CE – 2005
1. A horizontal bed channel is followed by a steep bed channel as shown in the figure.
The gradually-varied profiles over the horizontal and steep beds are
(A) H and S respectively (B) H and S respectively (C) H and S respectively (D) H and S respectively
2. Critical depth at a section of a rectangular channel is 1.5 m. The specific energy at that section is
(A) 0.75 m (B) 1.0 m
(C) 1.5 m (D) 2.25 m
3. A partially open sluice gate discharge water into a rectangular channel. The tail water depth in the channel is 3m and Froude number is
√ . If a free hydraulic jump is to be formed at downstream of the sluice gate after the vena contracta of the jet coming out from the sluice gate, the sluice gate opening should be (co-efficient of contraction C = 0.9)
(A) 0.3 m (B) 0.4 m
(C) 0.69 m (D) 0.9 m
4. A triangular irrigation lined canal carries a discharge of 25 m /s at bed slope = If the side slopes of the canal are 1 : 1 and Manning’s coefficient is 0.018, the central depth of flow is equal to
(A) 2.98 m (B) 3.62 m
(C) 4.91 m (D) 5.61 m
5. A launching apron is to be designed at downstream of a weir for discharge intensity of 6.5 m ⁄s m⁄ . For the design of launching aprons the scour depth is taken two times of Lacey scour depth. The silt factor of the bed material is unity. If the tailwater depth is 4.4m, the length of launching apron in the launched position is
(A) √5m (B) 4.7 m
(C) 5 m (D) 5√5 m CE – 2006
6. A channel with a mild slope is followed by a horizontal channel and then by a steep channel. What gradually varied flow profiles will occur?
(A) M , H , S (B) M , H , S
(C) M , H , S (D) M , H , S 7. Identify the FALSE statement from the
following the specific speed of the pump increase with
(A) Increase in shaft speed (B) Increase in discharge (C) Decrease in gravitational
acceleration (D) Increase in head
8. A hydraulic jump occurs in a rectangular horizontal, frictionless channel. What would be the pre-jump depth if the discharge per unit width is 2 m /s/m and the energy loss is 1m?
(A) 0.2 (B) 0.3m
(C) 0.8m (D) 0.9m
9. A very wide rectangular channel is designed to carry a discharge of 5 m /s per meter width. The design is based on the manning’s equations with the roughness coefficient obtained from the grain size using Strickler’s equation and results in a normal depth of 1.0m by Horizontal bed
Steep bed
mistake, however, the engineer used the grain diameter in mm in the Stricker’s equation instead of in meter, What should be the correct normal depth?
(A) 0.32m occur in the channel for this flow rate?
(A) M Statement for linked answer questions 12 & 13
A rectangular open channel needs to be designed to carry a flow of 2.0 m /s under uniform flow conditions. The Manning’s roughness coefficient is 0.018.
The channel should be such that the flow depth is equal to half width and the Froude number is equal to 0.5
12. The bed slope of the channel to be average boundary shear stress under uniform flow conditions is
(A) 5.6 N/m notices that the disturbance on the water surface is not traveling upstreams. This is because the flow in the canal is
(A) Sub-critical (B) Super-critical
(C) Steady (D) Uniform Common data questions 15, 16 and 17 A rectangular channel 6.0 m wide carries a discharge of 16.0 m /s under uniform flow condition with normal depth of 1.60 m. Manning's 'n' is 0.015.
15. The longitudinal slope of the channel is (A) 0.000585 without affecting the upstream flow condition is
The minimum width to which the channel can be contracted without affecting the upstream flow condition is
(A) 3.0 m
19. Water emerges from an ogee spillway with velocity = 13.72 m/s and depth = 0.3 m at its toe. The tail water depth required to form a hydraulic jump at the toe is
(A) 6.48 m (B) 5.24 m
(C) 3.24 m (D) 2.24 m
20. The base width of an elementary profile of a gravity dam of height H is b. The specific gravity of the material of the dam is G and uplift pressure coefficient is K.
The correct relationship for no tension at the heel is given by
(A) √
(B) √G
(C)
(D) √
CE – 2009
21. Direct step method of computation for gradually varied flow is
(A) Applicable to non-prismatic channels (B) Applicable to prismatic – channels (C) Applicable to both prismatic and
non-prismatic channels
(D) Not applicable to both prismatic and non-prismatic channels
22. A rectangular open channel of width 4.5m is carrying a discharge of 100m /sec. The critical depth of the channel is
(A) 7.09 m (B) 3.96 m
(C) 2.16 m (D) 1.31 m CE – 2010
23. The flow in a rectangular channel is subcritical. If width of the channel is reduced at a certain section, the water surface under no-choke condition will (A) Drop at a downstream section (B) Rise at a downstream section (C) Rise at an upstream section (D) Not undergo any change
24. For a rectangular channel section, match List – I (Geometrical elements) with List – II (Proportions for hydraulically efficient section) and select the correct answer using the codes given below the lists:
List – I List – II A. Top width 1. y /2 B. Perimeter 2. y C. Hydraulic Radius 3. 2y D. Hydraulic Depth 4. 4y y is the flow corresponding to hydraulically efficient section Codes:
A B C D
(A) 2 4 1 3
(B) 3 1 4 2
(C) 3 4 1 2
(D) 3 4 2 1
25. The froude number of flow in a rectangular channel is 0.8 if the depth is flow is 1.5 m, the critical depth is
(A) 1.80 m (B) 1.56 m
(C) 1.36 m (D) 1.29 m CE – 2011
26. A spill way discharges flood flow at a rate of 9m /s per metre width. If the depth of flow on the horizontal apron at the toe of the spillway is 46 cm, the tail water depth needed to form a hydraulic jump is approximately given by which of the following options?
(A) 2.54 m (B) 4.90 m
(C) 5.77 m (D) 6.23 m 27. For given discharge, the critical flow
depth in an open channel depends on (A) Channel geometry only
(B) Channel geometry and bed slope (C) Channel geometry, bed slope and
roughness
(D) Channel geometry, bed slope, roughness and Reynolds number
CE – 2013
28. For subcritical flow in an open channel, the control section for gradually varied flow profiles is
(A) At the downstream end (B) At the upstream end
(C) At both upstream and downstream ends
(D) At any intermediate section
29. The normal depth in a wide rectangular channel is increased by 10%. The percentage increase in the discharge in the channel is :
(A) 20.1 (B) 15.4
(C) 10.5 (D) 17.2 CE – 2014
30. A horizontal jet of water with its cross-sectional area of 0.0028 m hits a fixed vertical plate with a velocity of 5 m/s.
After impact the jet splits symmetrically in a plane parallel to the plane of the plate. The force of impact (in N) of the jet on the plate is
(A) 90 (B) 80
(C) 70 (D) 60
31. A rectangular channel having a bed slope of 0.0001, width 3.0 m and Manning’s coefficient ‘n’ 0.015, carries a discharge of 1.0 m s. Given that the normal depth of flow ranges between 0.76 m and 0.8 m.
The minimum width of a throat (in m) that is possible at a given section, while ensuring that the prevailing normal depth is not exceeded along the reach upstream of the contraction, is approximately equal to (assume negligible losses)
(A) 0.64 (B) 0.84
(C) 1.04 (D) 1.24
32. A horizontal nozzle of 30 mm diameter discharges a steady jet of water into the atmosphere at a rate of 15 litres per second. The diameter of inlet to the nozzle is 100 mm. The jet impinges normal to a flat stationary plate held close to the nozzle end. Neglecting air friction and considering the density of water as 1000 kg/m , the force exerted by the jet (in N) on the plate is _________
33. A rectangular channel of 2.5 m width is carrying a discharge of 4 m /s.
Considering that acceleration due to gravity as 9.81 m/s , the velocity of flow (in m/s) corresponding to the critical depth (at which the specific energy is minimum) is _______
Answer Keys & Explanations
1. [Ans. A]
2. [Ans. D]
For rectangular channel, E = 1.5y = 1.5 × 1.5 = 2.25m 3. [Ans. C]
For hydraulic jump, y
y 1
2* 1 √1 8F + Given y = 3m
F =
√
∴ y = * 1 √1 8 +
⇒ y = 0.62m
Sluice gate opening = = . . = 0.69m
4. [Ans. C]
By Manning’s equations, Q R S A
⇒ 25 = . × (
√ ) × ( ) × y
⇒ 25 = . × y × .
⇒ y = 4.91 m 5. [Ans. C]
Lacey’s scour depth, R 1.35 (q
f)
1.35 (6.5 1 )
4.7 m Scour depth =2R = 9.4m
∴ D 2R 4.4 5m 6. [Ans. D]
7. [Ans. D]
The specific speed of a pump is given by N N√Q H
8. [Ans. B]
We know that a rectangular channel,
y …… 1
∴ y * . +
⇒ y 0.74m
We know that hydraulic jump is formed when supercritical flow changes to subcritical flow, if the prejump depth and post jump depth are y and y
respectively then y <y <y . Therefore option (c) and (d) are ruled out.
From (i), we have =
⇒ . =
Solving the above equation by taking y = 0.3m which is option (b) and thus calculating the value of y
∴ 0.3y 0.3 y 8 9.81
⇒ y + 0.3y 2.72 = 0
⇒ y = 1.51 m We also known that
∆E =
⇒ ∆E = . . . .
⇒ ∆E = . . . .
⇒ ∆E = 1m
But energy loss ∆E given in problem is also 1m. Hence the assumed value of y , i.e. 0.3m is correct.
9. [Ans. B]
As per Stickler’s equation. n
∴
= ( )
Now, as per Mannings equation, q 1
n y √S
∴ Correct depth of flow, y (n
n ) y = [( ) ]
1 = 0.50m
10. [Ans. B]
All free fall curves are zone II profiles.
Since the critical depth (y ) is less than the normal depth (y ), therefore the slope is mild. Thus, the gradually varied profile is M
11. [Ans. B]
The side slope of triangular open channel given as z horizontal to 1 vertical.
When vertex angle is 90 , z = 1
Now, y = * + for a triangular channel
⇒ Q =
⇒ Q = . .
⇒ Q = 0.11 m /s 12. [Ans. B]
Given Q = 2 m3/s, n = 0.018, B = 2y, F = 0.5 We know that
90 Z
1
F = √
Where V is velocity of flow, D is hydraulic radius
Now D = y
∴ F =
√
0.5 =
√
0.5 =
√ Squaring both sides
0.25 =
y = * . . +
y = 0.836m
Using Manning’s equation, we get Q 1
nA R √S
2 1
0.018 2 0.836 (0.836
2 )
√S
√S = 0.0461
S = 0.0021 13. [Ans. D]
The average shear stress, τ0 γRS0
Bed slope is doubled i.e. S0 = 2 0.0021
= 0.0042 τ0 = 9810 . 0.0042
τ0 = 17.22 N/m2 14. [Ans. A]
15. [Ans. A]
The velocity as per Manning’s equation is given by
V = R S
Here, Q = 16m3/s. n = 0.015, B =6.0m A = 6.0 1.60 = 9.6 m2
R = .
. . 1.04m But Q = AV
∴ Q = A R S
16 = 9.6 . 1.04 S
S = 0.00059
16. [Ans. B]
When a hump is introduced on the channel bed the depth of flow at this location will reduce. If ∆Z is the maximum height of hump so that the depth of flow remains same, then
y + ∆Z E
∴ 1.6 16
2 9.81 9.6 ∆Z 3 2y
1.74 ∆Z 3
2 * 16 6 9.81 +
∆Z 1.74 – 1.35
∆Z 0.39 ≈ 0.4m 17. [Ans. C]
If the channel is contracted, the depth of flow at this location decreases. Thus width of the channel can be decreased till the specific energy becomes minimum. If the channel is contracted further, the depth of flow starts decreasing.
∴ y + E
1.6 + . . y
1.74 = ( )
1.74 = * . +
b = 2.557
b = 4.1m 18. [Ans. C]
The exit gradient may be given as
G H
d 1 √
Where 1 √ and Here b = 10 m, d = 4 m, H = 5 m
∴ b d
10 4 2.5 and 1 √1 2.5
2 1.85
∴ G 5 4
1 √1.85
⇒ G 1 3.4
19. [Ans. C]
Water depth required to form a hydraulic jump may be given as
y y
2[ 1 √1 8V gy ] 0.3
2 [ 1 √1 8 13.72 9.81 0.3 ] 3.24 m
20. [Ans. A]
Tension will not be developed at the heel with full reservoir, when
b H
√G 21. [Ans. B]
22. [Ans. B]
The critical depth for a rectangular channel is given by
y q
g
But q = . 22.22 m sec
∴ y . .
y 3.69m 23. [Ans. A]
24. [Ans. C]
Let the width of rectangular channel be B and depth of flow be y.
Area of flow. A = By
Wetted perimeter, P = B + 2y
= 2y
For hydraulically most efficient section, P should be minimum
∴ dP dy 0
A
y 2 0
A 2y
B 2y
B 2y
Hydraulic radius, R A
P 2y 2y 2y y
Top width, T B 2y2
Perimeter, P B 2y 2y 2y 4y Hydraulic depth, D A
T 2y 2y y 25. [Ans. D]
Froude Number for a rectangular channel is given by
F = √
V = 0.8 √9.81 1.5 = 3.07 m/s
∴ Discharge per unit width of rectangular channel is given by
q = Vy = 3.07 1.5 = 4.6 m3/s/m
∴ Critical depth, yc = ( ) (4.6
9.81)
1.29m
26. [Ans. C]
q 9m s m y 0.46m
y y y y 2 9
9.81 0.46 y 0.46 y y 5.77 m
27. [Ans. A]
y (
) Q Constant y ( )
Depends on geometry only.
28. [Ans. A]
y2
y1
29. [Ans. D]
Discharge Q = R S A manning’s formula
∴ Q ( ) S B y [for wide channels R = y/2]
⇒ Q y
∴∆ 100 . 100 17.2
30. [Ans. C]
Force exerted in x direction
= rate of change of momentum in x direction
i.e. F A v v v Herev 0ms x direction
⇒ F 1000 0.0028 5 5 70 N
31. [Ans. B]
n 0.015, Q 1m s, B 3.0m
Normal depth of flow ranges between 0.76m to 0.8 m
If prevailing normal depth of flow is not exceeded, there must not be choking of the section or it should be at boundary condition of choking. So, width of section should be such that there should be critical flow corresponding to the prevailing specific energy.
i. e. ,3 2(q
g)
E E q .
So3 2[(
) g ]
E
E y Q . A. R s ⇒ 1 . . B. y . ( . ) . S
⇒ 1 . . 3y . ( ) . 0.0001
⇒ y 0.78 m
So, E 0.78 . . ( ⁄ ) 0.789 m
So, [( )] 0.789 ⇒ B
⇒3 2
1
g B 0.7893
⇒ B 0.84m
32. [Ans. *] (Range 318 to 319) Velocity of jet, v Q
A
15 10 m s 0.03 21.22 m s
Force on plate, F a. v 1000
4 0.03 21.22 318.29 N
33. [Ans. *] Range 2.45 to 2.55 Q = 4m s
B = 2.5 m q 4
2.5 1.6 m s m
y q
g ⇒ y 0.639
At critical depth velocity head = V
2g
0.639 2 V √0.639 g = 2.504 m/s
15 100 mm
30 mm
Irrigation
CE – 2005
1. On which of the canal systems, R.G.
Kennedy, executive engineer in the Punjab Irrigation Department made his observations for proposing his theory on stable channels?
(A) Krishna Western Delta canals (B) Lower Bari Doab canals (C) Lower Chenab canals (D) Upper Bari Doab canals
2. Uplift pressure at points E and D (figure A) of a straight horizontal floor of negligible thickness with a sheet pile at downstream end are 28% and 20%, respectively. If the sheet pile is at upstream end of the floor (figure-B), the uplift pressures at points D and C are
(A) 68% and 60% respectively (B) 80% and 72% respectively (C) 88% and 70% respectively (D) 100% and zero respectively