Macroscopic Mechanical Energy Balance

1
Macroscopic MechanicalEnergy Balance
2
Macroscopic Energy Balance
Accumulation In Out Generation
Consumption

• Assume
• Energy is conserved
• Steady State

3
Macroscopic Energy Balance
How may Energy enter System?

• Via Mass Flow
• KE
• PE
• Int. Energy
• Heat Transfer (Q)
• Conduction
• Radiation
• Work on or by System (W)
• Pumps
• Compressors

Note Q and W positive for energy into system
4
Energy Transferred via Mass Flow

• Convective Term
• Internal Energy
• Kinetic Energy
• Potential Energy

• Flow Work Term
• Pressure work requiredto push fluid through
  system

5
Overall MechanicalEnergy Balance
6
Mechanical Energy Balance
Because they are difficult to determine exactly,
in fluid flow calculations it is common to group
all the thermal energy terms together.
The resulting term is called lost work or viscous
dissipation.
This term represents conversion of mechanical
energy into heat in the form of friction.
7
Mechanical Energy BalanceMEB
8
Variable Velocity at Cross Section
Again integrate across cross section and
introduce correction factor, a, to allow use of
average velocity.
9
Variable Velocity at Cross Section
Laminar FlowParabolic Flow
a
2
Turbulent FlowPlug Flow
a
10
MEB with Correctionfor Variable Velocity
Historical Note
Though this result is often called the Bernoulli
equation, Bernoulli actually only consideredW
hf 0.

11
Example
Water with a density of 998 kg/m3 is flowing at a
steady mass rate through a uniform diameter pipe.
The Reynolds number in the pipe is approximately
4000. The pump supplies 155.4 J/kg of fluid
flowing through the pipe. Given the other
conditions shown on the diagram, calculate the
viscous dissipation, hf, in the pipe system.