8 critical flow
DESCRIPTION
abe 72 critical flowTRANSCRIPT
Specific EnergyIn a channel with constant discharge, Q
2211 VAVAQ
2
2
2gA
QdE
g
VdE
2
2
Consider rectangular channel (Area= b.d) and Q= q.b
2
2
2gd
qdE
q is the discharge per unit width of channel
Area
b
d
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6 7 8 9 10
E
d
Specific Energy: Sluice Gate
2
2
2gd
qdE
1
2
21 EE
sluice gate
1d
2d
EGL
d1 and d2 are ___________ depths (same specific energy)
q = 5.5 m2/sd2 = 0.45 mV2 = 12.2 m/s
d1 = 8.07 m
alternateGiven downstream depth and discharge, find upstream depth.
0
1
2
3
4
0 1 2 3 4
E
dSpecific Energy:
Raise the Sluice Gate
2
2
2gd
qdE
1 2
E1 E2
sluice gate
1d
2d
EGL
as sluice gate is raised, d1 approaches d2
E is minimized for a given discharge or
Q is maximized for a given energy
Minimum E
2
2
2gA
QdE
P
A
T
dd
d dA
TdddA but
0
1
2
3
4
0 1 2 3 4
E
y
dc
Consider a channel with an irregular cross-section
dd
dA
gA
Q
dd
dE3
2
10
3
2
1gA
TQ 1Fr
Critical Flow exists
Maximum Q
2
2
2gA
QdE
P
A
T
dd
d dA
Consider a channel with an irregular cross-section
3
2
1gA
TQ 1Fr
Critical Flow exists
)(2 dEgAQ
0)(2
)(2
dEg
gAdEg
dd
dA
dd
dQ
but and AQdEg /)(2 TdddA /
General Equation
3
2
1gA
TQ
CRITICAL FLOW
Sample:
A flow of 280 L/s of water is carried by a
90˚-V notch flume with n = 0.011.
Find the critical depth.
dc = 0.44 m
CRITICAL FLOW
For rectangular sections
cc gdV 3
2
g
qd c
3/4
22
c
c
cR
nVS
g
Vd c
c
2
g
Vd cc
22
2
2
cc
ddE Edc
3
2
velocity head = 1/2 (dc)
g
VdE
2
2