CHAPTER 2 : OPEN CHANNEL FLOW

CHAPTER 2 : OPEN CHANNEL FLOW OPEN CHANNEL : A CHANNEL

WHERE THE WATER FLOWS WITH MAINLY BY GRAVITY

FORCE AND THERE HAS A FREE SURFACE AND ATMOSPHERE PRESSURE ON THE WATER.

The stream not

completely enclosed by solid boundaries.

It has free surface subjected only to atmospheric pressure

Referred as free-surface flow or gravity flow

Irregular Shape

Regular Shape

Types of open channel

CANAL is usually a long and mild-sloped channel

built in the ground.

FLUME is a channel usually supported on or above the surface of the ground to carry water across a depression.

CHUTE is a channel

having steep slopes.

DROP is similar to a chute, but the change in elevation is

affected in a short distance.

OPEN-FLOW TUNNEL is

acomparatively long covered channel used to carry water

through a hill or any obstruction on the ground.

CULVERT is a covered channel flowing partly full, which is installed to drain water through highway and railroad embankments.

Flow in open channels is classified as being uniform or non-uniform, depending upon the depth y.

Depth in Uniform Flow is called normal depth y_n

Uniform depth occurs when the flow depth (and thus the average flow velocity) remains constant

Common in long straight runs.

Average flow velocity is called uniform-flow velocity V₀

Uniform depth is maintained as long as the slope, cross-section, and surface roughness of the channel remain unchanged.

During uniform flow, the terminal velocity reached,

and the head loss equals the elevation drop

Time is the criterion

Flow in Open Channel

Steady Flow

Uniform Flow Non-Uniform Flow

Rapidly Varied Flow

Gradually Varied Flow Unsteady Flow

Space as the criterion

TYPE OF FLOW :

Geometric properties

necessary for

analysis

Geometric properties necessary for

analysis

Manning’s Equation and coefficient for several types of surface channel

Example #1: Water is flowing 0.3m deep in a 1m wide, open channel of

rectangular cross section, as shown in the diagram below. The channel is made of concrete (made with steel forms), with a constant bottom slope of 0.003, n = 0.011.

Estimate the flow rate of water in the channel

Based on the description, this will be uniform flow.

n = 0.011.

The bottom slope is given as: S = 0.003.

The cross-sectional area, A = 1m x 0.3m = 0.3m² The wetted perimeter , P = 1m + 2(0.3) = 1.6m

The hydraulic radius , R = A/P = 0.3/1.6 = 0.1875 m

Substituting values for all of the parameters into Equation

Q = (1 /n)A(R^2/3)S^1/2

Q = (1//0.011)(0.3)(0.1875^2/3)(0.003^1/2) = 0.489 m³/s

Solution Given b= 3m y= 1.2 m Q= 25m³/s n =0.022 S= ????

A= by =3x1.2 =3.6 m

R = 3.6/ (3+2(1.2))=0.667m

25

Worked Example 2d.

Find the bed slope of trapezoidal channel of bed width 5 m of water 3.5m. Side slope 3H: 4V when discharge flowing through the channel is 45 m

³

/s. Take

manning’s n = 0.0158 Solution;

Specific Energy, E

Total of depth and kinetic energy of the flow.

E = y + v ²

2g

Specific Energy, E

Alternath depth

Specific Energy, E Example 1:

A trapezoidal channel has dimension of bottom width 6m and side slope 1:1 flows water at rate 8 m³/s. Calculate specific energy for the water if the depth of water is 2m.

1 2m

1

6m

Discharge per unit width, q

q = Q b

Froude Number, Fr

-Used to determine characteristic of flow

* Only for square &

prismatic channel

Fr = v √(gy)

Fr < 1: subcritical (tranquil) flow Fr = 1: critical flow

Fr > 1: supercritical (rapid) flow b = width

CHARACTERISTIC OF FLOW

Subcritical flow

- Deep, calm, slow

Critical depth, y_c Supercritical flow - Shallow, fast

Critical flow

- Disturbance, small gravities wave

y_c = q² g

1 3

Minimum energy, E_min

Critical velocity, v_c E_min = 3

2

y_c

v_c = √(gy_c)

Example 2:

Water flows in square channel which the width of the channel is 6m and the depth of the water is 3m. If the flowrate is 30 m

³

/s, calculate:

a. Froude number (0.308) b. Type of flow

c. Critical depth (1.37 m)

HYDRAULIC JUMP

-THE SUDDEN INCREASE IN DEPTH OF FLOW IN SHORT DISTANCE

-THE TRANSITIONAL FLOW FROM SUPERCRITICAL TO SUBCRITICAL

y₂ y₁

HYDRAULIC JUMP IN LABORATORY

A rectangular channel 6m wide , discharging 30 m3/s of water. The flow depth is 3m, Find the

i) Froud number (ii) Types of flow (iii) Critical depth

WHERE HYDRAULIC JUMP OCCUR?

1.At the bottom of hydraulic

structure which supercritical flow through into stilling basin.

2.At downstream of flume which the supercritical flow transit to

subcritical flow.

3.In the trash rack channel

TYPES OF HYDRAULIC JUMP

1.Undular Jump Fr₁ 1.0 – 1.7 2. Weak Jump Fr₁ 1.7 – 2.5

3. Oscillating Jump Fr₁ 2.5 – 4.5 4. Steady Jump Fr₁ 4.5 – 9.0

5. Strong Jump Fr₁ > 9.0

Fr₁ – Nombor Froude sebelum lompatan =

THE APPLICATION OF HYDRAULIC JUMP

1. As Energy Disperser

2. For Chemical Diffusion 3. For Aeration

4. To increase Flow Level

Height of jump Energy lost

Power generated

Example 1 :

  Water flows at velocity 16m/s in a square channel. The upstream depth is 30cm. A hydraulic jump occurs after the water flows on the sill. Calculate the depth and

velocity at downstream. Calculate also the energy lost and power lost due to hydraulic jump.

Fr_i = 9.327 y₂ = 3.81m v₂ = 1.26 m/s E_L= 9.458m Q = 4.8m³/s

P = 445358.304 Watt

Example 2:

 

Water flows at rate 18m

³

/s in a square channel 4m width. The type of flow is supercritical. A hydraulic jump occurs in the channel. The Froude number at upstream is 3.5. Calculate height of jump.

y₁ = 0.55m y₂ = 2.46m y_j = 1.91 m

Optimum section

• Calculate the best hydraulic

rectangular cross-section to convey Q=10m ³ /s discharge with n = 0.02

and S = 0.0009 canal chareacteristic

• Design the trapezoidal channel as

best hydraulic cross-section with Q=

10 m ³ /sec, n= 0.014, S= 0.0004, and

m= 3/2.

HYDRAULIC

JUMP