Question 12.8: A rectangular channel, 9.14 m wide, carries 7.64 m^3/s when ...

Introduction to Fluid Mechanics and Fluid Machines

A rectangular channel, 9.14 m wide, carries $7.64 \mathrm{~m}^{3} / \mathrm{s}$ when flowing 914 mm deep. (i) What is the specific energy? (ii) Is the flow tranquil or rapid?

The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.

(i) We know from Eq. (12.31) that

E_{s}=h+\left(\frac{q^{2}}{2 g}\right) \frac{1}{h^{2}}

Or $E_{s}=0.914+\frac{1}{2 \times 9.81 \times(0.914)^{2}}\left(\frac{7.64}{9.14}\right)^{2}$

= 0.957 m

(ii) From Eq. (12.32),

h_{c}=\left(q^{2} / g\right)^{1 / 3}

h_{c}=\left[\left(\frac{7.64}{9.14}\right)^{2} \frac{1}{9.81}\right]^{1 / 3}=0.415 \mathrm{~m}=415 \mathrm{~mm}

Therefore, the flow is tranquil since the depth of flow is grater than the critical depth.

Related Answered Questions

Question: 12.1

The depth of a uniform steady flow of water in a 1.22 m wide rectangular cement lined channel laid on a slope of 4 m in 10000 m, is 610 mm. Find the rate of discharge using Manning’s value for c (Chezy coefficient). ...

Verified Answer:

We have to use Eq. (12.9) for the present purpose....

Question: 12.12

A control sluice spanning, the entry to a 3.5 m wide rectangular channel, admits 5.5 m^3/s of water with a uniform velocity of 4.14 m/s. Explain under what conditions a hydraulic jump will be formed and, assuming that these conditions exist, calculate (i) the height of the jump, and (ii) power ...

Verified Answer:

The upstream depth of flow is

h_{1}=\frac{...

Question: 12.11

A rectangular channel, 6.1 m wide, carries 11.32 m^3/s and discharges onto a 6.1 m wide apron having no slope with a mean velocity of 6.1 m/s. (i) What is the height of the hydraulic jump? (ii) What energy is absorbed (lost) in the jump? ...

Verified Answer:

(i)

V_{1}=6.1 \mathrm{~m} / \mathrm{s} [/...

Question: 12.10

A circular culvert has a capacity of 0.5 m^3/s when flowing full. Velocity should not be less than 0.7 m/s if the depth is one-fourth of the diameter. Assuming uniform flow, find the diameter and the slope, taking Manning’s roughness coefficient n = 0.012. ...

Verified Answer:

Putting h/d = 1/4 in Eq. (12.41), we get

\...

Question: 12.9

A trapezoidal channel has a bottom width of 6.1 m and side slope of 2 horizontal to 1 vertical. When the depth of water is 1.07 m, the flow is 10.47 m^3/s. (i) What is the specific energy of flow? (ii) Is the flow tranquil or rapid? ...

Verified Answer:

The cross sectional area of flow,

A=6.1(1....

Question: 12.7

A rectangular channel carries 5.66 m^3/s. Find the critical depth hc and critical velocity Vc for (i) a width of 3.66 m and (ii) a width of 2.74 m, (iii) what slope will produce the critical velocity in (i) if n = 0.020? ...

Verified Answer:

(i) Critical depth is defined as the depth at whic...

Question: 12.6

(i) Determine the most efficient section of trapezoidal channel, n = 0.025, to carry 12.74 m^3/s. To prevent scouring, the maximum velocity is to be 0.92 m/s and the side slopes of the trapezoidal channel are 1 vertical to 2 horizontal. (ii) What slope S of the channel is required? ...

Verified Answer:

(i) It is known from Eq. (12.18) that for the most...

Question: 12.5

In a hydraulics laboratory, a flow of 0.412 m^3/s was measured from a rectangular channel flowing 1.22 m wide and 0.61 m deep. If the slope of the channel was 0.0004, find its roughness factor using Manning’s formula. ...

Verified Answer:

Here,

A=1.22 \times(0.61)

...

Question: 12.4

Show that the vertical distribution of velocity is parabolic for a uniform laminar flow in a wide open channel with constant slope and depth of flow. ...

Verified Answer:

Let the depth of flow be h (Fig. 12.10). A control...

Question: 12.3

How deep will water flow at the rate of 6.79 m^3/s in a rectangular channel 6.1 m wide, laid on a slope of 0.0001? Use n = 0.0149. ...

Verified Answer:

Let the depth be h Then A (cross-sectional areas o...