# Fluid Mechanics Questions and Answers – Geometrical Properties of Trapezoidal Section

This set of Fluid Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Geometrical Properties of Trapezoidal Section”.

1. 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

Explanation: Total Wetted Area = 2(Area of triangle) + (Area of rectangle)
A = 2(12 Zy)(y) + (By)
A = Zy2 + By
A = y(Zy + B).

2. Estimate the wetted perimeter of a trapezoidal section of depth y, base B and side slope Z.
a) B+2y$$\sqrt{1+Z^2}$$
b) B+y$$\sqrt{1+Z^2}$$
c) 2y$$\sqrt{1+Z^2}$$
d) y$$\sqrt{1+Z^2}$$

Explanation: Total Wetted Perimeter = Base+Sides
Let each side = x
x= y$$\sqrt{1+Z^2}$$
Perimeter = B+2y$$\sqrt{1+Z^2}$$

3. 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

Explanation: Top Width = Base+2Zy
T = B+2Zy.

4. 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

Explanation:
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5. 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

Explanation:

6. 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

Explanation: Section Factor = A√D

7. 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

Explanation: Discharge (Q) = AV
A = (B+Zy)y
A = (6+1/2 (3))(3)= 22.5m2
Q = (22.5)(2)
Q = 45m3⁄s.

8. 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

9. 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

Explanation:

10. 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

Explanation: Zy=2;y=4m
A = (B+Zy)y;B=6m
Wetted Perimeter = B+2y√(1+Z2)
P = 14.94m.

11. 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

Explanation: Top Width = B+2Zy
12 = 6 +2(1/2)(y); y=6m
P = B+2y√(1+Z2)
P = 19.41m.

12. 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

Explanation:

13. 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

Explanation: Ratio = (section factor)/(hydraulic depth) = 324/25
324/25 =√A √T; √T=49
T = 7m.

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