Pipe systems and energy losses Flashcards
How does the Bernoulli equation work for pipe flow?
- An equation that works over the whole cross-section of the pipe
- Assume streamlines are approximately parallel
- Account for wall friction and other losses
What is the Bernoulli equation for the entire cross-section of a pipe?
H = h + ⍺U^2/2g
- U is the velocity averaged over the cross-section
What is the value of alpha for a uniform profile across a pipe?
1
What is the value of alpha for a turbulent profile in a pipe?
⍺ ≈ 1.06
What is a major loss?
Losses due to friction with the wall
What is a minor loss?
- Losses due to pipe bends, contractions, entries, exits, fittings and valves
- Minor losses can often dominate over major losses
How can minor an major losses be incorporated in energy balance?
Both major and minor losses can be incorporated by adding a head loss term to the Bernoulli equation
What value does the loss value usually have?
Between 0 and 1
What do big constrictions mean?
Higher loss factor
What is the entrance loss denoted by?
𝜉U^2/2g
What does a sudden expansion mean in terms of energy?
Large energy loss
What is the exit loss denoted by?
U^2/2g
Why is the exit loss the same as the velocity head?
All KE lost if a pipe discharges into a reservoir -> assume all KE in flow has been dissipated
What does the height in the pitot tube suggest?
The height in the pitot tubes suggests the height of the EGL
How can you caluclate the enrgy loss?
∆H_L = ∆H_x+∆H_e
How can you determine the pressure grade line?
hydraulic grade line - z
How does the flow rate change between two reservoirs in a pipe?
The volume flow rate is free to flow
Why might the hydraulic grade line dip between two reservoirs?
Flow accelerates so pressure decreases
When do the grade lines coincide?
At the free surface
What will happen to the velocity as a result of local energy losses?
Smaller flow velcoities
What is pipe skin friciton?
Energy is lost due to friction on the walls.
What is the formula for skin friction?
∆H_f = fL/DU^2/2g
What is f in the skin friciton equation?
f is the (dimensionless) Darcy-Weisbach friction coefficient.
When is the skin friction equation valid?
For ciruclar pipes only
Becuase of skin friciton how will the energy grade line be drawn?
Energy grade line is a downward slope with distance along the pipe
What does the frcition coefficient depend?
Depends on roughness and on the Reynolds number
When does f become constant?
Rough walls with high Re
Whats the difference between velocity heads in pipes with different diameters?
Velocity head in larger pipe is smaller than the smaller pipe
How will rate of fricitonal loss differ in pipes with different diameters?
Rate of frictional loss will be less in large pipes as the diameter is larger
What is the equation for major head loss for noncircular pipes?
∆H_f = fL/D_eU^2/2g
What is the diameter equivalent
It is the diameter of a circular duct or pipe that gives the same pressure loss as an equivalent rectangular duct or pipe for a particular flow rate.
How do you find the hyraulic diameter?
4A/P
