Energy conservation Part 1 Flashcards
Where is the steady Bernoulli equation derived from?
This equation is derived from the principle of conservation of energy, where the sum of kinetic energy, potential energy, and fluid pressure remains constant along a streamline in a steady, inviscid flow.
How does total energy behave along a streamline?
Constant
What is Bernoulli equation?
E = P + ρgz + 1/2ρU^2
True or false, pressure and velocity are directly related?
True
What are the assumptions made?
- Steady flow
- Constant density
- Dissipation-less flow
What is the Bernoulli equation in terms of head?
H = P/ρg + z + U^2/2g
What are the units of the head equation and all the terms in the head equation?
m
What does the pressure head represent?
Represents the column of fluid required to produce the pressure 𝒑
What is the piezometric head?
h = P/ρg + z
How does the piezometric head behave in the vertical when pressure is hydrostatic?
Constant
How can pressure be calculated?
P = ρg(h-z)
When is flow static?
When U=0 and H=h
What are the energy and hydraulic grade lines?
Graphical representation of the energy state of the fluid
What is the difference between the energy grade line and hydraulic grade line?
The velocity head
What is the continuity equation for volume flux?
A1U1=A2U2
How does Q, discharge behave horizontally?
Q discharge is constant on a horizontal streamline with points at the same elevation.
What happens as velocity increases?
Pressure decreases
If a vortex is created what is the pressure distribution?
Low pressure at the centre of the circle and high pressure on the outside
What does it mean if there is a stronger curvature in the vortex?
R is smaller and there is a larger ∆P
How does piezometric head behave along a streamline?
It is the same along it
What does the second Bernoulli equation provide information about?
The pressure inside a fluid body
When is Bernoulli valid?
- Converging streamlines
- Accelerating fluid
- Low energy losses
When is Bernoulli not valid?
- Diverging streamlines
- Decelerating fluid
- Turbulence - energy losses
How can you slow down a fluid?
In order to slow fluid down the pressure must increase and the flow separates
In a draining reservoir at what pressure does the flow exit?
Atmospheric pressure
What is a Vena Contracta?
Streamlines there are locally straight and parallel -> where the diameter is the least
In a draining resevoir how does velocity depend on distance to the free surface?
U = √2gh_s
What is the pressure at the stagnation point along the same streamline?
P_s = P1 + 1/2⍴U^2
What does it mean when there is a stagnation point in the mouth of the tube?
No flow out of or into the tube
How do you force flow along a pipe?
Apply a greater pressure
What is a syphon?
A syphon is a tube in an inverted U shape that causes a liquid to flow uphill
How does a syphon work?
- Doesn’t need a pump and discharging at low elevations
- The fluid is able to flow uphill because it knows about the lower level on the other side through pressure
What is the static pressure?
P_∞
What is the dynamic pressure?
1/2⍴U^_∞
What is the stagnation pressure?
P_s
