From the figure shown, the following data are given:
| D | 4 | inches |
| H1 | 0.2 | ft |
| K1 | 0.0038 | ft/min |
| h = 1.25ft. | ||
| d = 1.5 inches | ||
| H2 = 0.3 ft. | ||
| K2 = 0.00075 ft/min. | ||
| Total H = H1 + H2 = 0.5 ft. | ||
1) Determine the total flow of water q.
2) Find the equivalent value of K1, for both annual and inner ring
3) Determine the volume of water which percolate after 30 min in cm3
Solution:
Three pipes A, B and C are connected in parallel. If the combined discharged of the 3 pipes is equal to 0.61 m3/s, and assuming they have equal values of friction factor “f”, compute the following using the tabulated data shown.
PIPELINE LENGTH DIAM.
A 600 m. 150 m.
B 480 m. 200 m.
A 750 m. 100 m.
1) Compute the rate of flow of pipeline A in li/sec.
2) Compute the rate of flow of pipeline B in li/sec.
3) Compute the rate of flow of pipeline C in li/sec.
Solution:
From the results of sieve analysis and the grain size curves for soils 1 and 2.
1) Compute the value of uniformity coefficient Cu.
2) Classify soil No. 1 using USCS Method.
3) Classify soil No. 2 using USCS Method.
Soils 1 and 2
| SIEVE ANALYSIS | |||
| Sieve Number | Diameter mm | Percent Passing % | |
| Soils 1 | Soils 2 | ||
| 4 | 4.760 | 100 | 90 |
| 8 | 2.380 | 99 | 64 |
| 10 | 2.000 | 98 | 58 |
| 20 | 0.850 | 92 | 35 |
| 40 | 0.425 | 70 | 22 |
| 60 | 0.250 | 46 | 15 |
| 100 | 0.150 | 25 | 10 |
| 200 | 0.074 | 0 | 4 |
————–
Solution:
A retaining wall 8m. high is supporting a horizontal back fill having a dry unit weight of 1600 kg/m3. The cohesion less soil has an angle of friction of 33°.
1) Compute the Rankine active force on the wall.
2) Compute the Rankine active force on the wall if the water table is located at a depth of 3.5m. below the ground surface. The saturated unit weight is 18.7 kN/m3.
3) Compute the location of the resultant active force from the bottom for the second condition.
Solution:
A piece of wood floats in water with 50 mm projecting above the water surface. When placed in glycerine of sp.gr. 1.35, the block projects 75 mm above the liquid surface.
1) Find the height of the piece of wood.
2) Find the sp.gr. of wood.
3) Find the weight of the wood if it has a cross sectional area of 200 mm x 200 mm.
Solution:
A reservoir of glycerine has a mass of 1200kg and a volume of 0.952 m3.
1) Find its weight in kN.
2) Find its specific weight.
3) Find its specific gravity.
Solution:
From the given soil profile shown, the ground surface is subjected to a uniform increase in vertical pressure of 12 N/cm2.
1) Compute the buoyant unit weight of clay.
2) Compute the overburden pressure Po of mid-height of the compressible clay layer.
3) Compute the total settlement due to primary consolidation.
Solution:
Saturated clay having a thickness of 20m. has a void ratio of 0.68 and a specific gravity of 2.7.
1) Compute the density of clay.
2) Compute the total vertical stress at the bottom.
3) Compute the effective stress at the bottom.
Solution:
The total weight of soil when saturated 1526g and the weight of the soil after drying is 1053g. If the specific gravity of soil is 2.84.
1) Compute the moisture content.
2) Compute the void ratio.
3) Compute the porosity.
Solution:
A cylindrical tank 4m. in diameter and 6m. high is filled with water. It is tilted to a position enough for the water surface to cut the diameter of the base.
1) How much water retained in the tank.
2) If the tank is placed in vertical upright position, how deep is the water in the tank.
3) How fast in rpm could the tank be rotated about its vertical axis so that the depth of water at the center is zero.
Solution:
A wooden storage vat full of oil sp.gr. = 0.80 is in the form of a frustum of a cone, 2m. diameter at the top and 4 meters diam. at the bottom and 3m. high. It is provided with 2 steel hoops, one at the top and one at the bottom.
1) Compute the hydrostatic force on the side of the container.
2) How high is the said force above the bottom?
3) Compute the force in the bottom hoop.
Solution:
Water flows through an almost level channel 30m. wide at 12 m3/s. The depth gradually increases form 1.0m. to 1.1m. for a length of flow of 5m.
1) What is the head loss?
2) What is the slope of the energy gradient.
3) Compute the value of the roughness coefficient.
Solution:
A dense silt layer has the following properties
Void ratio e = 0.40,
Effective diameter d10 = 10 μm
Capillary constant C = 0.20 cm2
Free ground water level is 8.0 m. below the ground surface.
1) Find the height of capillary rise in the silt. Capillary rise is given h = C/ed10
2) Find the vertical effective stress in kPa at 5m. depth. Assume γs = 26.5 kN/m3 and that the soil above the capillary action rise and ground surface is partially saturated at 50%.
3) Find the vertical effective stress at 10m. depth. Assume γs = 26.5 kN/m3 and that the soil above the capillary action rise and ground surface is partially saturated at 50%.
Solution:
A footing 6m. square carries a total load, including its own weight, of 10,000 kN. The base of the footing is at a depth of 3m. below the ground surface. The soil strata at the site consist of a layer of stiff fully saturated clay 27.5m. thick overlying dense sand. The average bulk density of the clay is 1,920 kg/m3 and its average shear strength determined from undrained tri-axial test is 130 kN/m2. Given is Terzaghi’s ultimate bearing capacity for square footing:
qu = 1.3c Nc + γ Df Nq + 0.4 γ B N y
Use the table 1 of page G-364 to obtain the bearing capacity factors.
θ = 0°
1) Determine the gross foundation pressure.
2) Determine the net foundation pressure.
3) Calculate the factor of safety of the foundation against complete shear failure under the undrained condition (both gross and net). Side cohesion on the foundation may be neglected.
Solution:
A given layer of soil has a dry unit weight of 14.72 kN/m3 and a saturated unit weight of 20.12 kN/m3. The ground water table is located 2m. below the ground surface.
1) What is the total stress at point A 4.5 m. below the ground surface.
2) What is the pore pressure at point A 4.5 m. below the ground surface.
3) What is the effective stress at point A 4.5 m. below the ground surface.
Solution:
From the following data of a grain size analysis
Sieve Size *** Sieve *********% Finer ****************************** ************Opening (mm) *(by Weight)
# 4 4.75 90
# 8 2.36 64
# 10 2.00 58
# 25 0.71 30
# 60 0.250 22
# 100 0.150 10
# 200 0.075 4
1) What is the effective size.
2) Find the coefficient of uniformity.
3) What is the classification of soil according to USCS.
Solution:
Given the different layer of soil with their respective coefficient of permeability.
1) What is the equation in determining the equivalent horizontal coefficient of permeability.
2) What is the equivalent horizontal coefficient of permeability if each soil layer is 3m. thick.
3) What is the total flow if iav = 0.70
Solution:
A soil sample was determined in the laboratory to have a liquid limit of 41% and a plastic limit of 21.1%. If the water content is 30% determine the following:
1) Plasticity index.
2) Liquidity index.
3) What is the characteristic of soil.
Solution:
A soil sample has a natural water content of 22.5% and it is known to have a sp.gr. of 2.6. in order to determine the moist density of the soil, a portion of soil weighing 224 g is put in a 500cm3 container. It is filled with 382 cm3 of water to fill the container.
1) Determine the moist unit weight of soil.
2) Determine the dry unit weight of soil.
3) Determine the void ratio.
Solution:
Carbon tetrachloride with a mass of 500 kgs is placed in a container with 0.325 m3. In volume.
1) Calculate its density.
2) Calculate its specific weight.
3) Determine also its weight.
Solution:
A trapezoidal channel has a bottom width of 6m. and side slopes of 2 hor. to 1 vertical. When the depth of flow is 1.2m., the flow is 30.40 m3/s.
1) Compute the specific energy.
2) Compute the slope of channel if n = 0.014.
3) Compute the average shearing stress at the boundary.
Solution:
A pipe network consists of pipeline 1 from A to B it is connected to pipelines 2 and 2, where it merges again at joint C to form a single pipeline 4 up to point D. Pipelines 1, 2 and 4 are in series connection whereas pipelines 2 and 3 are parallel to each other. If the rate of flow from A to B is 10 liters/sec. and assuming f = 0.02 for all pipes, compute the following:
Pipelines Diameter Length
1 200 mm Ø 3000 m.
2 300 mm Ø 2200 m.
3 200 mm Ø 3200 m.
4 400 mm Ø 2800 m.
1) Rate of flow of pipeline 3.
2) Rate of flow of pipeline 2.
3) Total head loss from A to D.
Solution:
From the figure shown, the gate is 1m. wide and is hinged at the bottom of the gate.
1) Compute the hydrostatic force acting on the gate.
2) Compute the location of the center of pressure of the gate from the hinged.
3) Determine the minimum volume of concrete (unit weight = 23.6 kN/m3) needed to keep the gate in a closed position.
Solution:
A block of wood 0.6m. x 0.6m. x “h” meters in dimension was thrown into the water, it floats with 0.18m. projecting above the water surface. The same block was thrown into a container of a liquid having a sp.gr. of 0.90 and it floats with 0.14cm. projecting above the liquid surface.
1) Determine the value of “h”.
2) Determine the specific gravity
3) Determine the minimum volume of concrete (unit weight = 23.6 kN/m3) needed to keep the gate in a closed position.
Solution:
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