Questions in Hydrology
FLOOD AND FLOW ROUTING
Q (1) I1 I 2 Q Q S S1
Given t h e continuity equation, 1 2 2 , and the storage relation,
2 2 t
S 2 S1 K x I 2 I 1 1 x Q2 Q1 ,
develop the Muskingum routing equation and the equations of the three constants, C1, C2, and C3
Q (2)
The inflow and outflow hydrographs of a river reach are tabulated below.
Time (h) 1 2 3 4 5 6 7 8 9 10
Inflow
93 137 208 320 442 546 630 678 691 675
(m3/s)
Outflow
85 91 114 159 233 324 420 509 578 623
(m3/s)
Time (h) 11 12 13 14 15 16 17 18 19 20
Inflow
634 571 477 390 329 247 184 134 108 90
(m3/s)
Outflow
642 635 603 546 479 413 341 274 215 170
(m3/s)
a) Use these readings to obtain the Muskingum routing parameters K and x for thisriver
reach using the three methods: 1) The Graphical method, 2) The Trial and Error
method, and 3) The Least Squares Method. Consider the initial storage in the system
as 715,000 m3.
(Note: for the graphical method try plotting S2 S1 (I Q ) t against the average
weighted discharge xI (1 x) Q and try also plotting S2 S1 (I Q ) t against the
instantaneous values of xI (1 x) Q )
b) Use the Muskingum routing procedure to route the hydrograph tabulated below
through the same river reach of Part (a). Do the routing using the K and x values
obtained by each of the three methods stated in Part (a). Compare the resulting three
hydrographs (by plotting them) and comment on the results.
Time (h) 1 2 3 4 5 6 7 8 9 10
Inflow
50 100 200 325 450 600 700 780 790 775
(m3/s)
Time (h) 11 12 13 14 15 16 17 18 19 20
Inflow
750 680 590 500 420 350 300 250 225 200
(m3/s)
,Q (3)
The flow hydrograph at a certain section of a channel is given by:
Time
0 30 60 90 120 150 180 210 240 270 300 330 360 390
(min)
Flow
0.0 12.5 22.1 15.4 13.6 12.4 11.7 10.8 9.9 8.4 8.1 7.5 4.2 0.0
(m3/s)
Estimate the hydrograph 1000 m downstream the channel section using the Muskingum
method. Assume x = 0.3 and K = 35 minutes.
Q (4)
The following readings are the measured flows at upstream and downstream sections of a river:
Time (min) 0 30 60 90 120 150 180 210 240 270 300 330 360
Upstream
10.0 10.0 25.0 45.0 31.3 27.5 25.0 23.8 21.3 19.4 17.5 16.3 13.5
Flow (m3/s)
Downstream
10.0 10.0 12.2 23.4 35.1 32.1 28.8 26.2 24.3 22.1 20.1 18.3 16.6
Flow (m3/s)
Time (min) 390 420 450 480 510 540 570 600
Upstream
12.1 10.0 10.0 10.0 10.0 10.0 10.0 10.0
Flow (m3/s)
Downstream
14.4 12.6 11.0 10.3 10.1 10.1 10.0 10.0
Flow (m3/s)
Determine the Muskingum coefficients x and K that should be used in routing flows through
this section of the river. Use the three methods of estimating these parameters as in Problem
2(a).
Q (5)
A watershed has a soil group C and is cultivated with conservation tillage. For a 24-hr, 100-
year precipitation of 8 in, estimate the runoff depth using the SCS curve number method.
Assume wet conditions for this watershed.
Q (6)
a) Determine a composite SCS runoff curve number for a 600-acre basin that is totally
within soil group C. The land use is 40 percent lawns with poor conditions and 60
percent pasture in good conditions.
b) For the computed CN, estimate the amount of runoff if the direct rainfall is 20 cm.
Q (7)
A catchment with drainage area of 80 acres is subdivided into the following
30% - Water Tight Rooftops (24 acres)
10% - Streets and driveways in good order (8 acres)
20% - Average lawns @ 5% slope on sandy soil (16 acres)
40% - Woodland (32 acres)
Calculate the peak runoff resulting from rainfall storm of intensity 2.3 in/hr.
, Answers
Q 1:
(S2-S1)/t = [(I1+I2)/2 ]–[ (Q1-Q2)/2]
S2-S1=K[x (I2-I1) + (1-x) (Q2-Q1)]
(t/2) [(I1+I2)-(Q1+Q2)] = KxI2 - KxI1 + KQ2 – KxQ2 – KQ1 + KxQ1
[(t/2) + K – Kx] Q2 = [(t/2) +Kx] I1 + [(t/2) -Kx] I2 + [K – Kx - (t/2)] Q1
C1 = [(t/2) -Kx] / [(t/2) + K – Kx] *2 C1 = [t – 2Kx] / [t + 2K (1-
x)]
C2 = [(t/2) +Kx] / [(t/2) + K – Kx] *2 C2 = [t + 2Kx] / [t + 2K
(1-x)]
C3 = [K – Kx - (t/2)] / [(t/2) + K – Kx] *2 C3 = [2K (1-x) - t] / [2K
(1-x) + t]
1
FLOOD AND FLOW ROUTING
Q (1) I1 I 2 Q Q S S1
Given t h e continuity equation, 1 2 2 , and the storage relation,
2 2 t
S 2 S1 K x I 2 I 1 1 x Q2 Q1 ,
develop the Muskingum routing equation and the equations of the three constants, C1, C2, and C3
Q (2)
The inflow and outflow hydrographs of a river reach are tabulated below.
Time (h) 1 2 3 4 5 6 7 8 9 10
Inflow
93 137 208 320 442 546 630 678 691 675
(m3/s)
Outflow
85 91 114 159 233 324 420 509 578 623
(m3/s)
Time (h) 11 12 13 14 15 16 17 18 19 20
Inflow
634 571 477 390 329 247 184 134 108 90
(m3/s)
Outflow
642 635 603 546 479 413 341 274 215 170
(m3/s)
a) Use these readings to obtain the Muskingum routing parameters K and x for thisriver
reach using the three methods: 1) The Graphical method, 2) The Trial and Error
method, and 3) The Least Squares Method. Consider the initial storage in the system
as 715,000 m3.
(Note: for the graphical method try plotting S2 S1 (I Q ) t against the average
weighted discharge xI (1 x) Q and try also plotting S2 S1 (I Q ) t against the
instantaneous values of xI (1 x) Q )
b) Use the Muskingum routing procedure to route the hydrograph tabulated below
through the same river reach of Part (a). Do the routing using the K and x values
obtained by each of the three methods stated in Part (a). Compare the resulting three
hydrographs (by plotting them) and comment on the results.
Time (h) 1 2 3 4 5 6 7 8 9 10
Inflow
50 100 200 325 450 600 700 780 790 775
(m3/s)
Time (h) 11 12 13 14 15 16 17 18 19 20
Inflow
750 680 590 500 420 350 300 250 225 200
(m3/s)
,Q (3)
The flow hydrograph at a certain section of a channel is given by:
Time
0 30 60 90 120 150 180 210 240 270 300 330 360 390
(min)
Flow
0.0 12.5 22.1 15.4 13.6 12.4 11.7 10.8 9.9 8.4 8.1 7.5 4.2 0.0
(m3/s)
Estimate the hydrograph 1000 m downstream the channel section using the Muskingum
method. Assume x = 0.3 and K = 35 minutes.
Q (4)
The following readings are the measured flows at upstream and downstream sections of a river:
Time (min) 0 30 60 90 120 150 180 210 240 270 300 330 360
Upstream
10.0 10.0 25.0 45.0 31.3 27.5 25.0 23.8 21.3 19.4 17.5 16.3 13.5
Flow (m3/s)
Downstream
10.0 10.0 12.2 23.4 35.1 32.1 28.8 26.2 24.3 22.1 20.1 18.3 16.6
Flow (m3/s)
Time (min) 390 420 450 480 510 540 570 600
Upstream
12.1 10.0 10.0 10.0 10.0 10.0 10.0 10.0
Flow (m3/s)
Downstream
14.4 12.6 11.0 10.3 10.1 10.1 10.0 10.0
Flow (m3/s)
Determine the Muskingum coefficients x and K that should be used in routing flows through
this section of the river. Use the three methods of estimating these parameters as in Problem
2(a).
Q (5)
A watershed has a soil group C and is cultivated with conservation tillage. For a 24-hr, 100-
year precipitation of 8 in, estimate the runoff depth using the SCS curve number method.
Assume wet conditions for this watershed.
Q (6)
a) Determine a composite SCS runoff curve number for a 600-acre basin that is totally
within soil group C. The land use is 40 percent lawns with poor conditions and 60
percent pasture in good conditions.
b) For the computed CN, estimate the amount of runoff if the direct rainfall is 20 cm.
Q (7)
A catchment with drainage area of 80 acres is subdivided into the following
30% - Water Tight Rooftops (24 acres)
10% - Streets and driveways in good order (8 acres)
20% - Average lawns @ 5% slope on sandy soil (16 acres)
40% - Woodland (32 acres)
Calculate the peak runoff resulting from rainfall storm of intensity 2.3 in/hr.
, Answers
Q 1:
(S2-S1)/t = [(I1+I2)/2 ]–[ (Q1-Q2)/2]
S2-S1=K[x (I2-I1) + (1-x) (Q2-Q1)]
(t/2) [(I1+I2)-(Q1+Q2)] = KxI2 - KxI1 + KQ2 – KxQ2 – KQ1 + KxQ1
[(t/2) + K – Kx] Q2 = [(t/2) +Kx] I1 + [(t/2) -Kx] I2 + [K – Kx - (t/2)] Q1
C1 = [(t/2) -Kx] / [(t/2) + K – Kx] *2 C1 = [t – 2Kx] / [t + 2K (1-
x)]
C2 = [(t/2) +Kx] / [(t/2) + K – Kx] *2 C2 = [t + 2Kx] / [t + 2K
(1-x)]
C3 = [K – Kx - (t/2)] / [(t/2) + K – Kx] *2 C3 = [2K (1-x) - t] / [2K
(1-x) + t]
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