# Fluid Mechanics Questions and Answers – Gradually Varied Flow(GVF) – 1

This set of Fluid Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Gradually Varied Flow(GVF) – 1”.

1. Which of the following assumptions about a GVF is false?
a) Channel is prismatic
b) Pressure distribution is hydrostatic
c) Flow characteristics change with time
d) Roughness co efficient is constant

Explanation: In a GVF, the flow is steady and hence the flow characteristics does not change with time.

2. Calculate the total discharge though a rectangular channel having depth 2m and width 4m if the value of C = 50 and if the slope of the energy line is 0.00004.
a) 1.53 m3/s
b) 2.53 m3/s
c) 3.53 m3/s
d) 4.53 m3/s

3. Calculate Sf for a triangular channel if the depth of the channel is 5m and the side slope is 1H:2V. Given: Q = 5.80 m3/s , C = 40.
a) 0.00010
b) 0.00011
c) 0.00012
d) 0.00013

4. Calculate the discharge through a trapezoidal channel section if the depth of the channel is 3m and the base width is 3m. Given: C = 30, Sf = 0.0005, A = 12m2.
a) 6.10 m3/s
b) 7.10 m3/s
c) 8.10 m3/s
d) 9.10 m3/s

5. The discharge through a circular channel section having diameter 4m which is running half is 4.35 m3/s and the value of slope of energy line is Sf = 0.0003, calculate the value of C.
a) 50
b) 45
c) 40
d) 35

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6. Determine the dynamic equation for the rate of change of depth having bed slope S0 and slope of total energy line Sf.
a) $$\frac{dy}{dx} = \frac{S_0-S_f}{1-\frac{QT}{gA^2}}$$
b) $$\frac{dy}{dx} = \frac{S_0-S_f}{1-\frac{Q^2T}{gA^2}}$$
c) $$\frac{dy}{dx} = \frac{S_0-S_f}{1-\frac{Q^2T}{gA^3}}$$
d) $$\frac{dy}{dx} = \frac{S_0-S_f}{1-\frac{Q^2T}{gA}}$$

7. Determine the dynamic equation for the rate of change of depth having bed slope S0 and slope of total energy line Sf in terms of Froude’s number.
a) $$\frac{dy}{dx} = \frac{S_0-S_f}{1-F_r^2}$$
b) $$\frac{dy}{dx} = \frac{S_0-S_f}{1-F_r}$$
c) $$\frac{dy}{dx} = \frac{S_0-S_f}{1-\sqrt{F_r}}$$
d) $$\frac{dy}{dx} = \frac{S_0-S_f}{F_r^2}$$

8. Estimate the rate of change of specific energy having bed slope S0 and slope of total energy line Sf.
a) $$\frac{dE}{dx}$$ = Sf – S0
b) $$\frac{dE}{dx}$$ = Sf – $$\frac{S_0}{2}$$
c) $$\frac{dE}{dx}$$ = S0 – Sf
d) $$\frac{dE}{dx} = \frac{S_f}{2}$$ – S0

9. Calculate the rate of change of specific energy if the bed slope is 1 in 1000 and Sf = 0.00007.
a) 6.3×10-3m
b) 7.3×10-3m
c) 8.3×10-3m
d) 9.3×10-3m

10. Estimate the value of Sf if the value of bed slope is 1 in 800 and and dEdx = 10-3m.
a) 0.00015
b) 0.00025
c) 0.00035
d) 0.00045

Explanation: dEdx = S0 – Sf; Sf = 0.00025.

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