Assessment: Fluid Dynamics

Water (ρ=1000 kg/m³, η=0.001 Pa·s) flows through a pipe of diameter 0.05 m at 0.2 m/s. Find the Reynolds number.

A pipe narrows from A₁=0.04 m² (v₁=3 m/s) to A₂=0.02 m². Find v₂.

Water (ρ=1000 kg/m³) flows through a horizontal pipe at P₁=150000 Pa, v₁=1 m/s, speeding up to v₂=6 m/s. Find P₂.

A fluid layer (η=0.0012 Pa·s) of area 0.3 m² moves at 0.4 m/s relative to a fixed layer 0.0015 m away. Find the viscous force.

Water (γ=0.072 N/m, ρ=1000 kg/m³, θ≈0°) rises 0.02 m in a capillary tube. Find the tube's radius.

A needle of length 0.03 m floats on water (γ=0.072 N/m), supported by surface tension along both sides of the needle. Find the maximum supporting force.

A Venturi meter narrows a pipe to measure flow speed by measuring a pressure drop in the narrow section. Which principle explains why pressure drops there?

Blood flow slows down significantly in the body's tiny capillaries, even though each individual capillary is extremely narrow. What explains this?

Water (ρ=1000 kg/m³) flows through a pipe of constant cross-section (so v stays the same) from P₁=300000 Pa at height h₁=0 m up to height h₂=5 m. Find P₂.

Two capillary tubes of radii 0.0004 m and 0.0008 m are dipped in the same liquid (γ=0.05 N/m, ρ=800 kg/m³, θ≈0°). Find the difference in rise height between the narrower and wider tube.