The following post contains **Multiple Choice Questions** (MCQ) covering "**Gradually Varied Flow Theory**" of **Open Channel Flow / Hydraulics**. Try answering the questions by yourself. Then you can check the model answers for those **Open Channel Flow MCQ** on the following link :

Open Channel Flow MCQ - Gradually Varied Flow Theory - Set 1 (Model Answer)

These **Open Channel Flow MCQ** covers the following topics / points of "**Gradually Varied Flow Theory**" :

- Introduction to Gradually Varied Flow Theory
- Differential Equation of Gradually Varied Flow GVF
- Classification of Flow Profiles
- Control Sections
- Flow Profile Analysis
- Transitional Depth

The following **Open Channel Flow MCQ** is important for engineering students and professionals while getting ready for different engineering competitive exams. For any help, you can contact us through the comments and we will reply to you as soon as possible. You can also contact us through the following email **author@3nn.4fe.myftpupload.com**.

## Open Channel Flow MCQ - Gradually Varied Flow Theory - Set 1

### Question No.1

In terms of **conveyances** and **section factors**, the **basic differential equation** of **GVF** can written as ** dy/dx** =

- \[{S_o}\frac{{1 - {{({K_o}/K)}^2}}}{{1 - {{(Z/{Z_c})}^2}}}\]
- \[{S_o}\frac{{1 - {{(K/{K_o})}^2}}}{{1 - {{({Z_c}/Z)}^2}}}\]
- \[{S_o}\frac{{1 - {{({K_o}/K)}^2}}}{{1 - {{({Z_c}/Z)}^2}}}\]
- \[{S_o}\frac{{1 - {{(K/{K_o})}^2}}}{{1 - {{(Z/{Z_c})}^2}}}\]

### Question No.2

In **GVF profiles** as the depth *y*→ *y _{c}* :

- \[\frac{{dy}}{{dx}} \to 0\]
- \[\frac{{dy}}{{dx}} \to \infty \]
- \[\frac{{dy}}{{dx}} \to {S_o}\]
- \[\frac{{dy}}{{dx}} \to {\rm{a finite value}}\]

### Question No.3

For a **wide rectangular** channel, if the **Manning’s formula** is used, the **differential equation** of **GVF** becomes ** dy/dx** =

- \[{S_o}\frac{{1 - {{({y_o}/y)}^{3.33}}}}{{1 - {{({y_c}/y)}^{3.33}}}}\]
- \[{S_o}\frac{{1 - {{({y_o}/y)}^{3.33}}}}{{1 - {{({y_c}/y)}^3}}}\]
- \[{S_o}\frac{{1 - {{(y/{y_o})}^{3.33}}}}{{1 - {{(y/{y_c})}^3}}}\]
- \[{S_o}\frac{{1 - {{(y/{y_o})}^3}}}{{1 - {{({y_c}/{y_o})}^{3.33}}}}\]

### Question No.4

For a **very wide rectangular** channel, if **Chezy formula** is used, the **differential equation** of **GVF** is given by ** dy/dx** =

- \[{S_o}\frac{{1 - {{({y_o}/y)}^{3.33}}}}{{1 - {{({y_c}/y)}^{3.33}}}}\]
- \[{S_o}\frac{{1 - {{({y_o}/y)}^3}}}{{1 - {{({y_c}/y)}^3}}}\]
- \[{S_o}\frac{{1 - {{({y_o}/y)}^3}}}{{1 - {{({y_c}/y)}^{3.33}}}}\]
- \[{S_o}\frac{{1 - {{({y_o}/y)}^{3.33}}}}{{1 - {{({y_c}/y)}^3}}}\]

### Question No.5

**Uniform** flow is taking place in a **rectangular** channel having a longitudinal slope of 0.004 and Manning’s n = 0.013. The discharge per unit width in the channel is measured as 1.2 m^{3}/s/m. The **slope** of the channel is classified in **GVF analysis** as :

- mild
- critical
- steep
- very steep

### Question No.6

In a GVF, ** dy/dx** is

**positive**if :

*K*>*K*and_{o}*Z*>*Z*_{c}*K*>*K*and_{o}*Z*<*Z*_{c}*K*>_{o}*K*and_{c}*Z*>_{o}*Z*_{c}*Z*>*K*and*Z*>_{c}*K*_{o}

### Question No.7

A 2.0-m wide **rectangular** channel has **normal depth** of 1.25 m when the **discharge** is 8.75 m^{3}/s. The **slope** of the channel is classified as :

- steep
- mild
- critical
- essentially horizontal

### Question No.8

Identify the **incorrect** statement: The **possible GVF profiles** in :

- mild slope channels are M
_{1}, M_{2}and M_{3} - adverse slope channels are A
_{2}and A_{3} - horizontal channels are H
_{1}and H_{3} - critical slope channels are C
_{1}and C_{3}

### Question No.9

The following types of **GVF profiles** do **not** exist :

- C
_{2}, H_{2}, A_{1} - A
_{2}, H_{1}, C_{2} - H
_{1}, A_{1}, C_{2} - C
_{1}, A_{1}, H_{1}

### Question No.10

The **total number** of possible types of **GVF profiles** are :

- 9
- 11
- 12
- 15

### Question No.11

** dy/dx** is

**negative**in the following

**GVF profiles**:

- M
_{1}, S_{2}, A_{2} - M
_{2}, A_{2}, S_{3} - A
_{3}, A_{2}, M_{2} - M
_{2}, A_{2}, H_{2}

### Question No.12

If in a **GVF dy/dx** is

**positive**, then

**is :**

*dE*/*dx*- always positive
- negative for an adverse slope
- negative if
*y*>*y*_{c} - positive if
*y*>*y*_{c}

### Question No.13

In a channel the **gradient of the specific energy dE/dx** is equal to :

- \[{S_o} - {S_f}\]
- \[{S_f} - {S_o}\]
- \[{S_o} - {S_f} - \frac{{dy}}{{dx}}\]
- \[{S_o}(1 - F_n^2)\]

### Question No.14

In a **wide river** the depth of flow at a section is 3.0 m, S_{o} = 1 in 5000 and q = 3.0 m^{3}/s per meter width. If the **Chezy formula** with C = 70 is used, the **water surface slope** **relative** to the **bed** at the section is :

- −2.732 × 10
^{−4} - 1.366 × 10
^{−4} - 1.211 × 10
^{−5} - −6.234 × 10
^{−4}

### Question No.15

The **M _{3} profile** is indicated by the following inequality between the various depths :

- \[{y_o} > {y_c} > y\]
- \[y > {y_o} > {y_c}\]
- \[{y_c} > {y_o} > y\]
- \[y > {y_c} > {y_o}\]

### Question No.16

A **long prismatic** channel ends in an **abrupt drop**. If the flow in the channel far **upstream** of the drop is **subcritical**, the resulting GVF profile :

- starts from the critical depth at the drop and joins the normal depth asymptotically
- lies wholly below the critical depth line
- lies wholly above the normal depth line
- lies partly below and partly above the critical depth line

### Question No.17

When there is a **break in grade** due to a **mild slope A** changing into a **milder slope B**, the **GVF profile** produced is :

- M
_{3}curve on B - M
_{2}curve on B - M
_{1}curve on B - M
_{1}curve on A

### Question No.18

In a channel the **bed slope** changes from a **mild slope** to a **steep slope**. The resulting **GVF profiles** are :

- (M
_{1}, S_{2}) - (M
_{1}, S_{3}) - (M
_{2}, S_{2}) - (M
_{2}, S_{1})

### Question No.19

A **rectangular** channel has B = 20 m, n = 0.020 and S_{o} = 0.0004. If the **normal depth** is 1.0 m, a depth of 0.8 m in a **GVF** in this channel is a part of :

- M
_{1} - M
_{2} - M
_{3} - S
_{2}

### Question No.20

A **rectangular** channel has **uniform** flow at a normal depth of 0.50 m. The **discharge intensity** in the channel is estimated as 1.40 m^{3}/s/m. If an **abrupt drop** is provided at the **downstream end** of this channel, it will cause :

- M
_{2}type of GVF profile - S
_{2}type of GVF profile - No GVF profile upstream of the drop
- M
_{1}type of profile

### Question No.21

The flow will be in the **supercritical state** in the following types of **GVF profiles** :

- All S curves
- M
_{2} - A
_{3}, M_{3}, S_{2} - S
_{2}, M_{2}, S_{3}

### Question No.22

At the **transitional depth** :

*dy*/*dx*= ∞- the slope of the GVF profile is zero
*dy*/*dx*= −*S*_{o}- the slope of GVF profile is horizontal

After you have checked the **Open Channel Flow MCQ**, you can check the **model answers** for those MCQ on the following link :

Open Channel Flow MCQ - Gradually Varied Flow Theory - Set 1 (Model Answer)

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