Pipe systems and energy losses Flashcards
What are the two obstacles that need to be overcome to use Bernouilli for pipe flow problems?
- A version of the Bernouilli equation that is valid over the entire cross-section
- Energy losses due to wall friction and other reasons need to be accounted for
How is Bernouilli equation adapted for pipe flow?
Bernouilli’s equation can be adapted to be valid for an entire cross-section by adding a correction factor alpha which has a value 1 for a uniform velocity profile and 1.06 for a turbulent profile.
This is a small correction and is usually neglected ie. alpha assumed to be 1
What are major losses in pipe systems?
Losses due to friction with the wall
Note: Major/Minor only have a qualitative rather than quantitative meaning here
What are minor losses in pipe systems?
Losses due to pipe bends, contractions, entries, exits, fittings and valves
These losses represent additional energy dissipation in the flow, usually caused by secondary flows induced by curvature or recirculation
How are minor losses dealt with?
A loss factor xi (dimensionless constant between 0 and 1) is applied to the local kinetic energy (defined relative to the largest velocity head)
Loss factors are usually available from tables
What is the exit loss?
All KE is lost if a pipe discharges into a reservoir
What is the equation for major losses?
dHf = f(L/D)(U^2/2g)
where f is the dimensionless Darcy-Weisbach friction coefficient
D = 4A/P for non-circular pipes
What does the Darcy-Weisbach constant f depend on?
- roughness of the pipe
- Re number of flow
for rough walls and sufficiently high Re, f becomes constant
its determination will be covered in Y2
About pumps and turbines
Pumps and turbines are devices which exchange low KE and electrical energy.
Pumps provide energy to the flow, whereas turbines extract energy from the flow
Pumps are used for irrigation, water supply, sewage movement, flood control
Turbines are used to generate power such as in hydro dams and wind farms
