A rectangular channel has a width of

4.00 \, \mathsf{m}

and a slope of

0.1\%

. For a discharge of

4.80 \, \mathsf{m^3\!/s}

, the depth is measured to be

850\,\mathsf{mm}

. Determine the average flow velocity for these conditions.Then find the average flow velocity

v

and the discharge

Q

when the depth is

1.700\,\mathsf{m}

.

A rectangular channel with a base of

6.25\,\mathsf{m}

has a depth of

y = 1.650\, \mathsf{m}

when the discharge (volume flow rate) is

Q=23.5 \,\mathsf{m^3\!/s}

. Determine

E

, the specific energy, and classify the flow.

A rectangular channel flows at a depth of

{1.850\,\mathsf{m}}

at an average velocity of

2.25\,\mathsf{m/s}

. Determine the alternate depth for this flow.

A rectangular flume is built out of wood

{(n=0.012)}

and has a base width of

1.250\,\mathsf{m}

. The flume has a longitudinal slope of

0.14\%

and a flow depth of

950\,\mathsf{mm}

. Determine

Q,

the discharge, and the slope

S_c

at which this flow becomes critical. What is the critical depth

y_c

and the critical velocity

v_c

for this

Q

?

For discharge

Q

in a rectangular channel, the velocity of flow under critical conditions is

1.900\,\mathsf{m/s}

. If the channel is

4.50\,\mathsf{m}

in width, determine

Q

.

A triangular flume, built from unplaned wood

(n=0.013)

, has a design flow of

3.25\,\mathsf{m^3\!\!/s}

. The sidewalls of the flume are inclined at

45^{\circ}

to the horizontal (

{z=1}

). If the slope of the flume is

{S=0.001,}

determine the depth

y

of normal flow. Classify this flow.

A triangular channel with sides inclined at

60.0\degree

to the horizontal is lined with shotcrete

(n=0.017)

. Determine the volume flow rate if the depth of flow is

1.900\,\mathsf{m}

and the channel slope is

0.500\%

. At what slope will this flow become critical?

A portion of the Colorado River Aquaduct conveys

45.3\,\mathsf{m^3\!/s}

at a depth of

3.10\,\mathsf{m}

in a concrete (

n=0.014

) trapezoidal channel, as shown. Determine the channel slope for this flow.

A concrete-lined trapezoidal channel has a bed width of

6.00\,\mathsf{m}

and side slopes of

z=0.5

, a longitudinal slope of

1

in

850

and a Manning's coefficient of

n=0.014

. Calculate the discharge and average flow velocity for normal flow with a depth of

2.30\,\mathsf{m}

. Classify this flow.

A rough-formed concrete-lined trapezoidal channel

(n=0.015)

has a bed width of

3.50\,\mathsf{m}

and side slopes of

3H\!\!:\!\!2V

(i.e., three horizontal units for each two vertical units, or

{z=1.5}

). The bed slope is

S=0.05\%

. Determine the depth

y

when the discharge is

Q=32.0\,\mathsf{m^3/s}

.

An channel with trapezoidal cross-section is lined with fine gravel (

{n=0.024}

) that has a maximum allowable velocity of

{0.75\,\mathsf{m/s}}

. The channel sides have a slope defined by

{z=2.65}

and the channel bed has a width of

{7.00\,\mathsf{m}.}

The channel is designed for a flow of ${21.5\,\mathsf{m^3\!/s}}$ with the velocity of flow restricted to ${80\%}$ of the maximum allowable. Determine the depth of flow at this velocity and the slope required to generate this flow.

Given that the length of the channel is ${73.5\,\mathsf{km}}$ and that the elevation differences between the two ends is ${21.7\,\mathsf{m}}$ , determine the height $h$ of any drop structure required.

A circular storm water pipe,

1.500\,\mathsf{m}

in diameter, is laid on a slope of

1\!:\!500

. The pipe is high density polyethyline (HDPE) with design value

n=0.013

. Determine the pipe discharge and average flow velocity for each of the following flow depths, entering results into a table for easier comparison:

\footnotesize \begin{array}{|c|c|c|c|} \hline \textsf{Depth}, y & \textsf{Velocity}, v & \textsf{Discharge}, Q & \qquad \qquad \textsf{Comments} \qquad \qquad \\ \hline 0.600\,\textsf{m} & & & \\ \hline 0.750\,\textsf{m} & & & \textsf{Pipe flowing half full} \\ \hline 1.219\,\textsf{m} & & & \textsf{Max velocity at $y\approx 0.8D$}\\ \hline 1.230\,\textsf{m} & & & \\ \hline 1.407\,\textsf{m} & & & \textsf{Max discharge at $y=0.938D$}\\ \hline 1.500\,\textsf{m} & & & \textsf{Pipe flowing full} \\ \hline \end{array}

Engineering Statics

09 Complex Frames

Triangular Channel

Trapezoidal Section

Circular Section