Physic Labs

Fluid mechanics

Viscosity and the Reynolds number

Investigate the Reynolds number Re=ρvD/μRe = \rho vD/\mu and the laminar–turbulent transition: vary mean speed and viscosity to read Re on the sim, then check the Poiseuille profile u(r)=Δp(R2−r2)/(4μℓ)u(r) = \Delta p(R^2 - r^2)/(4\mu\ell) for fully developed laminar flow in a round pipe.

Undergraduate

Equipment

  • 3D pipe with particles moving laminar or turbulent according to Re (canvas, drag to rotate)
  • “Tốc độ trung bình” slider (readout in m/s)
  • “Độ nhớt động lực μ” slider (readout in Pa·s, shared by both figures)
  • Sliders “Bán kính R” (mm) and “Độ sụt áp Δp” (kPa)
  • Readouts “Re = ρvD/μ = …” and “u(r)=Δp(R²−r²)/(4μL); umax = …”

Procedure

  1. Measure the Reynolds number

    In section 1, move “Tốc độ trung bình” and “Độ nhớt động lực μ”, read both values (m/s and Pa·s) together with the readout “Re = ρvD/μ = … (water and D = 2 cm)”. Compute Re=ρvD/μRe = \rho vD/\mu yourself with ρ=1000 kg/m3\rho = 1000\ \mathrm{kg/m^3}, D=0.02 mD = 0.02\ \mathrm{m} and compare; watch the colored particles shift from smooth lines to chaotic wiggles once Re exceeds ≈ 2300.

  2. Separate inertia and viscosity effects

    Hold μ fixed and raise “Tốc độ trung bình” — Re grows linearly; then hold speed fixed and raise μ — Re falls inversely. Record two (v, μ) pairs giving the same Re and note they produce the same flow regime: the dimensionless number captures the physics, in line with the Buckingham Π principle of similitude.

  3. Check the Poiseuille profile

    In section 2, the u(r) versus r/R plot is a parabola; move “Bán kính R” and “Độ sụt áp Δp”, then read “umax = … m/s at r=0; u(R)=0”. Verify with umax⁡=ΔpR2/(4μL)u_{\max} = \Delta p R^2/(4\mu L) using L=0.5 mL = 0.5\ \mathrm{m}, and note the parabola gives zero velocity at the wall — the no-slip condition of laminar flow.

  4. Predict transition and limits

    Raise “Tốc độ trung bình” to its maximum while lowering μ; predict Re before reading the value. Note the readout caveat “Re ≈ 2300 is only a guide” — transition depends on disturbances and can reach higher Re in a quiet pipe. Compare: the Poiseuille profile in section 2 is exact only for fully developed laminar flow; in turbulence the mean profile is flatter.

Simulation

Experiment history

The notion of internal fluid friction was written by Newton in the Principia (1687) for shearing fluid layers; the linear relation τ=μ ∂u/∂y\tau = \mu\,\partial u/\partial y defines a Newtonian fluid. In the 1840s Claude-Louis Navier and George Gabriel Stokes built viscosity into the equations of motion (Navier–Stokes), while Jean Léonard Marie Poiseuille measured flows in capillary tubes and found the parabolic profile with the law Q∝R4Δp/(μℓ)Q \propto R^4\Delta p/(\mu\ell) bearing his name. In 1883 Osborne Reynolds published his celebrated pipe experiment: injecting dye into the center of water flowing through a glass tube, he watched the smooth dye filament break into irregular motion once the dimensionless ratio Re=ρvL/μRe = \rho vL/\mu exceeded a threshold — around 2300 for a round pipe, depending on disturbances. The Reynolds number became the central parameter separating laminar from turbulent flow.

Related physicists

Daniel BernoulliIsaac Newton

Related library topics

Viscosity and the Reynolds number