Open Channel Flow · Fluid Mechanics and Hydraulic Machines · GATE CE

A hydraulic jump occurs in an open channel when the slope of the channel changes from__________ .

G₁ and G₂ are the slopes of the approach and departure grades of a vertical curve, respectively.

Given |G₁| < |G₂| and |G₁| ≠ |G₂| ≠ 0

Statement 1 : +G₁ followed by +G₂ results in a sag vertical curve.

Statement 2 : −G₁ followed by −G₂ results in a sag vertical curve.

Statement 3 : +G₁ followed by −G₂ results in a crest vertical curve.

Which option amongst the following is true?

A hydraulic jump takes place in a 6 in wide rectangular channel at a point where the upstream depth is 0.5 m (just before the jump). If the discharge in the channel is 30 m³/s and the energy loss in the jump is 1.6 m, then the Froude number computed at the end of the jump is _________. (round off to two decimal places)

(Consider the acceleration due to gravity as 10 m/s².)

Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked condition in the channel. The depth of water at this section is y₂ and that at its upstream section is y₁. The correct statements for the chocked and un-chocked conditions in the channel is/are

A rectangular channel with Gradually Varied Flow (GVF) has a changing bed slope. If the change is from a steeper slope to a steep slope, the resulting GVF profile is

Depth of water flowing in a 3 m wide rectangular channel is 2 m. The channel carries a discharge of 12 m³/s. Take g = 9.8 m/s². The bed width (in m) at contraction, which just causes the critical flow, is _________ without changing the upstream water level. (round off to two decimal places)

Consider flow in a long and very wide rectangular open channel. Width of the channel can be considered as infinity compared to the depth of flow. Uniform flow depth is 1.0 m . The bed slope of the channel is 0.0001 . The Manning roughness coefficient value is 0.02 . Acceleration due to gravity, g can be taken as $9.81 \mathrm{~m} / \mathrm{s}^2$.

The critical depth (in m ) corresponding to the flow rate resulting from the above conditions is ________ (round off to one decimal place).

Lacey's regime equations, followed in India for making scour calculations while designing hydraulic structures across alluvial channels, are given below. Regarding these equations, which of the following statements is/are true:

$$ \begin{aligned} & D=0.470 \times\left[\frac{Q}{f_s}\right]^{1 / 3} \\ & P=4.75 \times \sqrt{Q} \\ & f_s=1.76 \times \sqrt{d} \end{aligned} $$

where, $Q$ is discharge and $f_s$ is silt factor

A hydraulic jump is formed in a 5 m wide rectangular channel, which has a horizontal bed and is carrying a discharge of $15 \mathrm{~m}^3 / \mathrm{s}$. The depth of water upstream of the jump is 0.5 m . The power dissipated by the jump (in kW ) is ________ (rounded off to the nearest integer).

Note:

Acceleration due to gravity $=9.81 \mathrm{~m} / \mathrm{s}^2$

Density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$

Kinetic energy correction factor $=1.0$

A 5.0 m wide rectangular channel carries a discharge of $10 \mathrm{~m}^3 / \mathrm{s}$ at a depth of 1.5 m under uniform flow. To produce critical flow conditions without affecting the upstream conditions, the channel bottom elevation should be raised (in m ) by _________ (rounded off to 2 decimal places).

Assume that there is no loss of head at the raise, kinetic energy correction factor is 1.0 , and acceleration due to gravity is $9.81 \mathrm{~m} / \mathrm{s}^2$.

A compound symmetrical open channel section as shown in the figure has a maximum of _______ critical depth(s).

B_m – Bottom width of main channel

B_f – Bottom width of flood channel

y_m – Depth of main channel

y – Total depth of the channel

n_m – Manning’s roughness of the main channel

n_f – Manning’s roughness of the flood channel

The critical flow condition in a channel is given by _______.

[Note: 𝛼 – kinetic energy correction factor; 𝑄 – discharge; A_c – cross-sectional area of flow at critical flow condition; T_c – top width of flow at critical flow condition; 𝑔 – acceleration due to gravity]

The cross-section of a small river is sub-divided into seven segments of width 1.5 m each. The average depth, and velocity at different depths were measured during a field campaign at the middle of each segment width. The discharge computed by the velocity area method for the given data is _____ m³/s (round off to one decimal place).

A very wide rectangular channel carries a discharge (Q) of 70 m³/s per meter width. Its bed slope changes from 0.0001 to 0.0009 at a point P, as shown in the figure (not to scale). The Manning’s roughness coefficient of the channel is 0.01. What water surface profile(s) exist(s) near the point P?