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For a wide rectangular channel using Manning’s formula, the differential equation of gradually varied flow (with the usual notations) is given by
For Chezy’s formula N = 3; M = 3
For Manning’s formula N = 10/3; M = 3
N is related to conveyance
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
∴
Water surface profiles that are asymptotic at one end and terminated at the other end would include
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:
Hydraulic jump is needed when critical depth line is to be crossed.
For a hydraulically efficient rectangular section, the ratio of width to normal depth is
For hydraulically efficient rectangular section.
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?
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.
If F_{1} and F_{2} are the Froude numbers of flow before and after the hydraulic jump occurring in a rectangular channel, then
Equating the equation (i) with inverse of equation (ii) we get,
The momentum correction factor for a flow through open channel is given by
The Froude number of a hydraulic jump is 5.5. The jump can be classified as a/an
The hydraulic jumps in horizontal rectangular channels are classified into five categories based on Froude number F_{1} of the supercritical flow as:
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?
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