1. Basic Hydrology & Hydraulics: DES 601
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Energy and Momentum Concepts

2. Energy of flow 2 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
Elevation 2 1 2
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3. 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
Pressure energy = h h1
hbottom 1
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4. 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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5. 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
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6. 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:
where is: Z1,2 - elevation above reference level; p1,2 - absolute pressure; v1,2 - velocity; ρ1,2 - density; g - acceleration of gravity
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7. 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 Hazen-Williams (water only!)
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8. Energy Equation
If friction losses are included, the equation is called the energy equation
Turbine extraction is probably uncommon for transportation infrastructure, but the other two (pumps and friction) are common
Added head (pump)
Extracted head (turbine)
Frictional Loss
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9. 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)
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10. Momentum Concept
Force on a pier
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