Basic Hydrology &
Hydraulics: DES 601
Module 13
Energy and Momentum Concepts
Energy of flow
• Three kinds of energy gradients cause flow
• Elevation (called potential energy)
• Pressure (another kind of potential)
• Kinetic (related to how fast water is moving)
p1, v1
Elevation 1
p2, v2
1
Elevation 2
2
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Pressure
• Pressure at point = p = g h
• For US customary units, g = 62.4 lb/ft3
• Example:
• At point 1, p1 = g h1
• At bottom of tank, pbottom = g hbottom
hbottom
1
h1
• Pressure energy = h
Module 13
Potential and Kinetic Energy
• Potential energy is the sum of the elevation head
and the pressure head
• Sometimes called the static head
• Kinetic energy is the energy of motion
• Proportional to the square of the mean section
velocity
• The sum of potential and kinetic energy is the total
energy (head).
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Total energy
• Express energy in consistent units, typically units of
length (ft).
• Elevation head (h) has units of ft.
• Pressure has units of lb/ft2.
• If we divide p by g (62.4 lb/ft3), we get units of
ft. for the pressure head.
• Velocity has units of ft/sec.
• velocity head is v2/2g where g = gravitational
acceleration.
• Total energy (head) = h + p/g + v2/2g
Module 13
Bernoulli Equation
• If friction losses are neglected and no energy is added to,
or taken from a piping system, the total head, H, which
is the sum of the elevation head, the pressure head and
the velocity head will be constant for any point on a fluid
streamline.
• This expression head conservation of head in a conduit
or streamtube is known as the Bernoulli equation:
2
2
p
v
p
v
Z1  1  1  Z 2  2  2
1 g 2 g
2 g 2g
where is: Z1,2 - elevation above reference level; p1,2 absolute pressure; v1,2 - velocity; ρ1,2 - density; g acceleration of gravity
http://www.pipeflowcalculations.com/pipe-valve-fitting-flow/flow-in-pipes.php
Module 13
Energy losses
• Due to
• Boundary resistance (friction losses)
• Effects of changes in flow geometry (local losses)
• Local losses often expressed as hL = K v2/2g in
which K = the head loss coefficient
• Friction losses commonly computed using empirical
equation, such as Manning’s equation, Chezy
equation, Darcy-Weisbach equation or HazenWilliams (water only!)
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Energy Equation
• If friction losses are included, the equation is called the
energy equation
2
2
p
v
p
v
Z1 + 1 + 1 + hP = Z 2 + 2 + 2 + hT + hL
r1g 2g
r2 g 2g
Added head (pump)
Extracted head (turbine)
Frictional Loss
• Turbine
extraction
is
probably
uncommon
for
transportation infrastructure, but the other two (pumps
and friction) are common
Module 13
Momentum Concept
• Momentum is defined as mass of object multiplied by
velocity of object; these are vector quantities
• The principle is that the change in momentum is
equal to the forces on the object (fluid element)
v v
v gQ(V2  V1 )
F 
g
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Momentum Concept
• Force on a pier
Module 13