Unit 5: Open channel flow Flashcards
What is open channel flow?
Open-channel flow indicates flow in a channel open to the atmosphere.
It can be natural or man made channels or conduits where the liquid does not fill the conduit completely, and thus there is a free surface
involves liquids exposed to a gas
What is the driving forces in open channel flow?
The driving force for open-channel flows is gravity.
Opposed by the friction force
What is special about the Hydraulic grade line in open channel flow?
The HGL coincides with the free surface
(the pressure is constant among the free surface)
What assumptions do we use in open channel flow?
- Flow is 1-dimensional
- Flow is Steady
- Uniform velocity at each cross section
How do you define flow depth?
The perpendicular distance measured from the lowest
point of the channel bed to the free surface
h
How do you define flow area?
The cross section of the flow perpendicular to the flow direction
A
How do you define wetted perimeter?
The length of the solid channel cross section surface in contact with the liquid
P
How do you define hydraulic radius?
The ratio between area and wetted perimeter
R = A/P
What is uniform flow?
The flow depth remains constant with distance along the channel
When can you expect to have unifiorm flow conditions?
Uniform flow can occur only in long and prismatic channels (man made)
channel cross section and bottom slope do not change with distance
What is the difference between gradually varied flows and rapidly varied flows?
GVF and RVF
Changes in the geometry of the riverbed create nonuniform flows
GVF is when the rate of variation of depth with respect to distance is small
RVF is when this rate of variation is large
How can you estimate Q, discharge, in uniform flow conditions?
Using the Chezy equation
V = C (R i)^(1/2)
we can create the manning equation
Q = 1/n R^(2/3) A i^(1/2)
n is the roughness coefficient
Write an expression for the total energy in open channel flow conditions
H = z + h + v^2 /2g
h = flow depth
What is the difference between total energy and specific energy?
E = h + v^2 /2g = h + [Q/A(h)]^2 /2g
E = H - z
specific energy is the sum of potential and kinetic head
Why does specific energy have a minimal value?
If h decreases and tends to zero, then the
velocity head increases and tends to infinity, thus
E = V^2 /2g
If h increases and tends to infinity, then the velocity head decreases and tends to zero; thus E = h
In both extremes E tends to infinity which means that somewhere between the values there exists a minimum.
What is the critical depth?
k
Critical depth is the flow depth at which the minimal value for the specific energy is achived.
At the critical depth the following equation satisfied:
Q^2 / g = A^3 / B
haverage = A/B
What is critical velocity?
The velocity at which the fluid flows at the critical depth
Vk = Q/A = sqrt(g kaverage)
What correlation has specific energy (E) and critical depth (k) in a rectangular cross section?
Eminimum = 3k/2
What is super- and sub-critical flow?
Supercritical flow:
h < k
v > vk
Fr>1
Subcritical flow:
h > k
v < vk
Fr<1
What is the alternate depth?
For every depth in subcritical flow conditions there are a corresponding depth in supercritical flow conditions.
These two depths are called alternate depths.
What is the Froude number (Fr)?
Fr = V/sqrt(gh) = inertia force/ gravity force
This is a way to determine whether the flow regime is:
1. critical (Fr =1),
2. sub-critical (Fr<1) or
3. super-critical (Fr>1)
What happens when the flow regime change from sub-critical flow to super-critical flow in an open channel?
The flow transitions smoothly from a higher flow depth to a lower flow depth
What happens when the flow regime change from super-critical flow to sub-critical flow in an open channel?
The flow transition happens turbulently through a hydraulic jump
Lower flow depth to a higher flow depth
What are the assumptions for hydraulic jump?
- Hydrostatic pressure distribution
- Uniform velocity distribution
- No air entrainment
- Steady flow
- Horizontal rectangular channel
- Constant channel width, B
What defines conjugate depths?
The different depths before and after a hydraulic jump.
The conjugate depths have equal momentum fluxes for a given discharge which distinguishes conjugate depths from alternate depths. This allows for new possible calculations.
the flow depth at supercritical and the at subcritical conditions
How can you find the conjugate depth if you have one of the depths?
The ratio of conjugate depths:
h2/h1 = 1/2 [sqrt(1+8 (Fr1)^2) -1]
What is pressure force and momentum flux and their connection with hydraulic jump?
pressure force:
FP = γAhG
momentum flux:
M = ρQv
For hydraulic jump:
S = FP1 + M1 = FP2 + M2
γbh1^2 /2 + ρQv1 = γbh2^2 /2 + ρQv2
Not on support sheet (s 50) Derived from the momentum equation
How do you calculate the head loss lost in the hydraulic jump?
ΔH = (h2-h1)^3 /(4h1h2)
A large Δh = h2-h1 leads to a big dip in the Energy grade line during the hydraulic jump
Not on support sheet (s 51)
How does the froude number and thus the level of supercritical flow effect the energy losses during the hydraulic jump?
- 1: critical flow regime - No hydraulic jump
- 1-1,7: Undular jump - negligible energy losses
- 1,7-2,5: Weakjump - low energy losses
- 2,5-4,5: oscillating jump - Large waves of irregular preriods that might travel far downstream and erode the river banks (to be avoided)
- 4,5-9,0: Steady jump - 45-70% energy dissipated. Not affected by tailwater (best economical design)
- > 9: strong jump - up to 85% energy dissipated. might cause erosion in the channel bed. (to be avoided)
