Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 1 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 2 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 3 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 4 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 5 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 6 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 7 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 8 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 9 of 16

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 1 0 of 16

A number of typical photographs for natural channels; information for these

photographs follows:

(a)- n = 0.024 (Columbia River at Vernita, Washington)

(b)- n = 0.075 (Rock Creek near Darby,Montana): The bottom consists of boulders,

d50 = 2.2 m; the banks are composed of boulders and have a trees.

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 1 1 of 16

Normal Depth Calculations In Uniform Channels

The normal depth is the flow depth that satisfies Manning Eq., and is denoted by yn.

Often need to calculate the normal depth for a given discharge and the channel

properties. For uniform channel material, it can assume that the Manning roughness

coefficient is constant. Also, for prismatic channels, the cross-sectional

relationships are available. (see Table 1-1)

** For Triangular cross-section channel the following explicit formula can be used

instead of Eq.17 directly to calculate a normal depth;

……………………………… (8)

Where “m” is a side slope.

For most other cross-sectional shapes an explicit expression for “yn” is not

available, and a trial-and-error procedure is needed to calculate the normal depth

mathematically. Given the discharge and the channel properties, for a trapezoidal

channel of known bottom width “b” and side slopes “m”, the Manning Eq.

becomes;

………………………………… (9)

The only unknown in Eq.9 is “yn”. Alternatively, it can use Fig.L8-1, which

presents predetermined solutions for Eq.9 in dimensionless form for normal depth

in rectangular and trapezoidal channels.

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 12 of 16

Fig.L8-1: Normal depth chart for rectangular and trapezoidal channels

Likewise, for a circular channel of diameter do;

With substitution in Manning Eq. the following implicit equations will result for

normal depth calculation in partially filled circular pipe;

……………………. (10-a)

……………………. (10-b)

Water and Hydraulics Structures Branch / 3rd Class [Hydraulic Structures]

Lect.No.3-First Semester [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 13 of 16

Eq.10 needs trial and error procedure to find a suitable normal depth (yn).

Alternatively, it can use the chart presented in Fig.L8-2 to determine the normal

depth graphically.

Fig.L8-2: Normal depth chart for circular channels

Hydraulics Structures Dept. / 3rd Class [Hydraulic Lectures]

Lect.No.8 [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 14 of 16

Normal Depth Calculations In Composite Channels The channel roughness may be different on different parts of the wetted perimeter.

For example, it is possible to use different types of lining materials on the sides and

the bottom of channel. Such channels are called composite channels. Different parts

of the perimeter of a composite channel are then represented by different Manning

roughness factors. This may cause different average velocities in various parts of a

composite channel section. However, in categorize as composite channels these

velocity differences are small, and the whole section can be represented by one

cross-sectional average velocity.

As well illustrated in figure below, the equivalent roughness coefficient can be

calculated by the following formula as proposed by Einstein and Banks, from the

condition that the total force resisting to flow is equal to the sum of forces resisting

to flow over the different segments of the perimeter;

…………………………………… (22)

The “ne” the substituted in Manning’s equation to find a discharge. If the discharge

known then trial and error procedure should be attempt for solution.

Hydraulics Structures Dept. / 3rd Class [Hydraulic Lectures]

Lect.No.8 [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 15 of 16

Conveyance For a given channel section and specified bottom slope, only one discharge is

possible for a given normal depth. However, if the value of this depth is known,

then we can determine the corresponding discharge directly from Eq.17. We may

write this equation as;

………………………………….. (23)

Where;

As can be seen from Eq.23 each channel has a specified conveyance factor, then the

change in bed slope will change the value of discharge.

Note that “K” is a function of the normal depth, properties of the channel section

and Manning “n”.

Hydraulics Structures Dept. / 3rd Class [Hydraulic Lectures]

Lect.No.8 [Open Channel Hydraulics]

Asst. Prof. Dr. Jaafar S. Maatooq 16 of 16