3 Open Channel Flow 1

OPEN CHANNEL

FLOW

PART 1

There are two main types of open channels:

- Natural

- Regular/ Artificial

Types of open channel flows :

Steady flow – when discharge Q does not change with time

Uniform flow – when depth of fluid does not change for a selected length or section

of the channel

Uniform steady flow – when discharge does not change with time and depth

remains constant for a selected section dv/dx = constant

Varied steady flow – when depth changes but discharge remains the same (how it

is possible?) dv/dx ǂ constant

Varied unsteady flow – when both depth and discharge change along a channel

length of interest.

Rapidly varying flow – depth change is rapid

Gradually varying flow – depth change is gradual

Hydraulic radius of open channel flow is a parameter that is defined as:

R = A/ WP

cross sectional area (A)

wetted perimeter (WP)

Hydraulic radius R for various channel shapes

Reynolds number for channel flow

NR= ρ v R/ μ

For channel flow

NR < 500 – laminar flow

NR > 2000 – turbulent flow

Froude Number

NF witch is gravity versus inertial forces:

NF= v/ (g* H)^1/2

Where H is referred as the hydraulic depth and given by

H = A/B

where A is the area and B is the top width of the channel.

NF = 1.0 or when v = (H)1/2 - critical flow

NF < 1.0 – subcritical flow

NF > 1.0 – super critical flow

A combination of both the numbers is used to describe channel flow conditions.

Uniform steady flow and Manning’s Equation

When discharge remains the same and depth does not change then we have

uniform steady flow.

In this condition the surface of water is parallel to the bed of the channel.

The slope of the channel can be expressed as :

• an angle = 1 degrees

• percent = 1%

Velocity of flow in a channel can be calculated many empirical equations.

One of them is

Manning’s equation:

Q = Flow Rate, (ft3/s)

v = Velocity, (ft/s)

A = Flow Area, (ft2)

n = Manning’s Roughness Coefficient

R = Hydraulic Radius, (ft)

S = Channel Slope, (ft/ft)

This is the SI units form of the equation with v (meters/sec) and R (meters).

The Manning’s coefficient (dimensionless) values are developed through experimentation.

Manning’s coefficient table example.

Task 1

Determine normal discharge for a 200 mm inside diameter

common clay drainage tile running half-full if the slope drops 1m over 1000 m.

S= 1/1000 = 0.001

A = (1/2) * (π D2 /4) = 0.5*π*(0.2)2 /4 = 0.0157 m2

WP = (1/2) * (π D) = 0.5*π*0.2 = 0.3141 m

R = 0.05 m

From Table n for clay tile = 0.013

Substitute these values in the equation:

Thus

Q = 5.18 x 10-3 m3/s

Task 2

Calculate slope of formed unfinished concrete channel, if Q = 50 ft3 /s.

Solution:

Transform the equation in terms of S

Compute

A = 12 ft2

WP = 9.66 ft

R = A/WP = 12/9.66 = 1.24 ft

Manning’s n for unfinished concrete channel = 0.017

Substitute

And S = 0.00169

Drop 1.69 ft for every 1000 ft.

Task 3

Design rectangular channel in formed unfinished concrete

Q = 5.75 m3 /s

S = 1.2%

Normal depth H = ½ of the width of the channel B

Use formula:

A*R2/3 = (n* Q)/ S1/2

Express Area and the hydraulic radius in terms of B.

A = B*H = B2 /2

WP = B+ 2H = 2B

R = A/WP = B/4

Back to the equation:

Therefore,

B = 1.76 m

H = 1.76/2 m