# Fluid Mechanics Questions and Answers – Gradually Varied Flow in Wide Rectangular Channels

This set of Fluid Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Gradually Varied Flow in Wide Rectangular Channels”.

1. What is the hydraulic radius for a wide rectangular channel section?
a) 3y
b) 2y
c) y
d) y/2

Explanation: For a wide rectangular channel B>>y
A = By; P = B+2y = B (since B>>y)
R = AP = y.

2. Which of the following equations is true for a wide rectangular channel?
a) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y}{y_n})^3)}{1-(\frac{y}{y_c})^3}$$
b) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y}{y_n})^3)}{1-(\frac{y_c}{y})^3}$$
c) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y_n}{y})^3)}{1-(\frac{y_c}{y})^3}$$
d) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y_n}{y})^3)}{1-(\frac{y}{y_c})^3}$$

Explanation:

3. Calculate the rate of change of depth of a wide rectangular channel having uniform flow depth of 2m and the depth during GVF is 1.5m. Given:yc=1m, S0=1 in 1500.
a) 1.4×10-4m
b) 2.4×10-4m
c) 3.4×10-4m
d) 4.4×10-4m

Explanation:

4. Which of the following equations is true considering Chezy’s equation?
a) $$\frac{S_0}{S_f} = (\frac{y_n}{y})^3$$
b) $$\frac{S_0}{S_f} = (\frac{y}{y_n})^3$$
c) $$\frac{S_f}{S_0} = (\frac{y_n}{y})^3$$
d) $$\frac{S_f}{S_0} = (\frac{y_n}{y})^3$$

Explanation:

5. Which of the following equations is true considering Manning’s equation?
a) $$\frac{S_f}{S_0} = (\frac{y_n}{y})^{\frac{10}{3}}$$
b) $$\frac{S_f}{S_0} = (\frac{y}{y_n})^{\frac{10}{3}}$$
c) $$\frac{S_0}{S_f} = (\frac{y}{y_n})^{\frac{10}{3}}$$
d) $$\frac{S_0}{S_f} = (\frac{y_n}{y})^{\frac{10}{3}}$$

Explanation:
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6. The slope of the energy line of a wide rectangular channel is 4×10-5 and the bed slope of the channel is 1 in 1200 using manning’s equation, calculate the depth in GVF if the uniform depth of flow is 1.5m.
a) 0.5m
b) 0.6m
c) 0.7m
d) 0.8m

Explanation:

7. The value of slope of energy line of a wide rectangular channel is 3×10-4 and the bed slope of the channel is 1 in 1500 using chezy’s equation, calculate the uniform flow depth if the depth during GVF is 2m.
a) 1.61m
b) 2.61m
c) 3.61m
d) 4.61m

Explanation:

8. If y = 2m and velocity of flow is 2.5m⁄s, calculate the critical depth.
a) 0.36m
b) 1.36m
c) 2.36m
d) 3.36m

Explanation:

9. Which of the following expressions is true?
a) $$\frac{dy}{dx} = S_0 \frac{((\frac{y}{y_n})^3-1)}{1-(\frac{y}{y_c})^3}$$
b) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y}{y_n})^3)}{1-(\frac{y}{y_c})^3}$$
c) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y_n}{y})^3)}{1-(\frac{y}{y_c})^3}$$
d) $$\frac{dy}{dx} = S_0 \frac{(\frac{y_n}{y})-1}{1-(\frac{y}{y_c})^3}$$

Explanation:

10. Which of the following expressions is true?
a) $$\frac{dy}{dx} = S_0 \frac{((\frac{y}{y_n})^{\frac{10}{3}}-1)}{1-(\frac{y}{y_c})^3}$$
b) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y}{y_n})^{\frac{10}{3}})}{1-(\frac{y}{y_c})^3}$$
c) $$\frac{dy}{dx} = S_0 \frac{(1-(\frac{y_n}{y})^{\frac{10}{3}})}{1-(\frac{y}{y_c})^3}$$
d) $$\frac{dy}{dx} = S_0 \frac{(\frac{y_n}{y})-1}{1-(\frac{y}{y_c})^3}$$

Explanation:

11. If dy/dx=3×10-4 m and the ratio of bed slope and slope of energy line is 0.7, calculate the value of slope of energy line if the uniform flow depth is 1.6m, critical depth is 1.2m.
a) 5.25×10-4
b) 6.25×10-4
c) 7.2510-4
d) 8.25×10-4

Explanation:

12. If the ratio of GVF depth to normal depth and the ratio of critical depth to normal are equal to 0.5, calculate the rate of change of depth if the bed slope of the channel is 1 in 1300.
a) 5.96×-4m
b) 6.96×-4m
c) 7.96×-4m
d) 8.96×-4m

Explanation:

13. Calculate the critical depth of a wide rectangular channel section if the normal depth and yn are 3.2m and 2.5m respectively. Given: dy/dx=3×10-4 m and S0=1/2000.
a) 0.29m
b) 1.29m
c) 2.29m
d) 3.29m

Explanation:

14. For a wide rectangular channel y>>B.
a) True
b) False

Explanation: For a wide rectangular channel B>>y, hence R=y in this case.

15. If the velocity of flow through a wide rectangular channel is 2m⁄s and the rate of change of depth is 3×10-5m, calculate the manning’s constant of the channel if the uniform flow depth is 1m and yn=0.6m. Given: Critical depth = 0.5m.
a) 0.38×10-3
b) 1.38×10-3
c) 2.38×10-3
d) 3.38×10-3

Explanation:

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