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We often want to know the the minimum area A for a given flow Q, slope S0 and roughness coef- ficient n.

**Best Hydraulic Cross- Section**

We often want to know the the minimum area A for a
given flow Q, slope S_{0} and roughness coef- ficient *n*.

This is
known as the best hydraulic cross section

The
quantity AR_{h}^{2/3} in Mannings’ equation
is called the *section factor*

Writing
the Manning equation with R_{h} = A/P, we get

·
( inside ) is a constant; Channel with minimum A is also minimum P

·
Minimum excavation area A also has minimum P

·
Best possible is semicircular channel, but
construction costs are high

Let’s find out what the
best hydraulic cross section is for a rectan- gular channel

**Example**: Water
flows uniformly in a rectangular channel of width b and depth y. Determine the**
aspect ratio **b/y for the best hydraulic cross section.

·
Thus best hydraulic cross- section for a
rectangular channel occurs when the depth is one-half the width of the channel

· Note for
1 < b/y < 4; Q ˜
.96 Q_{max}

Must include freeboard *f* in design between 5 to 30% of
y_{n}

Table gives Optimum properties of Open Channel Sections

.For trapezoid, half- hexagon

.For circular section, half- circle

.For triangular section, half- square

**Design of Erodible Channels**

Design velocity V small enough not to cause erosion

Find maximum permissible velocity based on channel material
(Roberson, Table 4- 3)

**Maximum
Permissible Velocities a nd n Values for
Different Materials **

**Material V(ft/s) n**

Fine Sand 1.50 0.020

Sandy loam 1.75 0.020

Silt loam 2.00 0.020

Firm loam 2.50 0.020

Stiff clay 3.75 0.025

Fine gravel 2.50 0.025

Coarse gravel 4.00 0.025

Assuming a trapezoidal channel, maximum side slopes
depend on material (Roberson,Table 4-2)

Maximum Channel Wall Slopes for Different Materials

**Material
: Side Slopes**

Rock : Almost Vertical

Stiff clay or earth with concrete : 1/2 : 1 to 1:1

Firm Soil 1:1

Loose sandy soil 2:1

Sandy loam soil 3:1

Once Q, V, n, S_{0} are determined, solve
for depth y and width b.

**Problem**: For an unlined trapezoidal
irrigation canal in firm loam soil, slope is 0.0006 and flow is** **100 cfs,
what dimensions?

For side slope, pick slope of 1 1/2 (h): 1 (v) (conservative)
V_{max} = 2.5 ft/s, *n* = 0.020

To find R_{h}

To construct choose b = 18 ft and y = 2.0 ft.

**Critical Slope**

·
Holding n and Q constant, changing slope slope
will change depth and velocity

·
Where velocity and depth give a Froude number =1,
this is defined as the critical slope S_{c} and crit- ical depth y_{c}

Tags : civil - Applied Hydraulic Engineering: Uniform Flow

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