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 = F v         (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)     = ρ u L / μ     = u L / 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