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Republic of the PhilippinesGILLESANIA Engineering Review and Training CenterCebuBOARD OF CIVIL ENGINEERINGHYDRAULICS & GEOTECHNICAL ENGINEERING SET ASaturday, November 4, 2017 Module 8INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item b...

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Republic of the Philippines GILLESANIA Engineering Review and Training Center Cebu BOARD OF CIVIL ENGINEERING HYDRAULICS & GEOTECHNICAL ENGINEERING Saturday, November 4, 2017

SET A Module 8

INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only. NOTE: WHENEVER YOU CAN ENCOUNTER A CARET (^) SIGN, IT MEANS EXPONENTIATION 1.

Evaluate the plastic settlement, in meters, in a layer of plastic clay due to an increase of pressure caused by loads above it under the following conditions: Initial intergranular pressure = 200 kPa Increase in intergranular pressure = 150 kPa Thickness of the clay layer = 12 m Coefficient of consolidation = 0.315 Void Ratio of the Clay = 1.5 A. 0.324 B. 0.381

C. 0.409 D. 0.367

H  12m

H 

2.

 H  log 1  eo 

pf 

 

po

 0.367 m

3

s

Z  120 m

HE  Z  HL  85 m

HL  35m

 w  9.81

Eff  80%

kN m

3

Pin  Q   w  HE  83.385 MW Po  Pin  Eff  66.708 MW

A vacuum gage connected to a tank reads 35 kPa at a location where the barometric reading is 755 mmHg. Determine the absolute pressure in the tank. Take ρHg = 13,590 kg/m³. A. 76.35 C. 65.62 B. 135.62 D. 118.35

3

pg   35 kPa h m  755 mm

Ww  10.9N

BF  Wa  Ww  0.9N

m  13590

pabs  pg  m  g  h m  65.621 kPa

kg m3

BF =  w  Vc

Wa = SGc  w  Vc



Ww = BF  SGc  1 SGc  1 

6. m

Wa  11.8N

Solution

In a hydroelectric power plant, 100 m³/s of water flows from an elevation of 120 m to a turbine, where electric power is generated. The total irreversible head loss in the piping system from point (excluding the turbine unit) is determined to be 35 m. If the overall efficiency of the turbine–generator is 80 percent, estimate the electric power output in Megawatts. A. 72.6 C. 62.4 B. 83.4 D. 66.7

Q  100

cu  52kPa   0.62

Lp  10m

Archimedes, when asked by King JGo if the new crown was pure gold (SG = 19.3), found the crown weight in air to be 11.8 N and in water to be 10.9 N. What is the specific gravity of the crown? A. 13.11 C. 15.4 B. 19.3 D. 16.7

5 Given

2

3.

D  0.4m

e o  1.5

p f  p o  p  350 kPa Cc

4

5.

p  150 kPa Cc  0.315

A pile of 0.4 m diameter and length of 10 m is embedded in a deposit of clay. The undrained strength parameters of the clay are cohesion = 52 kPa and the angle of internal friction is 0 . The skin friction capacity, in kN, of the pile for an adhesion factor of 0.62, is: A. 405 C. 362 B. 385 D. 423

Qf    cu  (   D)  Lp  405.14 kN

1

p o  200 kPa

4.



Ww  13.111 BF

A 50-ton, 6-m-diameter hemispherical dome on a level surface is filled with water, as shown in Figure HYD 10.21. Someone claims that he can lift this dome by making use of Pascal’s law by attaching a long tube to the top and filling it with water. Obtain the required height of water (in meters) in the tube to lift the dome. Disregard the weight of the tube and the water in it. A. 0.524 C. 0.768 B. 2.124 D. 1.236

6 M  50tonne

D  6m

W  M  g  490.332 kN

 w  9.81

 sw  10.06

kN m

3

r  0.5  D  3 m

2 2 W =  w    r  ( r  h )     r3 3   W h 

3

  r  w

V1  1

p 2  patm

V2  8

  sw  h  patm  V1 = p2  V2

 0.768 m

A contractor has compacted the base course for a new road and found that the mean value of the test samples shows w = 20.5%, G s = 2.81, and  = 18.2 kN/m3. The specifications require that e 0.80. Has the contractor complied with the specifications? A. yes C. maybe B. no D. it depends

7 MC  20.5%

 w  9.81 m = e1 

8.

G  2.81

 m  18.2

kN m

kN m

1  e1

 70.504 m

10. The normal and shearing stresses at failure plane in a triaxial test of a normally consolidated clay are f = 78 kPa and f = 52 kPa. Determine the major principal stress in kPa. A. 175.2 C. 196.3 B. 163.2 D. 154.9

f  78kPa

 f    atan    33.69 deg  f 

  45deg    2  61.845 deg

 w

 w  ( G  G  MC ) m

R   f  sec (  )  62.496 kPa

 1  0.8251

C  f   f  tan (  )  112.667 kPa

1  C  R  175.163 kPa

An 80-cm-high fish tank of cross section 2 m ⨯ 0.6 m that is initially filled with water is to be transported on the back of a truck. The truck accelerates from 0 to 90 km/h in 10 s. If it is desired that no water spills during acceleration, determine the maximum possible initial water height in the tank in cm. A. 72.35 C. 65.32 B. 54.51 D. 76.24

11. A 50-mm-diameter nozzle issuing a vertical jet of water supports a 40-kg load at a height of 1.5 m from the nozzle tip. Neglecting all losses, what is the flow through the nozzle in L/s. A. 26.8 C. 29.5 B. 28.2 D. 28.8  11

vo  0 L  2m

vf  90kph

t  10s



b  0.6m



y  0.5  b  tan ( )  7.648 cm y  0.5  L  tan ( )  25.493 cm

Dn  50mm

M  40kg

 a  g

  atan

 14.302 deg

h max1  H  y  72.352 cm h max1  H  y  54.507 cm

Assuming normal barometric pressure, how deep is the ocean at a point where an air bubble, upon reaching the surface, has eight times the volume that it had at the bottom? Use unit weight of seawater = 10.06 kN/m³. A. 50.4 m C. 60.4 m B. 80.6 m D. 70.5 m

h  1.5m

FD  Wt  392.266 N

Fd =   Q  v 2 An  0.25    Dn

Q = An  vn 2

  1000

kg m

Wt  M  g  392.266 N

H  80cm

m a  vf  vo  t  2.5 2 s

9

V1   sw

 f  52kPa

8

9.

V2 p 2  V1  p atm

 10

3

3

G  G  MC

p atm  101.325 kPa

3

p 1 ( h )   sw  h  p atm

h  7.

m

p 1  V1 = p 2  V2

  r3   w 2

kN

2

v = vn  2  g  h

v=

2

vn  2  g  h

FD =  An  vn  v Guess

m vn  10 s

Given

FD =   An  vn

2

vn  2  g  h

m vn  Find vn  14.664 s

 

L Q  An  vn  28.793 s

3

12.

The barometer of a mountain hiker reads 930 mbars at the beginning of a hiking trip and 780 mbars at the end. Neglecting the effect of altitude on local gravitational acceleration, determine the vertical distance climbed. Assume an average air density of 1.20 kg/m³. A. 1365 m C. 1058 m B. 1274 m D. 952 m

 12 p 1  0.93bar H 

p1  p 2

air  g

p 2  0.78bar

air  1.2

kg m

3

14. Which of the following is not a soil component? C. Gas A. Organic materials B. Minerals D. None of these 15. Milk with a density of 1020 kg/m³ is transported on a level road in a 7-m-long, 3-m-diameter cylindrical tanker. The tanker is completely filled with milk (no air space), and it accelerates at 2.5 m/s². If the minimum pressure in the tanker is 0 kPa, obtain the maximum force (in kN) acting on one end of the tanker. A. 338.3 C. 256.9 B. 232.2 D. 304.7

 1274.645 m

13. The pipe flow in Figure HYD 7.32 fills a cylindrical tank as shown. At time t = 0, the water depth in the tank is 30 cm. Estimate the time required to fill the remainder of the tank. A. 52 s C. 30 s B. 46 s D. 70 s

Figure HYD 3.658  14

Figure HYD 7.32

a  2.5

m 2

  1020

L  7m

m

s

  atan

 13 d  12cm m v1  2.5 s

D  75cm m v2  1.9 s

Apipe  0.25    d

2

H  1m

Ho  30cm

kg 3

D  3m

 a   14.302  deg  g

p cg    g  ( L  tan ( )  0.5  D)  32.854 kPa



Atank  0.25    D

2

F  pcg   D2  232.232 kN 4

3

m Q1  Apipe  v1  0.028 s

3

m Q2  Apipe  v2  0.021 s

m Qtank  Q1  Q2  0.007 s



3



Vol  Atank H  Ho  0.309 m3 time 

Vol Qtank

 45.573 s

16. Consider a large cubic ice block floating in seawater. The specific gravities of ice and seawater are 0.92 and 1.025, respectively. If a 12-cm-high portion of the ice block extends above the surface of the water, obtain the height of the ice block below the surface in cm. A. 105.14 C. 95.14 B. 117.14 D. 90.14  16

so  0.92

sl  1.025

h p = h  draft h p = h  h

so sl

h i ht f bl k b l

h p  12cm

draft = h h 

so sl

h p  sl sl  so

 117.143 cm

17. A soil has an angle of shearing resistance of 33ᵒ. Determine the bearing capacity factor for the overburden pressure at the bottom of the footing considering general shear failure.

2

 

Nq (  )  tan 45deg 

 2

2



 e  tan (  )





N (  )  2  Nq (  )  1  tan (  )

h2  400 mm

 h1    h2 

 ln 

t  1min

 10.812 10 3

cm s

 20

  33deg

D  10.5m

Nq (  )  26.092

d  10mm

20. A cylindrical caisson having an outside diameter of 9 m floats in sea water with its axis vertical and its lower end submerged 10.5 m, below the water surface. If its center of gravity is on the vertical axis and is 3.6 m above the bottom. Obtain the righting couple (kN-m) when the caisson is tipped through an angle of 8°. A. 2017 C. 2058 B. 2002 D. 2145

Nc(  )  Nq (  )  1  cot(  )

d  9m

G  3.6m

  1000

kg m

N (  )  35.188

MBo =

The 500-kg load on the hydraulic lift shown in Figure HYD 3.25 is to be raised by pouring oil (ρ = 780 kg/m³) into a thin tube. Obtain how high “h” should be in order to begin to raise the weight. A. 57 cm C. 65 cm B. 52 cm D. 43 cm

I VD

I



 d 4  322.062 m

64

VD  MBo 

 4

 4

4

2

 d  D  667981.138 L

I  0.482 m VD

D GBo   G  1.65m 2 BF 

3

  8deg

Ssw  1.03

Nc(  )  38.638

18.

2

D t

 17



d  Ls

k

C. 26.09 D. 21.57

A. 35.19 B. 38.64

Ls  200 mm

h1  900 mm

Hints: Nq = tan (45ᵒ + ϕ/2)2 e πtanϕ Nc = (Nq – 1)cot ϕ Nγ = 2(Nq + 1) tan ϕ



 19 D  50mm

MG  MBo  GBo  2.132 m

2

 d  D    g Ssw  6747.177 kN

RM  BF ( MG  sin ( ) )  2002.137 kN  m

21.

A soil sample has a water content of 15 percent and moist unit weight of 18 kN/m3. The specific gravity of the solids is 2.65. Obtain the porosity of the soil. A. 0.542 C. 0.661 D. 0.398 B. 0.618

 21 MC  15%

 m  18

Figure HYD 3.25 m=  18 Load  500 kg

D  1.2m

o  780

kg m

3

n

Load  g

h=

19.

p



h 

0.25    D

o  g

eo 

2

 56.679 cm

The permeameter in a falling head permeability test setup involves a cylindrical soil sample 50 mm in diameter and a height 200 mm. The hydraulic head ln the 10-mm diameter standpipe through which test water passed dropped from 900 mm to 400 mm in one-

kN m

3

Gs  2.65

Gs  Gs  MC  w 1  eo

 w  Gs  Gs  MC m eo 1  eo

 0.398

 1  0.661

 w  9.81

kN m

3

22. A crane is used to lower weights into the sea (density = 1025 kg/m³) for an underwater construction project. Obtain the tension (in N) in the rope of the crane due to a rectangular 0.4-m ⨯ 0.4-m ⨯ 3-m concrete block (density = 2300 kg/m³) when it is completely immersed in water. C. 6002 A. 6325 B. 10826 D. 5478  22

 25

w  1025 a  0.4m

kg m

b  0.4m



D  20cm

kg

c  2300

3

m

3

H  60cm

h  50cm

y  2  ( H  h )  0.2m

c  3m

y=



T  c  w  g  a  b  c  6001.67 N

23.

25. A 20-cm-diameter, 60-cm-high vertical cylindrical container is partially filled with 50-cm-high liquid whose density is 850 kg/m³. The cylinder is rotated at a constant speed. Evaluate the rotational speed (in rpm) at which the liquid will start spilling from the edges of the container. A. 163 C. 214 B. 152 D. 189

In a bakery, water enters a mixing chamber at the rate of 120 per liters per sec through Pipe A, while cooking oil with specific gravity of 0.80 is forced at 40 liters per sec through pipe B. Assuming the liquids are incompressible and from a homogeneous mixture of oil globules in water, evaluate the density of the mixture in kg/m³ leaving through a pipe C of diameter 300mm. A. 960 C. 950 B. 930 D. 920

 2  r2

2 g y



2 g

r  0.5  D

r

2

 189.131 rpm

26. A pressurized tank of water has a 10-cm-diameter orifice at the bottom, where water discharges to the atmosphere. The water level is 3 m above the outlet. The tank air pressure above the water level is 300 kPa (absolute) while the atmospheric pressure is 100 kPa. Neglecting frictional effects, obtain the initial discharge rate of water from the tank in m³/s. C. 0.1682 A. 0.1263 B. 0.1925 D. 0.0603  26

 23 L

Qw  120

s

L Qo  40 s

w  1000

Do  10cm

kg m

3

o  w so  800

so  0.80

kg m

 w  9.81

3

h  3m kN

m

p air  300kPa

patm  100kPa

3

p air  p atm

Dc  300mm

Head  h 

kg Mf  w  Qw  o  Qo  152 s 3 m Qt  Qw  Qo  0.16 s

Ao  0.25    Do  0.00785 m

Mf = mix  Qt

mix 

Mf Qt

 950

Qo  Ao 

2  g  Head  0.168

m

27.

P  132N Do  38mm

Sample area at failure: P



 0.00117 m2

Vertical displacement:

 



 Do2 

3

In tri-axial test, a cohesive soil sample has failed in a normal stress of 550 kPa and a shear stress of 350 kPa. Obtain the cohesion in kPa of the soil sample given that the angle of internal friction is 31ᵒ. A. 22.3 C. 28.9 B. 19.5 D. 31.4

 27

Given

n  550kPa x 

  2  C  112.8 kPa

m s

3

Solution

Major principal stress:

2

kg

 24 C  56.4kPa

 23.387 m

2

24. An unconfined compression test was carried out on a saturated clay sample. The maximum load on the clay sustained was 132 N. The size of the soil sample was 38 mm diameter and 80 mm long. The resulting un-drained shear strength of clay was 56.4 kPa. Evaluate the vertical displacement of the soil sample in mm. A. 2.84 C. 2.47 B. 1.87 D. 1.65

A 

w

L  80mm

 tan (  )

  350kPa  582.5 kPa

z  x  n  32.5 kPa c  z  tan (  )  19.53 kPa

  31deg

28.

Water is pumped from a lower reservoir to a higher reservoir by a pump that provides 20 kW of useful mechanical power to the water. The free surface of the upper reservoir is 45 m higher than the surface of the lower reservoir. If the flow rate of water is measured to be 0.03 m³/s, determine the lost mechanical power (in kW) during this process. A. 6.76 C. 5.89 B. 7.52 D. 2.96

 28

Pi  20kW

Z  45m

Power = Q  w HA

Q  0.03

m

3

s

 w  9.81

m

3

29. For a constant head permeability test, the following data are given: Length of the specimen = 460 mm Area of the specimen = 23 cm2 Constant – head difference = 0.71 m Water collected in 3 min = 390 cc Porosity = 0.48 Find the actual velocity (seepage velocity) in cm/sec. A. 0.094 C. 0.218 B. 0.196 D. 0.254  29 A  23cm

3

2

t  3min

V L A  H  t

 0.061

n

 0.196

0.318  Q  N ( r z) 2

z Part 1 r  0

z  3m

P ( r z)  63.6kPa

Part 2 r  0

z  6m

P ( r z)  15.9kPa

Part 3 r  3m

z  6m

P ( r z)  8.655 kPa

Situation 2 – The gravity dam shown in Figure HYD 9.336 has the following data: B = 15 m H = 20 m

a=3m c=3m

Unit weight of water = 9.81 kN/m³ Unit weight of concrete = 24 kN/m³ Coefficient of friction = 0.80

Evaluate the following when h = 18 m: cm sec

cm sec

Situation 1 - According to the Westergaard theory, the vertical stress at a point below the surface of a semi-infinite, homogeneous, isotropic soil mass due to a point load Q applied at the ground surface is given by the equation ΔP = 0.318QN/z² Where

1.5

Consider 1 m length of dam perpendicular to the figure.

 H   0.094 cm sec  L 

vd

 r 2 1  2    z  

n  0.48

Actual velocity: vs 

P ( r z) 

1

Assume that there is uplift pressure that varies uniformly from full hydrostatic head at the heel to zero...