management skills

`A 20cm diameter pipe of length 100m with z = 60m with f = 0.02 and loss of head due to entrance coefficient k = 0.5. What is the flow rate?
Solution:

Find the width in m of the channel at the back of a suppressed weir using the following data: H = 28.5cm; d = 2.485m; Q = 0.84 cu.m/sec. Consider the velocity of approach and use the Francis formula.

Solution:

Water flows in a 2m. wide rectangular flume at the rate of 2.75 cu.m./sec. with a mean velocity of 3.5 m/s. To what depth, in cm., can the water jump? Use g = 9.81

Solution:

rectangular concrete flume, 4m wide, carries water at the rate 5 cu.m/sec. Determine the critical depth in m. Use g = 9.81.

Solution:

The length of the crest of a trapezoidal weir is 2m. The sides are slopping at 75°57’49” with the horizontal. Find the discharge in cu.m/sec if the head on the weir is 0.5m.

Solution:

A trapezoidal flume of most efficient proportion has a base width of 1.5m. Its full discharge is 3cu.m/sec. If the same material were used for the most efficient rectangular section, by how much would the discharge decrease in cu.m/sec.

Solution:

An open tank 1.82m. square, weighs 3425N and contains 0.91 m. of water. It is acted by an unbalanced force of 10400 N parallel to a pair of sides. What is the force (N) acting in the side with the greatest depth?

Solution:

Hydraulic jump occurs in a trapezoidal channel with sideslopes of 1:1 and base of 4m. If the upstream depth before the jump is 1.0m. and downstream depth is 2m., what is the discharge?

Solution:

The jet of a horizontal nozzle strikes a vertical plate with a force equal to 7000N. If the discharge flowing at the nozzle is 0.12 m3/s. Compute the diameter of the jet.

Solution:

A tank filled with water to a depth of 2.4m. is accelerated upward at a rate of 3 m/s2. The velocity of the discharge at the orifice 2cm. in diameter located at the bottom of the tank is:

Solution:

An unbalanced vertical force of 270N upward accelerates a volume of 0.044 m3 of water. If the water is 0.9m. deep in a cylindrical tank, what is the force in N acting on the bottom of the tank?

Solution:

Determine the discharge in MLD of a 2800 mm gravity flow concrete aqueduct 4km long with a head loss of 5.6m. Assume pipe is flowing just full with roughness coeff. of 0.015.

Solution:

Determine the magnitude of the force on the inclined gate 1.5m. by 0.5m. shown in the figure. The tank is completely closed and the pressure gage at the bottom of the tank reads 90000 N/m2. Use 9800 N/m3 for H2O. sin 60 = x/1.5; x= 1.299/2 ; 0.65
Solution:

A circular pipe 2m. in diameter carries water at a depth of ¾ of its diameter. What is the hydraulic radius?

Solution:

An open vessel 30cm. in diameter and 90cm high is filled with water to a depth of 45 cm. Find the magnitude of the velocity such that the vortex is just at the bottom.

Solution:

A large cylindrical steel tank 4m. high with its bottom on level ground contains two layers of liquid. The bottom layer is water 2m. deep. The top layer is occupied by a liquid whose specific gravity is not known to a depth of 1m. A 50 mm diam. orifice with a coefficient of velocity of 0.98 is situated one meter from the bottom of the tank. The jet from the orifice hits the ground 2.75m horizontally away from the vena contracta. Determine the sp.gr. of the liquid.

Solution:

What is the discharge capacity of a concrete pipe culvert 4 ft. in diam. And 10m. long if the difference in water level at the outlet is 10m. Assume coefficient of discharge C = 0.74.

Solution:

A dam 40m. high has a spillway discharging at 2m. deep and a crest length of 10m. If c = 3.2, find the discharge in cu.m. sec.

Solution:

Q = C L H3/2
Q = 3.2(10)(2)3/2
Q = 90.5 m3/s

A 600 mm. diameter water main is bent at an angle of 45° from the horizontal. What vertical component of dynamic pressure is developed in the bend if the velocity in the pipe is 2 m/s?

Solution:

Pipes from three reservoirs meet at point C which is at elevation 366 m. Assume all pipes are PVC, with Hazen Williams C = 150. Pressure at point C is 18.3 psi.
Pipeline Diameter(inches) Length(ft) x 10 10000 y 8 4000 z 12 5000
Find the head loss of pipeline x.

Solution:

A water tank is filled with water to a height of 4.3m. above the 10 mmØ orifice which is connected at the side of the tank, how far would the water have traveled horizontally if the orifice is 4.3m. above the ground?

Solution:

Water flows in the triangular channel at a rate of 222 lites/sec. Find the depth of flow if the channel slope is 0.0008 and n = 0.016. The two sides of the channel is incline at an angle of 60° with the horizontal.

Solution:

A concrete spillway controls a reservoir having an area of 46000 sq.m. with a permanent crest elevation of 64m. and a length of crest of 38.9 ft. is drawn from elevation of the water surface after 0.70 hours. Use Francis Formula.

Solution:

For optimum dimension, determine the width of the rectangular channel with slope S = 0.0008 and n = 0.012 if the rate of flow is 4 m3/s.

Solution:
Other solution: A=2h(h)

A rectangular tank is divided by a partition into two chambers as shown. An orifice having a cross sectional area of 0.2 m2 for which C = 0.93 is located near the bottom of the chamber. At a certain time, the water level in chamber A is 305 cm. higher than in chamber B. Find the time it will take for the water surfaces in the two chambers to be at the same level. Use the most nearest value.

Solution:

An open channel having a trapezoidal section is required to discharge 200 m3/sec. of water when running full. If the slope S = 0.002 and n = 0.014, compute the bottom width for a most efficient section.

Solution:

A rectangular weir contracted a both ends is 10.27 m. wide extends across a rectangular channel. Find the head of water for a discharge of 3m3/sec.

Solution:
Q = 1.84(L – 0.2H) H3/2
3 = 1.84 [10.27 – 0.2H] H3/2
1.63 = 10.27 H3/2 – 0.2 H5/2
Try H = 0.295

A vessel has an orifice located in the vertical side of a cylindrical vessel under a head “h”. The jet strikes a horizontal plane 2.5m. below the center of the orifice at a point 2.5m. measured horizontally from the vertical plane of the orifice. Determine the value of “h”.

Solution:

The figure shows the column loads and the footing elevation. The depth of the pad is adequate and the DL of the footing maybe neglected. The columns are axially loaded only. Determine the dimension of the footing if the allowable soil pressure is 2000 psf.

Solution:

Locate the centroid of the axial loads.
90x = 50(12) + 40(0) x = 6.67 ft.
The centroid of footing should coincide with the centroid of the loads

Tow reservoirs having a difference in elevation of 82 ft. is connected by a 3 inch diam. pipe, 2500 feet long with a roughness coefficient n = 0.012. After 10 years, the roughness coefficient n = 0.0265. Find the percentage change in discharge.

Solution:

A spillway 2m. deep goes over a dam 40 m. high If Cw = 3.2, determine the discharge?

Solution:

Q = Cw L H3/2
Q = 3.2(1)(2)3/2
Q = 9.05 m3/s/meter

Oil with a specific gravity of 0.80 is 0.91 m. deep in an open tank which is otherwise filled with water. If the tank is 3.05 m. deep, what is the pressure at the bottom of the tank?

Solution:

PA = 9.81(0.8)(0.91) + 9.81(2.14)
PA = 28.14 kPa

A gate 2m. high and 4m. wide is flush with water at the top. Determine the moment at the bottom.

Solution:

A mat foundation having a length of 100ft. by 32ft. carries a total weight of structure plus live load of 5200 tons. The mat foundation is supported by sand underneath. Unit weight of sand is 120 pcf. The N value from the standard penetration test is equal to 18 with a correction factor Cn = 0.62. If the base of the footing is 8ft. below the ground level.

1) Compute the overburden pressure 8ft. below the ground.
2) Compute the allowable net soil pressure.
3) Compute the factor of safety against bearing capacity failure.

Solution:

Note:
Because the differential settlement of a mat foundation are less than those of an individual footing foundation designed for the same soil pressure, it is reasonable soil pressures on mat foundations. Experience has shown that a pressure approximately 2 times as great as that allowed for individual footings maybe used because it does not lead to detrimental differential settlements.

A dam gate in the figure shown admits water to a horizontal canal. Considering the pressure distribution hydrostatic at section O, compute the discharge per meter of width when y = 1.0 m.

Solution:

In the figure shown Zp = 4m., length of pipe from reservoir to pump is 150m., from pump to nozzle is 1500m., f = 0.02 and diameter of pipes are 450mm and 600mm respectively. Neglecting minor losses the water maybe pumped if the atmospheric pressure is 95kPa absolute and the water temperature is 27°C. At this temperature the vapor pressure Pv = 3.5kPa absolute.
Determine:

1) Velocity of water in 450mmØ pipe.
2) The velocity of water in 600mmØ pipe.
3) The power lost due to friction.

Solution:
Note: If the absolute pressure at any point in a system falls to the vapor pressure Pv, water vapor and dissolved gasses will collect in high spots and obstruct the flow. The lowest pressure in the system occurs at point C on the suction side of the pump and flow would stop when

Curve wall ABC is a quarter circle having a radius of 6m. What is the vertical force acting on the gate per unit width.

Solution:

The 100 duct is 60mm in diameter. If the fluid has ρ = 920kg/m3 and a viscosity of μ = 0.29 Pa.s.

1) Compute the velocity of flow on the duct.
2) Compute the Reynolds Number
3) Compute the discharge.

Solution:

A tank 10m. is filled with 2m. of water is accelerated horizontally 2.45 m/s2. What is the minimum pressure acting at the bottom of the tank? Assume the tank is high enough to prevent spilling.

Solution:

A dam triangular in shape has a height of 24m. and a base of 12m. Density of masonry is 2,500 kg/cu.m. If it is supporting was at a depth of 20m. Where is the location of the resultant vertical force from the heel office dam.

Solution:

Water flows from an upper reservoir to a lower one while passing through a turbine as shown. Neglect minor losses.

1) Find the velocity of water
2) Find the head loss due to friction
3) Find the power generated by the turbine.

Solution:

The jets from a garden sprinkler are one inch in diameter and are normal to the 2ft. radius The pressure at the base of the nozzles is 60 psi. Use Cv = 0.85, Cc = 1.0.

1) What is the velocity of the jet?
2) What is the force exerted by the jet?
3) What force must be applied on each sprinkler pipe 1 ft. from the center of rotation to maintain equilibrium.

Solution:

What is the critical depth of a trapezoidal canal for a flow of 2300 cfs. The width at the bottom of the canal is 12ft. with a side slope of 2 horizontal to 1 vertical.

Solution:

Find the total hydrostatic force acting on the gate shown.

Solution:

A rectangular weir having a length of one meter is constructed at one end of a tank having a square section 20×20m. and a height to 10m. If the initial head on the weir is 1m., determine the time required to discharge a volume of 72m3.

Solution:

The pipe flow in the figure is driven by pressurized air in the tank. Assuming f = 0.014 and the flow rate is 13.60 liters/sec.

1) Find the velocity of the water in the pipe.
2) Find the head loss in the pipe neglecting minor losses.
3) Find the gage pressure needed to provide a flow rate of 13.60 liters/sec.

Solution:

An open channel having a slope of 0.0065 is to carry 1.0 m3/s. The channel material has a “n” value of 0.011. Find the depth of the most efficient cross section for a triangular section.

Solution:

For the given soil: void ratio, e = 0.50, Gs = 2.70, h1 = 1.5m., h2 = 3.0m.

1) Which of the following gives the effective unit weight of soil.
2) Which of the following gives the effective stress at A
3) Which of the following gives the hydraulic gradient for quick sand condition.

Solution:

1) Effective unit weight of soil

2) Effective stress at A:
Effective stress at A = 11.12(3)
Effective stress at A = 33.36 kN/m2
3) Hydraulic gradient for quick sand condition

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:

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 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:

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 20.40 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:

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 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: 7-2.24= 4.76; 4.76-(6/2) = 1.76(h)

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:

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:

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: In A1 7/2=3.5 ; from surface to center of A1 = 2+3.5 = 5.5

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:

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:

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:

The field unit weight of the soil sample is 1960 kg/m3 and the unit weight of the soil particle is 2700 kg/m3. If the e max = 0.69 and e min = 0.44.

1) Compute the dry unit weight in kN/m3 if the water content is 11%.
2) Compute the void ratio of the soil sample.
3) Compute the relative density of the soil sample.
Solution:

A 0.30m. x 0.30m concrete pile 22m. long is driven in a clayey soil having an unconfined compressive strength of 110 kN/m2. The unit weight of clayey soil is 18 kN/m3. Frictional constant is 0.76 due to skin friction. Assume a factor of safety equal to 2.0 and a bearing capacity factor Nc = 9.

1) Compute the capacity of pile due to skin friction only.
2) Compute the end bearing capacity of pile.
3) Compute the design capacity of the concrete pile.

Solution:

The laboratory apparatus shown in the figure maintains a constant head in both the upper and lower reservoirs. The soil sample is a silty sand with a hydraulic conductivity K = 5 x 10-3 cm/sec. and a moisture content of 18.5%. Specific gravity of soil sample is 2.70.(2005)

1) Compute the seepage velocity in cm/sec.
2) Determine the time required for the plug of colored water to pass through the soil. Assume also that the colored water has the same unit weight and viscosity as plain water.
3) Compute the discharge of water.

Solution:

Two open cylindrical tanks are connected by an orifice having a cross sectional area of 0.004 m2. Tank A is 8m. in diam. and its water level is 10m. above that of B whose diameter is 5m. If the coeff. Of discharge is 0.60.

1) Find the discharge flowing in the orifice.
2) How long will it be before the water surfaces are at the same level?
3) How soon after will the water surfaces be 4m. apart?

Solution:

Two reservoirs A and B have elevations of 250 m and 100m respectively. It is connected by a pipe having a diameter of 25 mm Ø and a length of 100m. A turbine is installed at point in between reservoirs A and B. If C = 120, compute the following if the discharge flowing in the pipe is 150 liters/sec.(2005)

1) Head loss of pipe due to friction.
2) The head extracted by the turbine.
3) The power generated by the turbine.

Solution:

discharge of 750 liters/sec. flows through a pipe having a diameter of 400 mm Ø. Length of 65m. long, compute the head loss of the pipeline using(2005)

1) Mannings Equation with n=0.013
2) Darcy Weishback formula with f = 0.012.
3) Hazen Williams Formula with C = 100.
Solution:

A vertical tank having a horizontal cross-sectional area of 0.4 square meter has 0.0003m2 orifice at its bottom. The initial head on the orifice is h1 = 1.2m. It takes 312 second for the water level to drop from 1.2m to 0.6m.
1. What is the coefficient of discharge?
A. 0.65
B. 0.62
C. 0.68
D. 0.72
2. If C = 0.6, how long will it take for the water level to drop from 1.2m to 0.8m?
A. 202 s
B. 256 s
C. 185 s
D. 231 s
3. If C = 0.6, what is the head on the orifice after 240?
A. 0.52 m
B. 0.43 m
C. 0.85 m
D. 0.73 m
Solution:

Water flow at the rate of 1.2 m3/s at a depth of 1.5m in a 10-m wide irrigation canal. Assume uniform flow and use n = 0.035.
1. Calculate the nearest value to the specific energy in Joule/Newton.
A. 1.5124
B. 1.5087
C. 1.5003
D. 1.5024
2. Determine the slope of the channel bed in meter per kilometer.
A. 0.0064785
B. 0.000064785
C. 0.0000064785
D. 0.064785
3. Determine the boundary shearing stress at the walls in Pa.
A. 0.00733
B. 0.0733
C. 0.0007333
D. 0.733
Solution:

A 4.2m thick layer of sand is underlain by a layer of clay. The water table is 2m below the ground (sand) surface. For sand, Gs = 2.65 and the average void ratio is 0.52. The sand above water table has a degree of saturation of 0.37. The saturated nit weight of the clay layer is 20.2 kN/m3.

1. Determine the unit weight of sand above water table in kN/m3
A. 17.86
B. 20.46
C. 10.65
D. 18.35
2. Determine the total stress at a point 10m below the ground.
A. 199 kPa
B. 123 kPa
C. 232 kPa
D. 167 kPa
3. Determine the effective stress at a point 10m below the ground.
A. 134.5 kPa
B. 120.4 kPa
C. 156.9 kPa
D. 111.1 kPa

Solution:

A soil sample taken from subgrade have a density of 1900 kg/m3 with moisture content of 11%. Laboratory tests reveals that the soil solids have density of 2660 kg/m3 and the maximum and minimum void ratios of the soil mass are 0.63 and 0.44, respectively.
1. Determine the nearest value to the dry unit weight of the soil in kN/m3.
A. 17.4
B. 16.8
C. 16.1
D. 18.3
2. Determine the relative density of the sample.
A. 0.554
B. 0.654
C. 0.425
D. 0.722
3. Determine the relative density of the sample.
A. 0.63
B. 0.54
C. 0.40
D. 0.48
Solution:

A calibration test of a 0.00785-m2 circular sharp-edged orifice in a vertical side of a large tank showed a discharge of 22,300 N of water in 1minute & 40 seconds at a constant head of 1.20m. Measurement of the jet showed that it traveled 1.92m horizontally while dropping 0.8m.
1. Determine the coefficient of discharge.
A. 0.621
B. 0.597
C. 0.649
D. 0.721
2. Determine the coefficient of velocity.
A. 0.84
B. 0.93
C. 0.74
D. 0.98
3. Determine the coefficient of contraction.
A. 0.77
B. 0.97
C. 0.61
D. 0.67
Solution:

Water is flowing in a 200-mm diameter rigid pipe that is 650m long. The increase in pressure caused by instantaneous closure of the valve near the exit is 700kPa. Bulk modulus of elasticity of water is 2.07 x 109 Pa.
1. What is the celerity of pressure wave in m/s?
A. 1439
B. 1621
C. 1256
D. 1176
2. What is the maximum discharge in m3/s?
A. 0.0188
B. 0.0279
C. 0.0232
D. 0.0153
3. What water hammer pressure is expected if the valve is closed in 3 seconds?
A. 289kPa
B. 187kPa
C. 342kPa
D. 211kPa
Solution:

Given the following laboratory result of a sub grade material: γd max = 1.735 g/cc Wet weight = 2200 g
MC max = 15.75% Dry weight = 1879 g
Volume of soil = 1130 cc
1. Determine the dry unit weight of the soil in grams/cc.
A. 1.66
B. 1.95
C. 1.82
D. 1.54
2. Determine the moisture content in percent.
A. 15.4%
B. 17.1%
C. 21.8%
D. 19.3%
3. Determine the percent compaction and indicate whether it is adequate as subgrade material.
A. >95.6% yes
B.