Example: Exercise 5.9.4 (Pump)

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Example Exercise 5.9.4 (Pump)
Pump
Flow
Oil (S0.82)
Want Rate at which energy is delivered to oil by
pump
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Example Exercise 5.9.4 (Pump)
Pump
Flow
Oil (S0.82)
Want Rate at which energy is delivered to oil by
pump
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Example Exercise 5.9.4 (Pump)
Pump
Flow
Oil (S0.82)
Want Rate at which energy is delivered to oil by
pump
Need to find hp associated with the pump
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Example Exercise 5.9.4 (Pump)
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Example Exercise 5.9.4 (Pump)
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Example Exercise 5.9.4 (Pump)
Rate of transfer of energy
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Example Exercise 5.9.4 (Pump)

• Pumps (and also turbines) are characterized by
  their efficiency

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Example Exercise 5.9.4 (Pump)

• Pumps (and also turbines) are characterized by
  their efficiency

• Say, in exercise 5.9.4 the pump is 90
  efficient and we require
• 6.83 kW of output, then

input 6.83 kW / 0.9 7.59 kW
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Example Exercise 5.9.4 (Pump)

• Pumps (and also turbines) are characterized by
  their efficiency

• Say, in exercise 5.9.4 the pump is 90
  efficient and we require
• 6.83 kW of output, then

input 6.83 kW / 0.9 7.59 kW

• Pumps (and also turbines) are characterized by
  their efficiency.

Efficiency
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General Energy Equation for Steady Flow of Any
Fluid
First Law of Thermodynamics For steady flow,
external work done on any
system plus the thermal
energy transferred
into or out of the system is
equal to the change
of energy of the system
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General Energy Equation for Steady Flow of Any
Fluid
First Law of Thermodynamics For steady flow,
external work done on any
system plus the thermal
energy transferred
into or out of the system is
equal to the change
of energy of the system
(I) Using the first law of thermodynamics, (II)
taking into account non-uniform velocity at a
cross-section of flow region, and (III) assuming
flow goes from section 1 to section 2, we can
derive the following
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General Energy Equation for Steady Flow of Any
Fluid

• is a correction factor accounting for
  non-uniform velocity in cross-section

• If velocity is uniform in cross-section, then

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General Energy Equation for Steady Flow of Any
Fluid

• is a correction factor accounting for
  non-uniform velocity in cross-section

• If velocity is uniform in cross-section, then

• This general equation also takes into account
  changes in density (via )
• energy changes due to machines (via )
  and due to heat transfer to
• or from outside the fluid (via )

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General Energy Equation for Steady Flow of Any
Fluid

• is a correction factor accounting for
  non-uniform velocity in cross-section

• If velocity is uniform in cross-section, then

• This general equation also takes into account
  changes in density (via )
• energy changes due to machines (via )
  and due to heat transfer to
• or from outside the fluid (via )

• It also accounts for the conversions of other
  forms of fluid energy into internal
• heat ( )

internal energy per unit weight
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• Recall from chapter 2 that compressibility of a
  liquid is inversely proportional
• to the bulk modulus of the liquid

• From table 2.1 (page 17 of text), for a wide
  range of temperatures the bulk
• modulus of water is very high O(100,000 psi)
  relative to the usual pressures
• in our problems

• Thus the compressibility of our most common
  liquid (water) is low and we
• may treat it as incompressible
  while still undergoing
• changes in temperature and pressure

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General Energy Equation for Steady Flow of Any
Fluid

• On a unit weight basis, the change in internal
  energy is equal to the heat
• added to or removed from the fluid plus the
  heat generated by fluid friction

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General Energy Equation for Steady Flow of Any
Fluid

• On a unit weight basis, the change in internal
  energy is equal to the heat
• added to or removed from the fluid plus the
  heat generated by fluid friction

• The head loss due to friction is equal to the
  internal heat gain minus any
• heat added from external sources, per unit
  weight of fluid

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General Energy Equation for Steady Flow of Any
Fluid

• On a unit weight basis, the change in internal
  energy is equal to the heat
• added to or removed from the fluid plus the
  heat generated by fluid friction

• The head loss due to friction is equal to the
  internal heat gain minus any
• heat added from external sources, per unit
  weight of fluid

• Energy loss due to friction gets converted to
  internal energy (proportional to
• temperature)

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Example Exercise 5.3.5 (Friction Head Loss)
S of liquid in pipe 0.85
A
Diameter at A Diameter at B, thus by continuity
B
Want Pipe friction head loss and direction of
flow
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Example Exercise 5.3.5 (Friction Head Loss)
S of liquid in pipe 0.85
A
Diameter at A Diameter at B, thus by continuity
B
Want Pipe friction head loss and direction of
flow
Assume flow goes from A to B
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Example Exercise 5.3.5 (Friction Head Loss)
S of liquid in pipe 0.85
A
Diameter at A Diameter at B, thus by continuity
B
Thus flow goes from B to A and
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Example Exercise 5.3.5 (Friction Head Loss)
S of liquid in pipe 0.85
A
Diameter at A Diameter at B, thus by continuity
B
Thus flow goes from B to A and
Let . If flow goes from B to A,
and
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Role of pressure difference (pressure gradient)
A
B
Thus flow will go from B (high pressure) to A
(low pressure), only if
Otherwise flow will go from A (low pressure) to B
(high pressure)
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Role of pressure difference (pressure gradient)
A
B
Thus flow will go from B (high pressure) to A
(low pressure), only if
Otherwise flow will go from A (low pressure) to B
(high pressure)
In general, the pressure force (resulting from a
pressure difference) wants to move a fluid from a
high pressure region towards a low pressure
region
For a flow to actually go from a high pressure
region towards a low pressure region, the
pressure force must be higher than other forces
that could be trying to move fluid in opposite
direction (e.g. gravitational force in exercise
5.3.5)
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Energy Grade Line (EGL) and Hydraulic Grade Line
(HGL)
Graphical interpretations of the energy along a
pipeline may be obtained through the EGL and HGL
EGL and HGL may be obtained via a pitot tube and
a piezometer tube, respectively
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Energy Grade Line (EGL) and Hydraulic Grade Line
(HGL)

• head loss, say,
• due to friction

EGL
HGL
piezometer tube
pitot tube
Datum
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Energy Grade Line (EGL) and Hydraulic Grade Line
(HGL)
EGL
Large V2/2g because smaller pipe here
HGL
Steeper EGL and HGL because greater hL per
length of pipe
Head loss at submerged discharge
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Energy Grade Line (EGL) and Hydraulic Grade Line
(HGL)
Positive
Negative
Positive
EGL
HGL
If then and cavitation
may be possible
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Energy Grade Line (EGL) and Hydraulic Grade Line
(HGL)
Helpful hints when drawing HGL and EGL
1. EGL HGL V2/2g, EGL HGL for V0
2. If p0, then HGLz
3. A change in pipe diameter leads to a change in
V (V2/2g) due to continuity and thus a change
in distance between HGL and EGL
4. A change in head loss (hL) leads to a change
in slope of EGL and HGL
5. If then and
cavitation may be possible
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Helpful hints when drawing HGL and EGL (cont.)
6. A sudden head loss due to a turbine leads to a
sudden drop in EGL and HGL
7. A sudden head gain due to a pump leads to a
sudden rise in EGL and HGL
8. A sudden head loss due to a submerged
discharge leads to a sudden drop in EGL