A vertical rectangular gate as shown is 2m. wide, 6m. high is hinged at the top, has oil (sp.gr. = 0.84) standing 7m. deep on one side, the liquid surface being under a pressure of 18.46 kPa.
1) Compute the hydrostatic force acting on the gate.
2) How far is the force acting below the hinged.
3) How much horizontal force applied at the bottom is needed to open the gate.
Solution:
A tank 12m. high filled with oil having a unit weight of 9.4 kN/m3 is to be built on a site. The existing soil prefile consists of a 3.6m. sand layer underlain by a 16m. clay layer. The water table is on the ground surface. Neglecting the weight of the tank.
1) Compute the compression index of clay.
2) Compute the settlement under the center of the tank.
3) Find the minimum depth in the gournd to which the tank must be placed in order to minimize settlement.
Solution:
For a certain soil the cohesion c is 50 kN/m2, the unit weight is 19.2 kN/m3. Angle of friction Ø = 10°.
1) Assuming local shear failure, calculate the net ultimate bearing capacity in kPa for a strip footing of width = 1.25m. at a depth = 3m.
2) Considering shear failure only, calculate the safe load in kN of rectangular footing 6m. long by 1.25m. wide using a load factor of 2.5.
3) What soil properties is needed in the design of a footing.
a) Plasticity index
b) Atterbergs limit
c) Compressibility
d) Permeability
Solution:
A hollow cylinder 1.1m. in diameter and 2.4m. long weights 3825 N.
1) How many kN of lead weighing 110 kN/m3 must be fastened to the outside bottom to make the cylinder float vertically with 1.9m. submerged in fresh water?
2) How many kN of lead weighing 110 kN/m3 must be placed inside the cylinder to make the cylinder float vertically with 1.90m. submerged in fresh water?
3) What additional load must be placed inside the cylinder to make the top of the cylinder flush with the water surface?
Solution:
The three reservoirs A, B and C are connected by pipelines A, B and C respectively. The elevation of reservoir A is equal to 200m. while that of C is 178m. The discharge flowing towards reservoir B is 0.60 m3/s. Reservoir B is higher than that on C.
Pipes Diam. Length Friction factor “f”
A 800mm 1500m 0.0158
B 600mm 450m 0.0168
C 450mm 1200m 0.0175
1) Compute the rate of flow out of reservoir A
2) Compute the rate of flow towards reservoir C.
3) Compute the elevation of reservoir B.
Solution:
The velocity of oil flowing thru a 30mm diameter pipe is equal to 2 m/s. Oil has a kinematic viscosity of 5 x 10-5 m2/s. If the pipe has a length of 120m.
1) Compute the Reynolds Number.
2) Compute the friction factor.
3) Compute the head loss of the pipe.
Solution:
A retaining wall 7m. high is supporting a horizontal back fill having a dry unit weight of 1570 kg/m3. The cohesionless soil has an angle of friction of 34° and a void ratio of 0.68.
1) Compute the Rankine active force on the wall.
2) Compute the Rankine active force on the wall if water logging occurs at a depth of 3m. from the ground surface.
3) Compute the location of the resultant active force form the bottom.
Solution:
A consolidated drained tri-axial test was conducted on normally consolidated clay. The results were as follows:
Chamber confining pressure = 138 kPa
Deviator stress = 258 kPa
1) Compute the friction angle of the soil.
2) Compute the normal stress at failure.
3) Compute the shear at failure.
Solution:
A 600 mm Ø steel pipe, 10mm thick carries water under a head of 325m.
1) Determine the actual stress in kN per meter length of pipe.
2) If the head is increased to 500 meters, what is the actual stress on the wall in MPa?
3) If the head is increased to 500m, what thickness is required assuming an allowable tensile stress of 113 MPa and efficiency of the connection is 80%.
Solution:
From the following figure
| D | 4 | Inches |
| H1 | 0.3 | Feet |
| K1 | 0.00471 | ft/min |
| h | 1.25 | feet |
| d | 1.5 | inches |
| H2 | 0.2 | feet |
| K2 | 0.000522 | ft/min |
| H | 0.5 | Feet |
1) Determine the total flow in ft3/min.
2) Find the equivalent value of Kf for both sand and silt.
3) Determine the volume of water which percolate after 30 min in cm3.
Solution:
A dense silt layer has the following properties
Void ratio e = 0.30,
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/e D10
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:
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:
A retaining wall 5m. 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 32°.
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 2.5m. 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:
For a certain soil the cohesion c is 50 kN/m2, the unit weight is 19.2 kN/m3. Assuming local shear failure and angle of friction Ø = 10°.
1) Calculate the net ultimate bearing capacity in kPa for a strip footing of width = 1.25 m. at a depth = 4.5 m. Terzaghi’s ultimate bearing capacity equation for strip footing is given by
qu = c’ Nc’ + γ Df Nq’ + ½ γ B Ny’
2) Considering shear failure only, calculate the safe bearing pressure qs on a footing 6m. long by 1.25m. wide, using a load factor of 2.5. Given:
3) Calculate the safe total load in kN of the rectangular footing.
Solution:
A consolidated drained tri-axial test was conducted on a normally consolidated clay. The results were as follows:
Chamber confining pressure = 300 kPa
Deviator stress = 400 kPa
1) Compute the angle of friction of the clay sample.
2) Compute the shear stress on the failure plane.
3) Compute the effective normal stress on the plane of max. shear.
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:
A confined aquifer underlies an unconfined aquifer as shown in the figure.
1) Compute the equivalent horizontal coeff. Of permeability.
2) Compute the hydraulic gradient.
3) Compute the flow rate from one stream to another per meter width.
Solution:
The pipe connection shown shows a series parallel connection. The rate of flow in the pipeline (1) is 300 liters/sec. Assuming equal values of f = 0.02 for all pipes.
1) Compute the discharge of pipeline 2.
2) Compute the discharge of pipeline 3.
3) Compute the discharge of pipeline 4.
Solution:
An open cylindrical tank one meter in diam. and 2.5 m. high is 3/5 full of water. If the tank is rotated about its vertical axis, what speed should it have in rpm so that:
1) The water could just reach the rim of the tank without water being spilled out.
2) The depth of water at the center is zero.
3) There is no water at the bottom within 20 cm. from the vertical axis.
Solution:
A vertical plate shown is submerged in vinegar having a sp.gr. = 0.80. Assume unit weight of water to be 9.79 kN/m3.
1) Find the depth of the center of pressure of section A1 from the liquid surface.
2) Find the magnitude of the hydrostatic force on one side of the plate.
3) Find the depth of the center of pressure of the whole section from the liquid surface.
Solution:
A pump draws water from reservoir A and lifts it to reservoir B as shown. The loss of head from A to 1 is 3 times the velocity head in the 150mm pipe and the loss of head from 2 to B is 20 times the velocity head in the 100 mm pipe. When the discharge is 20 liters/sec.
1) Compute the horsepower output of the pump in kilowatts.
2) Compute the pressure head at 1.
3) Compute the pressure head at 2.
Solution:
The following data shows the results of the liquid limit and plastic limit test
A. Liquid Limit
| Test Number | 1 | 2 | 3 | 4 |
| No. of blows | 39 | 23 | 20 | 13 |
| Weight of Wet soil + container | 22.24g | 21.19g | 21.27g | 26.12g |
| Weight of Dry soil + container | 19.44g | 18.78g | 18.75g | 22.10g |
| Weight of Container | 12.74g | 13.24g | 13.06 | 13.27g |
B. Plastic Limit
| Test Number | 1 | 2 |
| Weight of Wet soil + container | 22.12g | 21.84g |
| Weight of Dry soil + container | 20.42g | 20.19g |
| Weight of Container | 13.07g | 13.18g |
C. Natural water content
| Test Number | 1 | 2 |
| Weight of Wet soil + container | 17.53g | 16.97g |
| Weight of Dry soil + container | 14.84g | 14.36g |
| Weight of Container | 7.84g | 7.5g |
1) Compute the liquid limit. Use the table shown.
2) Compute the plasticity index.
3) Compute the liquidity index.
Solution:
A jet of water 250 mm in diameter impinges normally on a flat steel plate. If the discharge is 0.491 m3/s.
1) Find the force exerted by the jet on the stationary plate.
2) If the flat plate is moving at 2 m/s in the same direction as that of the jet find the force exerted by the jet on the plate.
3) If the plate moving a 4 m/s in the same direction as that of the jet, find the work done on the plate per second.
Solution:
The cross section of a right triangular channel is shown with a coefficient of roughness n = 0.012. If the rate of flow = 4 m3/s.
1) Compute the critical depth.
2) Compute the critical velocity.
3) Compute the critical slope.
Solution:
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