First Law of Thermodynamics-The Energy Equation (4)

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First Law of Thermodynamics-The Energy Equation
(4)
Work transfer can also occur at the control
surface when a force associated with fluid normal
stress acts over a distance.
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• Work transfer can also occur at the control
  surface because
• of tangential stress forces. Rotating shaft work
  is transferred
• by tangential stresses in the shaft material.
  Combining all
• the information

Equation with total stored energy,
For steady flow, and uniformly distributed
properties,
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• For only one stream entering and leaving,

When shaft work is involved, the flow is
unsteady, at least locally, e.g., the
velocity and pressure at a fixed location
near the rotating blade of a fan is unsteady,
while upstream and downstream of the machine,
flow is steady.
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One dimensional energy equation for steady-in-the
mean-flow valid for both incompressible and
compressible flows. Using enthalpy, following
equation is obtained,
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Example 1

• A pump delivers water at a steady rate of 300
  gal/min as shown in the figure. The change in
  water elevation across the pump is zero. The rise
  in internal energy of water associated with a
  temperature rise is 3000 ft. lb/slug . Determine
  the power (hp) required by the pump for an
  adiabatic process.

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Example 2

• Steam enters a turbine with a velocity of 30 m/s
  and
• enthalpy of 3348 kJ/kg. The steam leaves
  the turbine
• as a mixture of vapor and liquid having a
  velocity of 60 m/s
• and an enthalpy of 2550 kJ/kg. If the flow
  through the
• turbine is adiabatic and changes in elevation are
  negligible,
• determine the work output involved per unit mass
  of steam
• through-flow.

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Comparison of the Energy Equation with the
Bernoulli Equation
When the one-dimensional energy equation for
steady- in-the mean flow is applied to a
flow that is steady, the equation becomes,
Dividing by the mass flow rate, and rearranging,
where
Heat transfer rate per unit mass flow rate
Comparing with Bernoullis equation, it can be
concluded for incompressible frictionless flow,
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Frictional loss

• Useful or available energy
• Loss of available energy

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An important group of fluid mechanics problems
involves one-dimensional, incompressible,
steady-in-the-mean flow with friction and shaft
work for pumps, blowers, fans and turbines. For
this kind of flow, expressing shaft work per unit
mass, the energy equation becomes,
Mechanical energy equation or extended
Bernoullis equation, involves energy per unit
mass (ft. lb/slugft2/s2 or N. m m2/s2)
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Example 3

• Axial flow fan- delivers 0.4 kW power
• to the fan blades produce a 0.6 m axial
• stream of air at 12 m/s.

Energy equation in energy per unit weight
involves heads
where
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Energy Equation for Nonuniform Flows

• If the velocity profile at any section where flow
  crosses the
• control surface is not uniform, the energy
  equation is

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The difference in loss calculated assuming
uniform velocity and actual velocity profiles in
not large compared to w shaft net in