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

View Answer

Explanation: Discharge (Q) = (A) (V)

75 = (A) (5)

A = 15m

^{2}

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

View Answer

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

View Answer

Explanation: Ratio = ½

Ratio = (A/P) / (A/T) = T/P; T = 6m

½ = 6/P

P = 12m = B + 2y

12 = 6 + 2y

y = 3m.

4. The section factor of a rectangular channel is 111.80m. The discharge and velocity of water are 250 m^{3}⁄s and 5 m⁄s respectively. Calculate the hydraulic depth of the channel.

a) 2m

b) 3m

c) 4m

d) 5m

View Answer

Explanation: Section factor (Z) = A√D

Discharge (Q) = AV

A = 250/5 = 50m

^{2}

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

View Answer

Explanation: Ratio = ¼

D/B = ¼

4D = B

Area (A) = 16m

^{2}

(B) (D) = 16 = 4D

^{2}; D = 4m

B = 2(4) = 8m.

6. Which geometric parameter determines the efficiency of the channel?

a) Hydraulic depth

b) Hydraulic radius

c) Section factor

d) Normal depth

View Answer

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) By^{3⁄2}

b) By^{1⁄2}

c) By

d) By^{2}

View Answer

Explanation: Section factor (Z) = A√D

Z = (B) (y)√y

Z = By

^{3⁄2}.

8. Calculate the wetted area for a rectangular channel which is

5.2m in width and 3m in depth.

a) 15.6m^{2}

b) 16.6m^{2}

c) 17.6m^{2}

d) 18.6m^{2}

View Answer

Explanation: Wetted area (A) = (5.2) (3) = 15.6m

^{2}.

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

View Answer

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

View Answer

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

View Answer

Explanation: Hydraulic Radius (R) = A/P

= (4) (5)/(5 + 2(4))

= 1.54m.

12. Determine the section factor for the channel section having area 20m^{2}.

a) 20m

b) 30m

c) 40m

d) 50m

View Answer

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

View Answer

Explanation: Section factor (Z) = A√D

40 = A√4 ; A = 20m

^{2}

A = (Depth) (Width)

Width = 5m.

14. The hydraulic depth of a rectangular channel is 2m and its wetted area is 12m^{2}. Estimate its hydraulic radius.

a) 1.2m

b) 1.3m

c) 1.4m

d) 1.5m

View Answer

Explanation: Hydraulic Depth (D) = A/ Top Width

2 = 12/ T

T = 6m

Hydraulic Radius (R) = A/P

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

View Answer

Explanation: Hydraulic Radius(R) = A/P

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

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