Download 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