Basic Hydrology & Hydraulics: DES 601 Module 13 Energy and Momentum Concepts

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 Module 13

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 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). Module 13

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: 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 Hazen-Williams (water only!) Module 13

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 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) Module 13

Momentum Concept Force on a pier Module 13