#### Transcript Reynolds number

Energy • Energy is the capacity or capability to do work and energy is used when work are done. • The unit for energy is joule - J, where • 1 J = 1 Nm • which is the same unit as for work. Energy Efficiency • Energy efficiency is the ratio between useful energy output and input energy, and can be expressed as • μ = Eo / Ei (1) • where • μ = energy efficiency • Eo = useful energy output • Ei = energy input • It is common to state efficiency as a percentage by multiplying (1) with 100. Example - Energy Efficiency • A lift moves a mass 10 m up with a force of 100 N. The input energy to the lift is 1500 J. The energy efficiency of the lift can be calculated as • μ = (100 N) (10 m) / (1500 J) • = 0.67 or • = 67 % Power • Power is a measure of the rate at which work is done and can be expressed as • P = W / dt (1) • where • P = power (W) • W = work done (J) • dt = time taken (s) • Since work is the product of the applied force and the distance, (1) can be modified to • P=Fv (1b) • where • F = force (N) • v = velocity (m/s) Energy converted • Power is also a measure of the rate at which energy is converted from one form to another and can be expressed as • P = E / dt (2) • where • P = power (W) • E = energy converted (J) • dt = time taken (s) Example - Work done by Electric Motor • The work done by a 1 kW electric motor in 1 hour can be calculated by modifying (1) to • W = P dt • = (1 kW) (1000 W/kW) (1 h) (3600 s/h) • = 3600000 J • = 3600 kJ Reynolds Number • The Reynolds Number is a non dimensional parameter defined by the ratio of • dynamic pressure (ρ u2) and • shearing stress (μ u / L) • and can be expressed as • Re = (ρ u2) / (μ u / L) • =ρuL/μ • =uL/ν (1) • • • • • • • where Re = Reynolds Number (non-dimensional) ρ = density (kg/m3, lbm/ft3 ) u = velocity (m/s, ft/s) μ = dynamic viscosity (Ns/m2, lbm/s ft) L = characteristic length (m, ft) ν = kinematic viscosity (m2/s, ft2/s) Reynolds Number for a Pipe or Duct • For a pipe or duct the characteristic length is the hydraulic diameter. The Reynolds Number for a duct or pipe can be expressed as • Re = ρ u dh / μ • = u dh / ν (2) • where • dh = hydraulic diameter (m, ft) Reynolds Number for a Pipe or Duct in common Imperial Units • The Reynolds number for a pipe or duct can also be expressed in common Imperial units like • Re = 7745.8 u dh / ν (2a) • where • Re = Reynolds Number (non dimensional) • u = velocity (ft/s) • dh = hydraulic diameter (in) • ν = kinematic viscosity (cSt) (1 cSt = 10-6 m2/s ) • The Reynolds Number can be used to determine if flow is laminar, transient or turbulent. The flow is • laminar when Re < 2300 • transient when 2300 < Re < 4000 • turbulent when Re > 4000 Example - Calculating Reynolds Number • A Newtonian fluid with a dynamic or absolute viscosity of 0.38 Ns/m2 and a specific gravity of 0.91 flows through a 25 mm diameter pipe with a velocity of 2.6 m/s. • The density can be calculated using the specific gravity like • ρ = 0.91 (1000 kg/m3) • = 910 kg/m3 • The Reynolds Number can then be calculated using equation (1) like • Re = (910 kg/m3) (2.6 m/s) (25 mm) (10-3 m/mm) / (0.38 Ns/m2) • = 156 (kg m / s2)/N • = 156 ~ Laminar flow • (1 N = 1 kg m / s2) Potential energy • When a body of mass is elevated against the gravitational force the potential energy can be expressed as • Ep = Fg dh • = m g dh (1) • where • Fg = gravitational force (weight) acting on the body (N) • Ep = potential energy (J) • m = mass of body (kg) • g = gravitational acceleration (9.81 m/s2) • dh = change in elevation (m) Example - Potential Energy when body is elevated • A body of 1000 kg is elevated 10 m. The change in potential energy can be calculated as • Ep = (1000 kg) (9.81 m/s2) (10 m) • = 98100 J • = 98 kJ • = 0.027 kWh To be continued n Thank you