radius 0.01 m and length 2 m, with a pressure difference of 4000 Pa across it.

Two identical small drops of radius r merge to form one bigger drop. Find the ratio of the bigger drop's radius to r (using volume conservation).