Unit 5: Open channel flow

Question 1

What is open channel flow?

Answer 1

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

Question 2

What is the driving forces in open channel flow?

Answer 2

The driving force for open-channel flows is gravity.
Opposed by the friction force

Question 3

What is special about the Hydraulic grade line in open channel flow?

Answer 3

The HGL coincides with the free surface
(the pressure is constant among the free surface)

Question 4

What assumptions do we use in open channel flow?

Answer 4

1. Flow is 1-dimensional
2. Flow is Steady
3. Uniform velocity at each cross section

Question 5

How do you define flow depth?

Answer 5

The perpendicular distance measured from the lowest
point of the channel bed to the free surface

h

Question 6

How do you define flow area?

Answer 6

The cross section of the flow perpendicular to the flow direction

A

Question 7

How do you define wetted perimeter?

Answer 7

The length of the solid channel cross section surface in contact with the liquid

P

Question 8

How do you define hydraulic radius?

Answer 8

The ratio between area and wetted perimeter

R = A/P

Question 9

What is uniform flow?

Answer 9

The flow depth remains constant with distance along the channel

Question 10

When can you expect to have unifiorm flow conditions?

Answer 10

Uniform flow can occur only in long and prismatic channels (man made)

channel cross section and bottom slope do not change with distance

Question 11

What is the difference between gradually varied flows and rapidly varied flows?

GVF and RVF

Answer 11

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

Question 12

How can you estimate Q, discharge, in uniform flow conditions?

Answer 12

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

Question 13

Write an expression for the total energy in open channel flow conditions

Answer 13

H = z + h + v^2 /2g

h = flow depth

Question 14

What is the difference between total energy and specific energy?

Answer 14

E = h + v^2 /2g = h + [Q/A(h)]^2 /2g
E = H - z
specific energy is the sum of potential and kinetic head

Question 15

Why does specific energy have a minimal value?

Answer 15

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.

Question 16

What is the critical depth?

k

Answer 16

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

Question 17

What is critical velocity?

Answer 17

The velocity at which the fluid flows at the critical depth

Vk = Q/A = sqrt(g kaverage)

Question 18

What correlation has specific energy (E) and critical depth (k) in a rectangular cross section?

Answer 18

Eminimum = 3k/2

Question 19

What is super- and sub-critical flow?

Answer 19

Supercritical flow:
h < k

v > vk
Fr>1

Subcritical flow:
h > k
v < vk
Fr<1

Question 20

What is the alternate depth?

Answer 20

For every depth in subcritical flow conditions there are a corresponding depth in supercritical flow conditions.
These two depths are called alternate depths.

Question 21

What is the Froude number (Fr)?

Answer 21

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)

Question 22

What happens when the flow regime change from sub-critical flow to super-critical flow in an open channel?

Answer 22

The flow transitions smoothly from a higher flow depth to a lower flow depth

Question 23

What happens when the flow regime change from super-critical flow to sub-critical flow in an open channel?

Answer 23

The flow transition happens turbulently through a hydraulic jump

Lower flow depth to a higher flow depth

Question 24

What are the assumptions for hydraulic jump?

Answer 24

1. Hydrostatic pressure distribution
2. Uniform velocity distribution
3. No air entrainment
4. Steady flow
5. Horizontal rectangular channel
6. Constant channel width, B

Question 25

What defines **conjugate depths**?

Answer 25

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

Question 26

How can you find the **conjugate depth** if you have one of the depths?

Answer 26

The ratio of conjugate depths: h2/h`1` = 1/2 [sqrt(1+8 (Fr`1`)^2) -1]

Question 27

What is **pressure force** and **momentum flux** and their connection with **hydraulic jump**?

Answer 27

**pressure force**: F`P` = γAh`G` **momentum flux**: M = ρQv For **hydraulic jump**: S = F`P1` + M`1` = F`P2` + M`2` γbh`1`^2 /2 + ρQv`1` = γbh`2`^2 /2 + ρQv`2` ## Footnote Not on support sheet (s 50) Derived from the momentum equation

Question 28

How do you calculate the **head loss** lost in the **hydraulic jump**?

Answer 28

ΔH = (h`2`-h`1`)^3 /(4h`1`h`2`) A large Δh = h`2`-h`1` leads to a big dip in the **Energy grade line** during the **hydraulic jump** ## Footnote Not on support sheet (s 51)

Question 29

How does the **froude number** and thus the level of **supercritical flow** effect the **energy losses** during the **hydraulic jump**?

Answer 29

1. 1: c**ritical flow regime** - **No** hydraulic jump 2. 1-1,7: **Undular** jump - **negligible** energy losses 3. 1,7-2,5: **Weak**jump - **low** energy losses 4. 2,5-4,5: **oscillating** jump - Large waves of irregular preriods that might travel far downstream and erode the river banks *(to be avoided)* 5. 4,5-9,0: **Steady** jump - **45-70%** energy dissipated. Not affected by tailwater **(best economical design)** 6. >9: **strong** jump - up to 85% energy dissipated. might cause erosion in the channel bed. *(to be avoided)*