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# MCQs on Geometrical Properties of Trapezoidal Section

. What is the total wetted area of a trapezoidal section of depth y base B and side slope Z?

a) Z(B+Zy)

b) y(B+Zy)

c) Zy2

d) Zy

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b

Explanation: Total Wetted Area = 2(Area of triangle) + (Area of rectangle)

A = 2(1⁄2 Zy)(y) + (By)

A = Zy2 + By

A = y(Zy + B).

Estimate the wetted perimeter of a trapezoidal section of depth y, base B and side slope Z.

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a

Explanation:

What is the top width of a trapezoidal channel having depth y, side slope Z and base B?

a) 2Zy

b) Zy

c) B+Zy

d) B+2Zy

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d

Explanation: Top Width = Base+2Zy

T = B+2Zy.

Calculate the hydraulic depth of a trapezoidal channel section having depth 4m, base of 5m and side slope 1H:2V.

a) 2.11m

b) 3.11m

c) 4.11m

d) 5.11m

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b

Explanation:

Calculate the hydraulic radius of a trapezoidal section having depth 5m, side slope 1H:3V and base of 6m.

a) 1.32m

b) 2.08m

c) 1.08m

d) 2.32m

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d

Explanation:

Calculate the section factor of a trapezoidal channel section having depth 8m, base 5m and side slope 1H:2V.

a) 139.44

b) 149.44

c) 159.44

d) 169.44

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d

Explanation: Section Factor = A√D

Estimate the discharge of water in a trapezoidal channel section having a depth 3m, width of 6m, side slope of 1H:2V and velocity of water is 2m⁄s.

a) 40m3⁄s

b) 45m3⁄s

c) 50m3⁄s

d) 55m3⁄s

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b

Explanation: Discharge (Q) = AV

A = (B+Zy)y

A = (6+1/2 (3))(3)= 22.5m2

Q = (22.5)(2)

Q = 45m3⁄s.

Calculate the side slope of a trapezoidal channel section having base 8m, depth 4m and the hydraulic radius is 2.36m.

a) 1⁄6

b) 1⁄3

c) 1⁄2

d) 1⁄4

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c

Explanation: Hydraulic Radius(R) = A/P

Calculate the top width of a trapezoidal channel section having a side slope1H:4V, base of 5m and the wetted area is 17.25m2.

a) 5.5m

b) 6.5m

c) 7.5m

d) 8.5m

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b
Explanation
The product Zy in a Trapezoidal channel is 2 and the side slope is1/2. Calculate the wetted perimeter of the channel section if the wetted is 32m2.

a) 13.94m

b) 14.94m

c) 15.94m

d) 16.94m

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b

Explanation: Zy=2;y=4m

A = (B+Zy)y;B=6m

Wetted Perimeter = B+2y√(1+Z2)

P = 14.94m.

The top width of a trapezoidal channel is 12m, the bottom width of the channel is 6m and the side slope is 1H:2V, calculate the wetted perimeter.

a) 17.41m

b) 18.41m

c) 19.41m

d) 20.41m

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c

Explanation: Top Width = B+2Zy

12 = 6 +2(1/2)(y); y=6m

P = B+2y√(1+Z2)

P = 19.41m.

The wetted area of a trapezoidal section is 15m^2 and the top width is 6m, calculate the section factor.

a) 23.72

b) 24.72

c) 25.72

d) 26.72

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a
Explanation
The ratio of section factor and hydraulic depth in a trapezoidal section is 324/25, calculate the top width if the total wetted area of the channel is 24m2.

a) 4m

b) 5m

c) 6m

d) 7m

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d

Explanation: Ratio = (section factor)/(hydraulic depth) = 324/25

324/25 =√A √T; √T=49

T = 7m.