#622 Determine the cross-section of the greatest

Determine the cross-section of the greatest - Civil Engineering

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Determine the cross-section of the greatest hydraulic efficiency for a trapezoidal channel with a side slope of 1 vertical to 2 horizontal if the design discharge is 10 m3/s. The channel slope is 0.001 and Manning’s roughness factor is 0.020.

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1. Step 1 of 3

   Find the uniform flow depth in the trapezoidal channel using manning’s formula.

   

   Denote the Discharge in the channel as, Area of the trapezoidal channel as A, Hydraulic radius as, Manning’s roughness coefficient as n, and Bottom slope as .

   Substitute  for  and  for .

    …… (1)

   Denote the Bottom width of the trapezoidal channel as , depth of flow as y, and Side slope as 1 vertical to horizontal.

2. Step 2 of 3

   Design the trapezoidal channel for maximum discharge

   Select the channel with a minimum wetted perimeter for a given discharge.

   Express the hydraulic radius formula.

   

   Express the area of flow in the channel formula.

   

   Find the Bottom width of the trapezoidal.

    …… (2)

   Find the uniform flow depth.

   Substitute  for A, 0.020 for n, 0.001 for  and  for R in Equation (1).

   

   

   Thus, the flow depth of the trapezoidal channel is .

3. Step 3 of 3

   Find the bottom width of the trapezoidal channel.

   Substitute 1.9328 m for y in Equation (2).

   

   

   Thus, the bottom width of the trapezoidal channel is .

   Thus, the cross-section with the greatest hydraulic efficiency is .

#618 Water flows down a wide and shallow rectangular

Water flows down a wide and shallow rectangular - civil engineering

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Water flows down a wide and shallow rectangular channel of concrete (n=0.015) laid on a slope of 0.004. find the depth and the rate of flow in SI units for critical conditons in the channel

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For thin film flow, the critical slope is defined as:

S_c = (g*n²)/(y_c)^1/3

where:

g = gravity = 9.81 m/s²

n = 0.015

y_c = critical depth

Rearranging the equation:

y_c = [(g*n²)/S_c]³

substituting in values and solving:

y_c = [(9.81*0.015²)/0.004]³ --> y_c = 0.168 m

Next note the critical velocity is found by the following relationship:

(V_c²/g) = (A_c/T_c) --> V_c = sqrt[(A_c/T_c)*g]

where:

T_c = the top width = b

A_c = flow area = b*y_c = 0.168*b

V_c = critical velocity

substituting in values and solving:

V_c = sqrt[(0.168*b/b)*9.81] = sqrt(0.168*9.81) --> V_c = 1.284 m/s

#604 The concrete seawall has a curved surface

The concrete seawall has a curved surface- Civil Engineering

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The concrete seawall has a curved surface and restrains seawater at a depth of 7.5m. The trace of the surface is a parabola as illustrated. Determine the moment of the fluid force (per unit length) with respect to an axis through the toe (point A).

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#587 An A cylinder of / m slides down in a vertical pipe

An A cylinder of / m slides down in a vertical pipe - Civil Engineering

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Mass m = 1.962 N s

2nd

An A cylinder of / m slides down in a vertical pipe.

There is a thin layer of oil on the cylinder surface and inside the pipe. Cylinder and tube axes

overlaps. (oil = 8044.2 N / m3

; υoil = 6⋅10-6 m2 / s)

a) The speed change corresponding to the unit displacement of the cylinder in the pipe and in the oil layer

Find the slip resistance that will occur.

Determine the final speed that the cylinder will reach in the pipe. (The effect of air pressure will be neglected.)

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#567 The following EN and XY coordinates

The following EN and XY coordinates - Civil Engineering

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The following EN and XY coordinates for points A through C are given. Determine a 2-D conformal coordinate transformation to convert the XY coordinates into the EN system. ?

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#564 The following EN and XY coordinates for points A through

The following EN and XY coordinates for points A through - Civil Engineering

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The following EN and XY coordinates for points A through C have given Determine a 2-D conformal coordinate transformation to convert the XY coordinates into the EN system

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#526 The member in Figure P6.6-12 is laterally supported

The member in Figure P6.6-12 is laterally supported - Civil Engineering

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The member in Figure P6.6-12 is laterally supported only at its ends If A572 Grade 50 steel is used, does the member satisfy the provisions of the AISC Specification? The loads are 50% live load and 50% dead load.

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