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civil - Applied Hydraulic Engineering: Uniform Flow

Best Hydraulic Cross- Section

   Posted On :  12.07.2016 08:39 pm
Best Hydraulic Cross- Section

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 S0 and roughness coef- ficient n.

 

This is known as the best hydraulic cross section

 

The quantity ARh2/3 in Mannings’ equation is called the section factor

Writing the Manning equation with Rh = 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 Qmax

 


Must include freeboard f in design between 5 to 30% of yn

 

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, S0 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) Vmax = 2.5 ft/s, n = 0.020

 

To find Rh

 


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 Sc and crit- ical depth yc

 

 

Tags : civil - Applied Hydraulic Engineering: Uniform Flow
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