Formula Sheets: Open Channel Flow | Fluid Mechanics for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


Open Channel Flow F ormula Sheet for GA TE
Civil Engineering
Fluid Mechanics: Open Channel Flow
1. Basic Concepts
• Hydr aulic Radius (R ) :
R =
A
P
whereA = cross-sectional area,P = wetted perimeter .
• Hydr aulic Depth (D ) :
D =
A
T
whereT = top width of the channel.
2. Types of Flow
• Froude Number (Fr ) : Determines flow regime (subcritical, critical, supercrit-
ical)
Fr =
V
v
gD
whereV = velocity ,g = gr avitational acceler ation,D = h ydr aulic depth.
– Subcritical: Fr< 1
– Critical: Fr = 1
– Supercritical: Fr> 1
• Reynolds Number (Re ) :
Re =
?VR
µ
=
VR
?
where? = density ,µ = dynamic viscosity ,? = kinematic viscosity .
1
Page 2


Open Channel Flow F ormula Sheet for GA TE
Civil Engineering
Fluid Mechanics: Open Channel Flow
1. Basic Concepts
• Hydr aulic Radius (R ) :
R =
A
P
whereA = cross-sectional area,P = wetted perimeter .
• Hydr aulic Depth (D ) :
D =
A
T
whereT = top width of the channel.
2. Types of Flow
• Froude Number (Fr ) : Determines flow regime (subcritical, critical, supercrit-
ical)
Fr =
V
v
gD
whereV = velocity ,g = gr avitational acceler ation,D = h ydr aulic depth.
– Subcritical: Fr< 1
– Critical: Fr = 1
– Supercritical: Fr> 1
• Reynolds Number (Re ) :
Re =
?VR
µ
=
VR
?
where? = density ,µ = dynamic viscosity ,? = kinematic viscosity .
1
3. Manning’ s Equation
• V elocity:
V =
1
n
R
2/3
S
1/2
where n = Manning’ s roughness coefficient, S = slope of energy gr ade line or
bed slope (for uniform flow).
• Dis charge:
Q =
1
n
AR
2/3
S
1/2
4. Chezy’ s F ormula
• V elocity:
V =C
v
RS
whereC = Chezy’ s coefficient.
• Relation with Manning’ sn :
C =
1
n
R
1/6
5. Specific Energy
• Specific energy ( E ):
E =y+
V
2
2g
wherey = flow depth, V = velocity .
• Critical depth (y
c
): Occurs whenE is minimum.
Fr =1 =?
Q
2
gA
2
=
A
T
F or rectangular channels:
y
c
=
(
q
2
g
)
1/3
whereq =Q/B ,B = channel width.
6. Hydr aulic Jump
• Conjugate depths (y
1
,y
2
) for rectangular channels:
y
2
=
y
1
2
(
v
1+8Fr
2
1
-1
)
wherey
1
= initial depth,Fr
1
= Froude number before jump.
• Energy loss (?E ):
?E =
(y
2
-y
1
)
3
4y
1
y
2
2
Page 3


Open Channel Flow F ormula Sheet for GA TE
Civil Engineering
Fluid Mechanics: Open Channel Flow
1. Basic Concepts
• Hydr aulic Radius (R ) :
R =
A
P
whereA = cross-sectional area,P = wetted perimeter .
• Hydr aulic Depth (D ) :
D =
A
T
whereT = top width of the channel.
2. Types of Flow
• Froude Number (Fr ) : Determines flow regime (subcritical, critical, supercrit-
ical)
Fr =
V
v
gD
whereV = velocity ,g = gr avitational acceler ation,D = h ydr aulic depth.
– Subcritical: Fr< 1
– Critical: Fr = 1
– Supercritical: Fr> 1
• Reynolds Number (Re ) :
Re =
?VR
µ
=
VR
?
where? = density ,µ = dynamic viscosity ,? = kinematic viscosity .
1
3. Manning’ s Equation
• V elocity:
V =
1
n
R
2/3
S
1/2
where n = Manning’ s roughness coefficient, S = slope of energy gr ade line or
bed slope (for uniform flow).
• Dis charge:
Q =
1
n
AR
2/3
S
1/2
4. Chezy’ s F ormula
• V elocity:
V =C
v
RS
whereC = Chezy’ s coefficient.
• Relation with Manning’ sn :
C =
1
n
R
1/6
5. Specific Energy
• Specific energy ( E ):
E =y+
V
2
2g
wherey = flow depth, V = velocity .
• Critical depth (y
c
): Occurs whenE is minimum.
Fr =1 =?
Q
2
gA
2
=
A
T
F or rectangular channels:
y
c
=
(
q
2
g
)
1/3
whereq =Q/B ,B = channel width.
6. Hydr aulic Jump
• Conjugate depths (y
1
,y
2
) for rectangular channels:
y
2
=
y
1
2
(
v
1+8Fr
2
1
-1
)
wherey
1
= initial depth,Fr
1
= Froude number before jump.
• Energy loss (?E ):
?E =
(y
2
-y
1
)
3
4y
1
y
2
2
7. Uniform Flow
• Bed slope (S
0
) equals energy gr ade line slope (S ).
• N ormal depth (y
n
): Depth at which uniform flow occurs, solved using Man-
ning’ s equation.
8. Gr adually V aried Flow (G VF)
• W ater s urface profile slope:
dy
dx
=
S
0
-S
f
1-Fr
2
whereS
f
= friction slope (from Manning’ s or Darcy-W eisbach).
• Flow profiles classified based on channel slope (mild, steep, critical) and depth
relative to normal (y
n
) and critical (y
c
) depths.
9. Specific F orce
• Specific force ( F ) per unit width (rectangular channels):
F =
Q
2
gA
+y
A
B
• Constant across a h ydr aulic jump.
10. Critical Flow
• Occurs whenFr = 1 .
• Critical velocity:
V
c
=
v
gD
• Minimum specific energy at critical depth.
3