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QUESTION: 1

For a wide rectangular channel using Manning’s formula, the differential equation of gradually varied flow (with the usual notations) is given by

Solution:

For Chezy’s formula N = 3; M = 3

For Manning’s formula N = 10/3; M = 3

N is related to conveyance

QUESTION: 2

The stage in a river is 4.8 m, the water surface- slope is 1 in 10,000 and the discharge in the stream is 600 m^{3}/s. If the stage remains the same and the water surface slope is 1 in 14,400, then the discharge in the stream will be

Solution:

∴

QUESTION: 3

Water surface profiles that are asymptotic at one end and terminated at the other end would include

Solution:

The curves which are asymptotic at one end and terminated at the other end are M_{2} and H_{2}.

Using Manning’s equation for wide rectangular channel.

i.e. the water surface approaches normal depth line asymptotically

i.e. the water surface meets the criticai depth line vertically in region 2 and 3.

i.e. the water surface meets a very large depth as horizontal asymptote in region 1.

it means that the surface profile meets the channel bed vertically in region 3.

Thus,

(i) M_{1}, M_{2}, S_{2} and S_{3} meet y_{0} line asymptotically

(ii) M_{1} and S_{1} curve tend to horizontal as y → ∞

(iii) M_{2}, M_{3} and S_{2} meet y_{c} line normally

(iv) M_{3} and S_{3} meet channel bed. normally.

The slope of:

- C
_{1}and C_{3}curves comes out to be equal to critical slope of the bed, if Chezy’s equation is used. Otherwise they are slightly curved.

QUESTION: 4

A hydraulic jump is always needed in case of

Solution:

Hydraulic jump is needed when critical depth line is to be crossed.

QUESTION: 5

For a hydraulically efficient rectangular section, the ratio of width to normal depth is

Solution:

For hydraulically efficient rectangular section.

QUESTION: 6

Consider the following statements in regard to the critical flow:

1. Specific energy is maximum for a given discharge.

2. Specific force is maximum for a given discharge

3. Discharge is maximum for a given specific force.

4. Discharge is maximum for a given specific energy.

Which of these statements are correct?

Solution:

At critical flow, specific energy and specific force is minimum for a given discharge. In other words for a given specific energy or specific force, discharge is maximum at critical flow.

QUESTION: 7

If F_{1} and F_{2} are the Froude numbers of flow before and after the hydraulic jump occurring in a rectangular channel, then

Solution:

Equating the equation (i) with inverse of equation (ii) we get,

QUESTION: 8

The momentum correction factor for a flow through open channel is given by

Solution:

QUESTION: 9

The Froude number of a hydraulic jump is 5.5. The jump can be classified as a/an

Solution:

The hydraulic jumps in horizontal rectangular channels are classified into five categories based on Froude number F_{1} of the super-critical flow as:

QUESTION: 10

A hydraulically efficient trapezoidal section of open channel flow carries water at the optimal depth of 0.6 m. Chezy coefficient is 75 and bed slope is 1 in 250. What is the discharge through the channel?

Solution:

### Flow Dynamics in Open Channels and Rivers (Part - 1)

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### Flow Dynamics in Open Channels and Rivers (Part - 2)

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### Flow Dynamics in Open Channels and Rivers (Part - 3)

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