10 Open Channel Flow

SY
1. Introduction

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
Q.4 A sluice gate used to control the flow in a
horizontal channel of unit width is shown in the
Q.1 A right-angled triangular channel symmetrical
figure.
in section about the vertical carries a discharge

(a) 0.3
(c) 0.5
(b) 0.4
(d) 0.6
EA
of 5 m3/s with a velocity of 1.25 m/s. What is
the approximate value of the Froude number of
the flow ?

[ESE : 2007]
d1 = 1.0 m
d2 = 0.2 m

1 2

Q.2 A person standing on the bank of a canal drops

It is obeserved that the depth of flow is 1.0 m
E
a stone on the water surface. He notices that
upstream of the gate, while the depth is 0.2 m
the disturbance on the water surface is not
downstream of the gate. Assuming a smooth
traveling upstream. This is because the flow in
flow transition across the sluice gate, i.e., without
D

the canal is
any energy loss, and the acceleration due to
(a) sub-critical (b) super-critical
gravity as 10 m/s2, the discharge (in m3/s, up
(c) steady (d) uniform
to two decimal places) passing under the sluice
[GA TE : 2008]
[GATE
gate is __________.
A

Q.3 A steady flow occurs in an open channel with [GA TE : 2017]

[GATE
lateral inflow of q m3/s per unit width as shown
in the figure. The mass conservation equation is
3
qm /s/m
M

Q.5 Velocity distribution in a rectangular channel of

3
Qm /s + x
width ‘B’ and depth of flow y0 is v = k y .
Calculate average velocity, α and β value for
∂q ∂Q
(a) =0 (b) =0 the cross section.
∂x ∂x
∂Q Q.6 While measuring the discharge in the small
(c) –q=0 (d) ∂Q + q = 0
∂x ∂x channel, it was found that the depth of flow
[GA TE : 2004]
[GATE increases at the rate of 0.2 m/hr. If the dischage

www.madeeasypublications.org © Copyright
 Workbook 65

at downstream section was 10 m3/sec and Q.3 A hydraulically efficient trapezoidal section of
surface width of stream was 20 m, estimate the open channel flow carries water at the optimal
discharge at the section 2 km upstream. depth of 0.6 m. Chezy coefficient is 75 and bed

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
slope is 1 in 250. What is the discharge through
Q.7 Show that in an unsteady flow in a prismatic
the channel?
open channel the continuity equation is given
(a) 1.44 m3/s (b) 1.62 m3/s
by (c) 1.92 m3/s (d) 2.24 m3/s
[ESE : 2006]
T
Q.4 A rectangular channel 3 m wide is laid on a slope

SY
dy of 0.0002. When the depth of flow in the channel
y A is 1.5 m what is the average boundary shear
stress (nearly) ?
(a) 0.3 N/m2 (b) 0.15 N/m2
(c) 3.0 N/m2 (d) 1.5 N/m2
∂Q ∂y
+T =0 [ESE : 2007]
∂x ∂t
where, T = Top width of channel
Q = Discharge at any instant

2. Uniform Flow
EA Q.5 When discussing most efficient section of flow
into open channels, what is the perimeter P as
a proportion of depth of flow h (i.e., P/h) for
(i) a triangular section, and (ii) a trapezoidal
section, respectively?
(a) 2.25, 2.83 (b) 2.25, 3.15
(c) 2.83, 3.15 (d) 2.83, 3.46
[ESE : 2008]
E
Q.6 For a rectangular channel section, Match List-I
Q.1 The Chezy’s coefficient C is related to Darcy- (Geometrical elements) with List-II (Proportions
Weisbach friction factor ‘f’ as for hydraulically efficient section) and select the
D

correct answer using the codes given below the

(a) C = (g / 8f ) (b) C = (8g / f 1/4)
lists:
(c) C = (8g / f ) (d) C = (f / 8g) List-I List-II
A. Top width 1. ye /2
A

[ESE : 2002] B. Perimeter 2. ye

Q.2 A triangular irrigation lined canal carries a C. Hydraulic Radius 3. 2 ye
D. Hydraulic Depth 4. 4 ye
1 y e is the flow depth corresponding to
discharge of 25m3/s at bed slope = . If
M

6000 hydraulically efficient section.

the side slopes of the canal are 1:1 and Codes:
Manning’s coefficient is 0.018, the central depth A B C D
of flow is equal to (a) 2 4 1 3
(a) 2.98 m (b) 3.62 m (b) 3 1 4 2
(c) 4.91 m (d) 5.61 m (c) 3 4 1 2
[GA TE : 2005] (d) 3 4 2 1
[GATE
[GA
[GATETE : 2010]

© Copyright www.madeeasypublications.org
 •
66 Civil Engineering Fluid Mechanics including Hydraulic Machines

Q.7 Best s i d e s l o p e f o r m o s t e c o n o m i c a l
trapezoidal section in open channel flow,
wherein side slopes are defined by: X

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
horizontal to 1 vertical, is when X equals
(a) 0.404 (b) 0.500
Q.12 A hydraulically most efficient trapezoidal
(c) 0.577 (d) 0.673
channel section carries water at the optimal
[ESE : 2011]
depth of 0.72 m, Chezy coefficient is 75 and
Q.8 For a hydraulically efficient rectangular channel the longitudinal slope is 1 in 2500. The discharge
of bed width 4.0 m, the depth of flow is through the channel will be _____ m3/s.

SY
(a) 4 m (b) 0.5 m
(c) 1 m (d) 2 m
[ESE : 2012]

Q.9 A trapezoidal channel is 10.0 m wide at the base

Q.13 A most efficient trapezoidal section is required
and has a side slope of 4 horizontal to 3 vertical.
to keep a maximum discharge of 21.5 m3/sec.
The bed slope is 0.002. The channel is lined
with smooth concrete (Manning’s n = 0.012). The
hydraulic radius (in m) for a depth of flow of
3.0 m is
(a) 20.0
(c) 3.0
(b) 3.5
(d) 2.1
[GA
[GATE
EA
TE : 2012]
If bed slope, S0 =
1
2500
and Chezy’s constant,

C = 70, determine the value of Manning’s

roughness coefficient (n) taking velocity of flow
as obtained for the channel by Chezy’s equation.

Q.14 Design a most efficient trapezoidal channel for

Q.10 A rectangular open channel of width 5.0 m is conveying a discharge of 100 m3/sec, given
E
carrying a discharge of 100 m3/s. The Froude Manning’s, n =0.015 and channel bottom slope,
number of the flow is 0.8. The depth of flow (in m) 1
in the channel is S0 = . Assume a free board of 10% of
2500
D

(a) 4 (b) 5 depth of flow. Compute Froude′’s number and

(c) 16 (d) 20 sketch the cross section.
[GA
[GATETE : 2012]
Q.15 A trapezoidal channel with side slope 2
Q.11 A circular pipe has a diameter of 1 m, bed horizontal to 1 vertical is carrying a discharge
A

slope of 1 in 1000, and Manning’s roughness 1

of 25 m3/sec. Given, S0 = and Chezy’s
coefficient equal to 0.01. It may be treated as 2500
an open channel flow when it is flowing just full, C = 45. Design the channel.
i.e., the water level just touches the crest. The
M

discharge in this condition is denoted by Qfull. 3. Energy Depth Relationship

Similarly, the discharge when the pipe is flowing
half-full, i.e., with a flow depth of 0.5 m, is
Qfull
denoted by Qhalf. The ratio is
Q half
(a) 1 (b) 2 Q.1 Water flow in a channel at a Froude number
(c) 2 (d) 4 greater than 1. If the channel is contracted, then
[GATE : 2015]
[GATE in the contracted section

www.madeeasypublications.org © Copyright
 Workbook 67

(a) both y and v increase Q.6 A hump is to be provided on the channel bed.
(b) both y and v decreases The maximum height of the hump without
(c) y increases and v decreases affecting the upstream flow condition is

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
(d) y decreases and v increases (a) 0.50 m (b) 0.40 m
[CSE : 2002] (c) 0.30 m (d) 0.20 m

Q.2 Consider the following statements: Q.7 The channel width is to be contracted. The
A constant discharge flows in a channel across minimum width to which the channel can be
which a hump of moderate height has been contracted without affecting the upstream flow
constructed. Then, along the flow direction condition is

SY
1. depth of flow reduces (a) 3.0 m (b) 3.8 m
2. specific energy remains unchanged (c) 4.1 m (d) 4.5 m
3. Froude number reduces [GATE : 2008]
[GATE
4. critical depth remains unchanged Q.8 For a given discharge, the critical flow depth in
Which of these statements is/are correct? an open channel depends on
(a) 1 only (b) 1 and 4 (a) channel geometry only

Q.3
(c) 2 and 3 (d) 2, 3 and 4

A rectangular channel is 6 m wide and

EA
[CSE : 2003]

discharges 30 m3s–1. The upstream depth is

2.0 m, acceleration due to gravity is 10 ms–2.
Then, what is the specific energy (approximate)?
(b) channel geometry and bed slope
(c) channel geometry, bed slope and
roughness
(d) channel geometry, bed slope, roughness
and Reynolds number
[GA
[GATETE : 2011]
(a) 2.5 (b) 0.3 Q.9 A rectangular channel carries a uniform flow with
(c) 2.3 (d) None of the above a Froude number of 2.83. The ratio of critical
E
[ESE : 2007] depth to normal depth of this flow is:
Q.4 For a smooth hump in a sub-critical flow to (a) 1.68 (b) 2.83
function as a broad crested weir, the height ΔZ (c) 2.00 (d) 4.75
D

of the hump above the bed must satisfy which [ESE : 2013]
one of the following (Neglect friction effects)? Q.10 A triangular open channel has a vortex angle of
(a) Δ Z ≥ (E1 – yc) 90° and carries flow at a critical depth of 0.3 m.
(b) Δ Z ≥ (E1 – Ec)
A

The discharge in the channel is

(c) Δ Z ≤ (E1 – yc) (a) 0.41 m3/s (b) 0.11 m3/s
(d) Δ Z ≤ (E1 – Ec) (c) 0.21 m3/s (d) 031 m3/s
(E1 = Specific head upstream of the hump, [ESE : 2014]
M

Ec = Specific head at the critical depth yc)

[ESE : 2007]
Data for Q.5, Q.6 and Q.7 ar e given below
are below.. Solve
the problems and choose correct answers.
A rectangular channel 6.0 m wide carries a discharge
Q.11 A rectangular channel is 3 m wide and carries a
of 16.0 m3/s under uniform flow condition with normal
flow of 2.7 m 3 /s at a depth of 0.9 m. A
depth of 1.60 m. Manning’s ‘n’ is 0.015.
contraction of the channel width is proposed at
Q.5 The longitudinal slope of the channel is a certain section. The smallest allowable
(a) 0.000585 (b) 0.000485 contracted width that will not affect the upstream
(c) 0.000385 (d) 0.000285 flow conditions is _________ m.

© Copyright www.madeeasypublications.org
 •
68 Civil Engineering Fluid Mechanics including Hydraulic Machines

Q.12 For a constant specific energy of 1.5 N-m/N,

2y12y22
the maximum discharge that may occur in a yc3 =
y1 + y2
parabolic channel 5.0 m wide is _____m3/s.

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
Q.13 A 1 m wide rectangular channel carries a Q.18 Prove that for rectangular channel
discharge of 2 m3/s. The specific energy-depth y12 + y 22 + y1y 2
E=
diagram is prepared for the channel. It is y1 + y2
observed in this diagram that corresponding to
a particular specific energy, the subcritical depth where y 1 and y 2 are alternate depths
is twice the supercritical depth. The subcritical corresponding to specific energy E.

SY
depth (in meters, up to two decimal places) is
Q.19 If F1 and F2 are Froude numbers for alternate
equal to ___________.
depths y1 and y2 respectively, then prove that
[GA TE : 2017]
[GATE
for a
Q.14 For discharge measurement, the width of a
(a) Rectangular channel :
rectangular channel is reduced gradually from
2/3
3 m to 2 m and the floor is raised by 0.3 m at a ⎛ F2 ⎞ 2 + F22
given section. When the approaching depth of
EA
flow is 2 m, the rate of flow indicated by a drop
of 0.15 m in the water surface elevation at the
contracted section is _____ m3/s.
⎜⎝ F ⎟⎠
1

(b) Triangular channel :

⎛ F2 ⎞
⎜⎝ F ⎟⎠
1
2/ 5
=

=
2 + F12

4 + F22
4 + F12

Q.20 A rectangular channel is 3 m wide and carries a

flow of 1.85 m3/sec at a depth of 0.5 m. Find
E
the greatest allowable contraction in the width
Q.15 An expansion in a horizontal rectangular channel so that upstream flow is not affected.
takes place from a width of 2 m to 3 m. Depth of
Q.21 A rectangular channel 2.4 m wide carries a
D

flow for a discharge of 7.2 m3/sec are 1.2 m

uniform flow of water at a rate of 7 m3/s at a
and 1.4 m in the narrower and wider section
depth of 1.5 m. If there is rise of 15 cm in the
respectively. Assume Kinetic Energy correction bed, calculate the change in water level. What
factor (α) to have value of 1.05 and 1.15 at the is the maximum rise in bed that will be
A

inlet and outlet of transistion. Estimate the permissible so that there will be no change in
energy loss (EL). upstream depth of flow?
Q.16 For given shape of channel section, estimate
the discharge and specific energy
M

corresponding to a critical depth of 1.4 m.

0.5 T1. Water flows in a wide rectangular channel at a

1
depth of 1.20 m and a velocity of 2.4 m/sec.
What would be the effect of a local rise in the
2.4 m
channel bed of 0.60 m on the water surface?
[Ans. Depth of upstream surface will increase]
Q.17 If y1 and y2 are alternate depths in a rectangular
T2. A trapezoidal channel with a base width of
channel and yc is critical depth, then prove that
6 m and side slopes of 2H :1V carries a flow of

www.madeeasypublications.org © Copyright
 Workbook 69

60 m3/sec at a depth of 2.5 m. There is a smooth Q.3 What Gradually Varied Flow profile exists at this
transition to a rectangular section 6 m wide section?
accompanied by a gradual lowering of the (a) M2 (b) M3

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
channel bed by 0.6 m. Find the depth of water (c) S2 (d) S3
within the rectangular section. What is the [GA
[GATE TE : 2003]
minimum amount by which the bed must be
Q.4 At what distance from this section the flow depth
lowered for the upstream flow to be possible as
will be 0.9 m? (Use the direct step method
specified?
employing a single step.)
[Ans. 2.572 m, 0.528 m]
(a) 65 m downstream(b) 50 m downstream

SY
(c) 50 m upstream (d) 65 m upstream
4. Gradually Varied Flow [GA
[GATETE : 2003]

Q.5 In a reach of open channel flow, with q = 2 m2/s,

depth of flow at section A is 1.5 m and at section
B, 1.6 m. The difference in specific energies at
two sections can be correspondingly taken as
Q.1

EA
A hydraulic jump is always needed in case of
(a) an A2 profile followed by an A3 profile
(b) an A3 profile followed by an A2 profile
(c) an H2 profile followed by an M2 profile
(d) an M1 profile followed by an M3 profile
[ESE : 2001]
0.09 m. The bed slope is 1 in 2000. The mean
energy slope between the sections is given as
0.003. What is the length of reach AB?
(a) 54 m with A on the upstream
(b) 54 m with B on the upstream
(c) 36 m with A on the upstream
Q.2 A prismatic channel is laid out as shown below (d) 36 m with B on the upstream
with two stretches, one with slope less than [ESE : 2004]
E
critical followed by another stretch with slope
more than critical. At the end of second stretch Q.6 Match List-I (Type of curve) with List-II (Flow
is built a weir of considerable height across the condition) and select the correct answer using
D

flow. The type of flow profiles along the direction the codes given below the lists:
of flow will be List-I List-II
A. M1 1. Slope upward in the direction
of flow
A

S < Scr B. H3 2. Back water profile

S> C. S2 3. Hydraulic jump occurs
S
cr
D. A2 4. Hydraulic drop occurs
(a) S1, M2 then M1 (b) M2, S2 then S1 Codes:
M

(c) S2, M2 then C1 (d) M1, S2 then S3 A B C D

[CSE : 2002] (a) 1 3 4 2
(b) 2 4 3 1
Data for Q.3 and Q.4 ar e given below
are below.. Solve the
(c) 1 4 3 2
problems and choose correct answers.
(d) 2 3 4 1
A very wide rectangular channel carries a discharge
[ESE : 2005]
of 8m3/s per m width. The channel has a bed slope of
0.004 and Manning’s roughness coefficient, Q.7 Which of the following equations are used for
n = 0.015. At a certain section of the channel, the flow the derivation of the differential equation for water
depth is 1m. surface profile in open channel flow?

© Copyright www.madeeasypublications.org
 •
70 Civil Engineering Fluid Mechanics including Hydraulic Machines

1. Continuity Equation
2. Energy Equation
3. Momentum Equation

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
Select the correct answer using the codes given
below : Q.11 A short reach of a 2 m wide rectangular open
(a) 1, 2 and 3 channel has its bed level rising in the direction
(a) Only 1 and 3 of flow at a slope of 1 in 10000. It carries a
(c) Only 1 and 2 discharge of 4 m3/s and its Manning’s roughness
(d) Only 2 and 3 coefficient is 0.01. The flow in this reach is

SY
[ESE : 2006, 2013] gradually varying. At a certain section in this
reach, the depth of flow was measured as
Q.8 In connection with a gradually varied flow with
0.5 m. The rate of change of the water depth
notations y0 = normal depth, yc = critical depth
and y = depth in the gradually varied flow, match dy
with distance, , at this section is __________
List-I with List-II and select the correct answer dx
using the codes given below the lists: (use g = 10 m/s2).
List-I
A. yc > y0 > y
B. y0 > y > yc
C. y > yc > y0
D. y > y0 > yc
Codes:
List-II
1. M1
2. S3
3. M2
4. S1
EA [GATE : 2015]
[GATE

Q.12 At the foot of a spillway, water flows at a depth

of 23 cm with a velocity of 8.1 m/s, as shown
in the figure.

A B C D
(a) 4 1 2 3
E
(b) 2 3 4 1
(c) 4 3 2 1
Hydraulic
(d) 2 1 4 3 Spillway M-3 Profile Jump
D

23 cm y1 = ?
[ESE : 2007]

Q.9 The flow rate in a wide rectangular open channel

is 2.0 m3/s per metre width. The channel bed
A

slope is 0.002. The Manning’s roughness The flow enters as an M-3 profile in the long
coefficient is 0.012. The slope of the channel is wide rectangular channel with bed slope =
classified as 1
(a) Critical (b) Horizontal and Manning's n = 0.015. A hydraulic
1800
M

(c) Mild (d) Steep

jump is formed at a certain distance from the
Q.10 A mild-sloped channel is followed by a steep- foot of the spillway. Assume the acceleration
sloped channel. The profiles of gradually varied due to gravity, g = 9.81 m/s2. Just before the
flow in the channel are hydraulic jump, the depth of flow y1 (in m,
(a) M3, S2 (b) M3, S3 round off to 2 decimal places) is ________.
(c) M2, S1 (d) M2, S2 [GATE
[GA TE : 2019]
[GATE : 2010]
[GATE

www.madeeasypublications.org © Copyright
 Workbook 71

(a) y1 and y3 (b) y1 and y4

(c) y2 and y3 (d) y2 and y4
[CSE : 2004]

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
Q.13 A rectangular section 7.5 m wide has a uniform Q.2 A partially open sluice gate discharges water
depth of flow of 2 m and has a bed slope of into a rectangular channel. The tail water depth
1/3000. If due to weir construction at downstream in the channel is 3 m and Froude number
end of the channel, water surface at that section
1
is raised by 0.75 m, determine the water surface is . If a free hydraulic jump is to be formed
2 2
slope at that section.

SY
at downstream of the sluice gate after the vena
[Given, Manning’s n = 0.02]
contracta of the jet coming out from the sluice
Q.14 Determine the length of back water curve caused gate, the sluice gate opening should be
by an afflux of 1.5 m in the rectangular channel (coefficient of contraction Cc = 0.9)
of width 50 m and depth of flow 2 m. [Given, (a) 0.3 m (b) 0.4 m
1 (c) 0.69 m (d) 0.9 m
bed slope S0= , Manning’s n = 0.03] [GA
[GATETE : 2005]
2000

EA
Q.15 Water flows in a triangular channel of side slope.
1H:1V and longitudinal slope is 0.001. Determine
whether the channel is mild, steep or critical,
when discharge of 0.2 m3/sec flows through it.
Q.3 The sequent depth ratio in a hydraulic jump
formed in a horizontal rectangular channel is
16.48. The flow is supercritical. What is the value
of the Froude number of flow?
(a) 4.0 (b) 8.0
[Given, Manning’s n = 0.015]
(c) 12.0 (d) 120.0
[CSE : 2005]
E
5. Rapidly Varied Flow
Q.4 A hydraulic jump occurs in a rectangular,
horizontal, frictionless channel. What would be
the pre-jump depth if the discharge per unit width
D

is 2 m3/s/m and the energy loss is 1m?

(a) 0.2 m (b) 0.3 m
(c) 0.8 m (d) 0.9 m
Q.1 For a given discharge in a prismatic channel,
[GATE : 2006]
[GATE
A

specific force and specific energy curves have

been drawn (see figure). The hydraulic jump Q.5 A sluice gate discharges water into a horizontal
can take place with pre and post jump depths rectangular channel with a velocity of 12 m/s
as and depth of flow of 1 m. What is the depth of
M

flow after the hydraulic jump?

Depth vs. specific force curve
Depth Depth vs. specific energy curve (a) 6.42 m (b) 5.84 m
(c) 4.94 m (d) 2.21 m
y4 [ESE : 2009]
y3
Q.6 A spillway discharges flood flow at a rate of
9 m3/s per metre width. If the depth of flow on
yC
the horizontal apron at the toe of the spillway is
y2 46 cm, the tail water depth needed to form a
y1
hydraulic jump is approximately given by which
of the following options?

© Copyright www.madeeasypublications.org
 •
72 Civil Engineering Fluid Mechanics including Hydraulic Machines

(a) 2.54 m (b) 4.90 m

(c) 5.77 m (d) 6.23 m
[GATE : 2011]
[GATE

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
Q.7 At a hydraulic jump, the depths at the two sides
are 0.3 m and 1.4. The head loss in the jump is Q.11 The conjugate depths at a location in a horizontal
nearly rectangular channel, 4 m wide, are 0.2 m and
(a) 1.0 m (b) 0.95 m 1.0 m. The discharge in the channel is________
(c) 0.79 m (d) 0.45 m m3/sec.
[ESE : 2014] [GA
[GATETE : 1991]

SY
Q.8 A hydraulic jump takes place in a frictionless Q.12 The discharge from a spillway on a horizontal
rectangular channel. The pre-jump depth is yp. floor is 8 cumecs per meter width. If the depth
The alternate and sequent depths corresponding before the jump of 50 cm, the depth after the
to yp are ya and ys respectively. The correct jump in metres will be _______.
relationship among yp, ya and ys is [GA
[GATETE : 1991]
(a) ya < ys < yp

Q.9
(b) yp < ys < ya
(c) yp < ys = ya
(d) ya = ys = yp

Asser
[GA
EA
TE : 2015]
[GATE

tion (A) : At the critical state of flow, the

Assertion
Q.13 A hydraulic jump occurs in a rectangular channel.
The energy loss and Froude number after the
jump are 9.0 m and 0.12 respectively. The
discharge intensity is _____ m3/s/m

Q.14 The relatively rapid flow of water in a horizontal

rectangular channel can suddenly “jump” to a
specific force is a minimum for the given
higher level (an obstruction downstream may
discharge.
E
be the cause). This is called a hydraulic jump.
Reason (R) : For a minimum value of specific The situation is shown in the figure below. The
force, the first derivative of force with respect higher depth at downstream is ________ m.
to depth should be unity.
D

[Assume uniform flow]

Of these statements
y2
(a) Both A and R are individually true and R is
y1 = 50 cm Jump
correct explanation of A
A

(b) Both A and R are individually true but R is

not correct explanation of A Water

(c) A is true but R is false V1 = 5 m/s V2

(d) A is false but R is true

M

[ESE : 2005]

Q.10 Hydraulic jump forms in a horizontal rectangular Q.15 A hydraulic jump is formed in a 2 m wide
channel carrying a unit discharge of 1.019 rectangular channel which is horizontal and
m3/sec/m at a depth of 10.19 mm. This jump frictionless. The post-jump depth and velocity
is classified as are 0.8 m and 1 m/s, respectively. The pre-
(a) Weak jump (b) Oscillating jump jump velocity is _________ m/s.
(c) Steady jump (d) Strong jump (Use g = 10 m/s2)
[ESE : 2017] [GA TE : 2015]
[GATE

www.madeeasypublications.org © Copyright
 Workbook 73

(a) 16 m/s (b) 13.6 m/s

(c) 2.4 m/s (d) 1.6 m/s
[ESE : 2012]

© Copyright: Subject matter to MADE EASY Publications, New Delhi. No part of this book may be reproduced or utilised in any form without the written permission.
Q.2 Assertion (A ) : Surges can be positive or
Q.16 In a hydraulic jump occuring in a rectangular negative.
channel, discharge per unit width is 2.5 m2/s
Reason (R) : Negative surges may occur when
and depth before the jump is 0.25 m. Calculate
a gate at the head of a channel is suddenly
the sequent depth and energy loss?
opened or when a gate at tail end of a channel

SY
Q.17 In a Hydraulic Jump occuring in a horizontal is suddenly closed.
rectangular channel, Froude number before the (a) Both A and R are individually true and R is
jump is 10 & energy loss is 3.2 m. Calculate correct explanation of A
sequent depths. (b) Both A and R are individually true but R is
not correct explanation of A
(c) A is true but R is false
(d) A is false but R is true

T1. EA
A hydraulic jump occurs in a wide, rectangular
channel with initial and sequent depths of
0.5 m and 2.0 m respectively. Calculate
(i) the discharge in m3/s per metre width
[ESE : 2000]

(ii) the possible critical depth for this discharge Q.3 A bore is a hydraulic jump which propagates
(iii) the energy loss in the jump, (in metres head) upstream into a still or slower moving fluid as
E
[Ans. (i) 3.5 m2/sec, (i) 1.077 m, (iii) 0.84 m]
shown in the figure below. Assume that the still
T2. A spillway has its crest at elevation of +144.0 m water is 2 m deep and the water behind the
and a horizontal apron at an elevation of bore is 3 m deep. The induced water velocity
D

+105.0 m on the downstream side. Find the tail will be ________ m/s.
water elevation required to form a hydraulic jump
when the elevation of energy line above the crest
is +146.5 m. The Cd for the flow can be assumed
A

as 0.73. The energy loss over the spillway face y2

y1
may be neglected. (Assume Cv = 0.9) V2 V1
[Ans. 6.46 m]
M

6. Surges Q.4 The depth and velocity of flow in a rectangular

channel are 0.9 m and 1.5 m/s respectively. If a
gate at the downstream end of the channel is
abruptly closed then the height of resulting
surge will be _____ m.
Q.1 The velocity with which an elementary surge
„„„„
wave can travel upstream in a channel with
depth y = 1.6 m and velocity V = 2.4 m/s is
(Take g = 10 m/s2)

© Copyright www.madeeasypublications.org
 0.1
Laminar Critical
→
0.09 flow zone
0.07
0.08
0.06

0.05
0.07
0.045
0.04
0.06 0.035
0.03
0.055
0.025
0.05
0.02
0.0175
0.045
64 0.015

2
f=
Re

hf
0.0125

L V
0.04

D 2g
0.01

0.035 0.008

0.006
0.03
0.004
D
k

0.003
0.025
0.002
0.0015

0.02 0.001

Darcy-Weishbach friction factor, f =

0.0008
Relative roughness s (ks in mm, D in mm)

0.018
0.0006

0.016 0.0004
Smooth pipes

0.014
0.0002

0.012 0.0001

ks 0.00005
= 0.000005
0.01 D

0.009 0.00002
ks
= 0.000001
D
0.008 0.00001
6 7 8 3 2 3 4 5 6 7 8 4 2 3 4 5 6 7 8 5 2 3 4 5 6 7 8 6 2 3 4 5 6 7 8 7 2 3 4 5 6 7 8 8
10 10 10 10 10 10
VD 2
Reynolds number Re = (V in m/s, D in m, ν in m /s)
ν

Moody Diagram