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

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

1. The discharge and velocity of water in a rectangular channel are 75m^3/s and 5m/ s respectively. The hydraulic depth being 3m calculate the hydraulic radius.
a) 1.36m
b) 1.87m
c) 1.98m
d) 2.0m

Explanation: Discharge (Q) = (A) (V)
75 = (A) (5)
A = 15m2
A = (B) (y)
B = 15/ 3 = 5m
R = A/ P = 15/ (5 + 2(3))
R = 1.36m.

2. Calculate the hydraulic diameter for a rectangular duct having 10m width and 6m depth.
a) 5.5m
b) 6.5m
c) 7.5m
d) 8.5m

Explanation: Hydraulic diameter = 2By / B + y
Hydraulic diameter = 2(10) (6) / 16
Hydraulic diameter = 7.5m.

3. The ratio of Hydraulic radius and Hydraulic depth is ½ and the top width of the channel is 6m, calculate the hydraulic depth of the channel.
a) 1m
b) 2m
c) 3m
d) 4m

Explanation: Ratio = ½
Ratio = (A/P) / (A/T) = T/P; T = 6m
½ = 6/P
P = 12m = B + 2y
12 = 6 + 2y
y = 3m.
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4. The section factor of a rectangular channel is 111.80m. The discharge and velocity of water are 250 m3⁄s and 5 m⁄s respectively. Calculate the hydraulic depth of the channel.
a) 2m
b) 3m
c) 4m
d) 5m

Explanation: Section factor (Z) = A√D
Discharge (Q) = AV
A = 250/5 = 50m2
111.80 = 50√D
D = 5m.

5. The ratio between depth and width of a rectangular channel is ¼ and the area of the rectangular section is 16m^2. Calculate the top width of the channel.
a) 5m
b) 6m
c) 7m
d) 8m

Explanation: Ratio = ¼
D/B = ¼
4D = B
Area (A) = 16m2
(B) (D) = 16 = 4D2; D = 4m
B = 2(4) = 8m.

6. Which geometric parameter determines the efficiency of the channel?
a) Hydraulic depth
c) Section factor
d) Normal depth

Explanation: The Hydraulic Radius is given by R = A/P and as R increases P decreases. As P is less the channel is more efficient.

7. A rectangular channel has depth y and top with B. Determine its section factor.
a) By3⁄2
b) By1⁄2
c) By
d) By2

Explanation: Section factor (Z) = A√D
Z = (B) (y)√y
Z = By3⁄2.

8. Calculate the wetted area for a rectangular channel which is
5.2m in width and 3m in depth.
a) 15.6m2
b) 16.6m2
c) 17.6m2
d) 18.6m2

Explanation: Wetted area (A) = (5.2) (3) = 15.6m2.

9. Calculate the wetted perimeter for a rectangular channel having top width of 4.5m and depth of 3m.
a) 12m
b) 10.5m
c) 7.5m
d) 15m

Explanation: Wetted Perimeter = Width + 2(Depth)
= 4.5 + 2(3)
= 10.5m.

10. A rectangular channel has a depth of 5m and width of 12m. Calculate the hydraulic depth of the channel.
a) 5m
b) 6m
c) 7m
d) 8m

Explanation: Hydraulic Depth (D) = Area/Top width
= (5) (12)/ 12
= 5m.

11. The depth and widths of a rectangular channel are 4m and 5m respectively. Determine the hydraulic radius of the channel.
a) 4.22m
b) 3.54m
c) 2.22m
d) 1.54m

Explanation: Hydraulic Radius (R) = A/P
= (4) (5)/(5 + 2(4))
= 1.54m.

12. Determine the section factor for the channel section having area 20m2.
a) 20m
b) 30m
c) 40m
d) 50m

Explanation: Section factor (Z) = A√D
= 20√4
= 40m.

13. The section factor and hydraulic depth for a rectangular channel are 40m and 4m respectively. Determine the top width of the channel.
a) 3m
b) 4m
c) 5m
d) 6m

Explanation: Section factor (Z) = A√D
40 = A√4 ; A = 20m2
A = (Depth) (Width)
Width = 5m.

14. The hydraulic depth of a rectangular channel is 2m and its wetted area is 12m2. Estimate its hydraulic radius.
a) 1.2m
b) 1.3m
c) 1.4m
d) 1.5m

Explanation: Hydraulic Depth (D) = A/ Top Width
2 = 12/ T
T = 6m
P = T+ 2(D)
P = 6+ 2(2) = 10m
R = 12/ 10 = 1.2m.

15. Let the top width of a rectangular channel be B and the depth be y, determine the hydraulic radius of the channel.
a) By/ B+2y
b) By/ B+ y
c) y
d) B

R = (B)(y)/ B + 2y.

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