Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Hydrodynamic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Turbulence in Open Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Sediment Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5 Bedload Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6 Suspended-Load Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7 Total-Load Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
8 Bedforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
9 Fluvial Processes: Meandering and Braiding . . . . . . . . . . . . . . . . . . . . . 231
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
10 Scour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
11 Dimensional Analysis and Similitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
xv
@seismicisolation
@seismicisolation
,About the Authors
Subhasish Dey is a hydraulician and an educator. He is internationally known for
his research and is acclaimed for his contributions to developing theories and solu-
tion methodologies for various problems in hydrodynamics and sediment transport.
He currently holds the position of distinguished professor of Indian Institute of
Technology Jodhpur.
Dey’s areas of research interest include applied hydrodynamics, turbulence, and
sediment transport, in which he has about 40 years of experience. He was conferred
with the Hans Albert Einstein Award from the American Society of Civil Engineers
in 2022.
Sk Zeeshan Ali is a researcher and an academician. Currently, he is an assistant
professor in the department of civil engineering at the Indian Institute of Technology
Hyderabad, where he teaches fluid mechanics, hydraulic engineering, open-channel
flow, and sediment transport.
Ali contributes to the field of classical and applied hydrodynamics. He is one
of the leading collaborators of the first author of this book. His areas of research
interest include boundary layer flows, turbulent flows, scaling laws of turbulence,
fluvial hydraulics, sediment transport, and morphodynamic instabilities.
xvii
@seismicisolation
@seismicisolation
,Chapter 1
Introduction
Problem 1.1 The longest, intermediate, and shortest lengths of an ellipsoidal sedi-
ment particle are 2, 1.5, and 0.8 mm, respectively. Determine the nominal diameter
d n , area diameter d a , sieve diameter d, phi () unit, sphericity S c , Corey shape factor
S p , shape parameter S sp , volume coefficient k v , and surface coefficient k c . Take the
surface area of the ellipsoidal particle with a1 , a2 , and a3 being the longest, interme-
diate, and shortest lengths as S = π{[(a1 a2 )q + (a2 a3 )q + (a1 a3 )q ]/3}1/q with q =
1.6.
Solution
The volume V of an ellipsoidal sediment particle is
π
V = a1 a2 a3 (S1.1)
6
where a1 , a2 , and a3 are the longest, intermediate, and shortest lengths. With a1 =
2 mm, a2 = 1.5 mm, and a3 = 0.8 mm,
π
V = × 2 × 1.5 × 0.8 = 1.26 mm3 .
6
The nominal diameter d n is
1/3
6V
dn = ⇐ Eq. (1.6)
π
1/3
6 × 1.26
⇒ dn = = 1.34 mm.
π
Note Figure, table, and equation numbers devoid of the letter ‘S’ refer to those in the companion
book Dey (2024).
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 1
S. Dey and S. Z. Ali, Fluvial Hydrodynamics - Solutions Manual, GeoPlanet: Earth and
Planetary Sciences, https://doi.org/10.1007/978-3-031-25737-7_1
@seismicisolation
@seismicisolation
, 2 1 Introduction
The surface area of the particle is
1/q
(a1 a2 )q + (a2 a3 )q + (a1 a3 )q
S=π (S1.2)
3
With q = 1.6,
1/1.6
(2 × 1.5)1.6 + (1.5 × 0.8)1.6 + (2 × 0.8)1.6
S=π = 6.35 mm2 .
3
The area diameter d a is
0.5
S
da = ⇐ Eq. (1.7)
π
6.35 0.5
⇒ da = = 1.42 mm.
π
For sediment size (0.2–20 mm) of natural streambeds, the sieve diameter d is
approximately 0.9d n . Therefore, d = 0.9 × 1.34 = 1.2 mm.
The unit is
log10 d
= − log2 d = − ⇐ Eq. (1.8)
log10 2
where d is in mm. For d = 1.2 mm,
log10 1.2
=− = −0.26.
log10 2
The sphericity is defined as the ratio of the surface area of a sphere of the same
volume as that of a given sediment particle to the actual surface area of the particle.
πdn2 π × 1.342
Sc = = = 0.89.
S 6.35
The sphericity is also
1/3 1/3
V a2 a3 dn
Sc = = = (S1.3)
Vc a12 a1
where V c is the volume of circumscribing sphere (= πa13 /6).
1.34
Sc = = 0.67.
2
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@seismicisolation
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 Hydrodynamic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Turbulence in Open Channel Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Sediment Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5 Bedload Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
6 Suspended-Load Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7 Total-Load Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
8 Bedforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
9 Fluvial Processes: Meandering and Braiding . . . . . . . . . . . . . . . . . . . . . 231
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
10 Scour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
11 Dimensional Analysis and Similitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
xv
@seismicisolation
@seismicisolation
,About the Authors
Subhasish Dey is a hydraulician and an educator. He is internationally known for
his research and is acclaimed for his contributions to developing theories and solu-
tion methodologies for various problems in hydrodynamics and sediment transport.
He currently holds the position of distinguished professor of Indian Institute of
Technology Jodhpur.
Dey’s areas of research interest include applied hydrodynamics, turbulence, and
sediment transport, in which he has about 40 years of experience. He was conferred
with the Hans Albert Einstein Award from the American Society of Civil Engineers
in 2022.
Sk Zeeshan Ali is a researcher and an academician. Currently, he is an assistant
professor in the department of civil engineering at the Indian Institute of Technology
Hyderabad, where he teaches fluid mechanics, hydraulic engineering, open-channel
flow, and sediment transport.
Ali contributes to the field of classical and applied hydrodynamics. He is one
of the leading collaborators of the first author of this book. His areas of research
interest include boundary layer flows, turbulent flows, scaling laws of turbulence,
fluvial hydraulics, sediment transport, and morphodynamic instabilities.
xvii
@seismicisolation
@seismicisolation
,Chapter 1
Introduction
Problem 1.1 The longest, intermediate, and shortest lengths of an ellipsoidal sedi-
ment particle are 2, 1.5, and 0.8 mm, respectively. Determine the nominal diameter
d n , area diameter d a , sieve diameter d, phi () unit, sphericity S c , Corey shape factor
S p , shape parameter S sp , volume coefficient k v , and surface coefficient k c . Take the
surface area of the ellipsoidal particle with a1 , a2 , and a3 being the longest, interme-
diate, and shortest lengths as S = π{[(a1 a2 )q + (a2 a3 )q + (a1 a3 )q ]/3}1/q with q =
1.6.
Solution
The volume V of an ellipsoidal sediment particle is
π
V = a1 a2 a3 (S1.1)
6
where a1 , a2 , and a3 are the longest, intermediate, and shortest lengths. With a1 =
2 mm, a2 = 1.5 mm, and a3 = 0.8 mm,
π
V = × 2 × 1.5 × 0.8 = 1.26 mm3 .
6
The nominal diameter d n is
1/3
6V
dn = ⇐ Eq. (1.6)
π
1/3
6 × 1.26
⇒ dn = = 1.34 mm.
π
Note Figure, table, and equation numbers devoid of the letter ‘S’ refer to those in the companion
book Dey (2024).
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 1
S. Dey and S. Z. Ali, Fluvial Hydrodynamics - Solutions Manual, GeoPlanet: Earth and
Planetary Sciences, https://doi.org/10.1007/978-3-031-25737-7_1
@seismicisolation
@seismicisolation
, 2 1 Introduction
The surface area of the particle is
1/q
(a1 a2 )q + (a2 a3 )q + (a1 a3 )q
S=π (S1.2)
3
With q = 1.6,
1/1.6
(2 × 1.5)1.6 + (1.5 × 0.8)1.6 + (2 × 0.8)1.6
S=π = 6.35 mm2 .
3
The area diameter d a is
0.5
S
da = ⇐ Eq. (1.7)
π
6.35 0.5
⇒ da = = 1.42 mm.
π
For sediment size (0.2–20 mm) of natural streambeds, the sieve diameter d is
approximately 0.9d n . Therefore, d = 0.9 × 1.34 = 1.2 mm.
The unit is
log10 d
= − log2 d = − ⇐ Eq. (1.8)
log10 2
where d is in mm. For d = 1.2 mm,
log10 1.2
=− = −0.26.
log10 2
The sphericity is defined as the ratio of the surface area of a sphere of the same
volume as that of a given sediment particle to the actual surface area of the particle.
πdn2 π × 1.342
Sc = = = 0.89.
S 6.35
The sphericity is also
1/3 1/3
V a2 a3 dn
Sc = = = (S1.3)
Vc a12 a1
where V c is the volume of circumscribing sphere (= πa13 /6).
1.34
Sc = = 0.67.
2
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@seismicisolation
