Fluid Mechanics PDF

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FLUID MECHANICSProperties of Fluid Fluid Density, Unite weight and specific volume Situation 30: A 325 L of carbon tetrachloride weighs 500 kg. 958. Which of the following most nearly given its density? a. 1.850 kg/m 3 b. 2,010 kg/m 3 c. 1,538 kg/m 3 d. 1,774 kg/m 3 959. Which of the following most ...

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FLUID MECHANICS Properties of Fluid Fluid Density, Unite weight and specific volume Situation 30: A 325 L of carbon tetrachloride weighs 500 kg. 958. Which of the following most nearly given its density? a. 1.850.60 kg/m3 b. 2,010.29 kg/m3 c. 1,538.46 kg/m3 d. 1,774.32 kg/m3 959. Which of the following most nearly gives its specific weight? a. 19.72 kN/m3 b. 15.09 kN/m3 c. 17.41 kN/m3 d. 18.15 kN/m3 960. Which of the following most nearly gives its specific gravity? a. 1.54 b. 1.77 c. 1.85 d. 2.01 Hydrostatic Pressure Situation 31: A closed tank with pressure gages tapped into it at three different elevations contains air, oil and water as shown in the figure

963. Which of the following most nearly gives the pressure reading at C? a. 72.95 kPa b. 72.26 kPa c. 71.43 kPa d. 72.61 kPa Manometry Situation 32: A piezometer column mercury manometer and a pressure gage are connected to a tank of water. The top of the water is pressured air. See figure:

Air

Water

4m

A 1m

Mercury

964. If the pressure at A is 85 kPa, how high will the water rise in the 0.50 m Air piezometer column at the left? 50 kPa a. 4.00 m b. 6.23 m A c. 5.52 m d. 8.66 m 1m 965. Which of the following nearly Oil 58.53 kPa gives the reading in the pressure B 0.50 m gage? a. 37.72 kPa b. 35.23 kPa 1m c. 45.76 kPa d. 39.24 kPa Water 966. Which of the following most nearly gives the mercury in the C manometer? a. 0.71 m b. 0.60 m 961. Which of the following most c. 0.52 m d. 0.45 m nearly gives the specific weight of the Hydrostatic Force oil? Hydrostatic Force on Plane Surface a. 7.83 kN/m3 3 Situation 33: A rectangular gate 1.50 b. 8.53 kN/m m wide and 4 m high supports oil (S = c. 6.18 kN/m3 0.80 whose liquid surface is exposed d. 9.23 kN/m3 to a constant pressure of -10 kPa as 962. Which of the following most shown in the figure. The top of the nearly gives the specific gravity of the gate is hinged and the bottom is kept oil? closed by a stop. a. 0.94 b. 0.63 c. 0.87 d. 0.80

Hinge P = -10 kPa

Oil

4m Stop

967. Which of the following most nearly gives the total hydrostatic pressure acting on the gate? a. 54.67 kN b. 34.18 kN c. 43.58 kN d. 57.72 kN 968. Which of the following most nearly gives the distance of the total hydrostatic pressure measured from the hinge? a. 3.84 m b. 2.13 m c. 2.85 m d. 3.25 m 969. Which of the following most nearly gives the reaction at the stop? a. 46.25 kN b. 38.61 kN c. 41.50 kN d. 32.78 kN Situation 34: In the figure, rectangular flashboard MN shown in cross section (a = 5.40 m) is provided at B.

971. If the flashboard is pivoted at the location determined above and the water surface is 1 m below M. which of the following most nearly gives the horizontal reaction at B? a. 86.25 kN/m b. 77.39 kN/m c. 62.30 kN/m d. 95.12 kN/m 972. Which of the following most nearly gives the reaction at N? a. 15.23 kN/m b. 19.75 kN/m c. 16.12 kN/m d. 17.59 kN/m Hydrostatic Force on Curved Surface Situation 35: In the figure, surface AB is a quarter arc with radius of 2 m and a width of 1 m. The fluid above surface AB is water at a depth of 2 m and above the water is oil of depth 4 m. Atmospheric pressure prevails on the free surface of oil and on the bottom side of surface AB.

Oil (S = 0.80) 4m

2m

B

Water

M A

a

B

N

970. Which of the following most nearly gives the maximum height f B above N if the flashboard is on the verge of tipping when the water surface rises to M? a. 1.80 m b. 1.50 m c. 1.70 m d. 1.60 m

973. Which of the following most nearly gives the horizontal component of the total hydrostatic pressure acting on surface AB? a. 82.40 kN b. 109.32 kN c. 78.58 kN d. 98.14 kN 974. Which of the following most nearly gives the vertical component of the total hydrostatic acting on surface AB? a. 78.57 kN b. 93.60 kN c. 76.69 kN d. 91.55 kN 975. Which of the following most nearly gives the total hydrostatic pressure acting on surface AB? a. 120.65 kN b. 133.54 kN c. 125.72 kN d. 124.70 kN

Buoyancy Situation 36: An object 75 N when submerged in oil (S = 0.80) and a force of 100 N is required to hold it submerged in mercury. 976. Which of the following most nearly gives the weight of the object? a. 85.94 N b. 72.13 N c. 95.06 N d. 64.79 N 977. Which of the following most nearly gives the volume of the object? a. 0.00125 m3 b. 0.00139 m3 c. 0.00096 m3 d. 0.00214 m3 978. Which of the following most nearly give the specific gravity of the object? a. 5.21 b. 6.29 c. 6.62 d. 7.16 Situation 37: A solid of diameter 1m and average mass density of 780 kg/m3 is completely submerged in a tank filled with water. It is held is place by a string attached to the bottom of the tank, as shown. The mass distribution inside the sphere is non-uniform, so the center of mass lies at a distance 0.50R from the geometric center. Suppose that the sphere is attached rigidly to massless horizontal rod of length 0.75 m and negligible volume oriented along the line formed by the center of mass and the geometric center of the sphere, as shown. The rod is attached on the side of the sphere nearer the center of mass, and the far end of the rod is attached to a fixed pivot.

CM

R

0.75 m T

979. Which of the following most nearly gives the force acting on the sphere? a. 6.12 kN b. 5.14 kN c. 7.05 kN d. 4.97 kN

980. Which of the following most nearly gives the tension T that is needed to hold the sphere in place? a. 1.93 kN b. 3.15 kN c. 2.08 kN d. 2.46 kN 981. Which of the following most nearly gives the reaction on the pivot? a. 1.05 kN b. 1.20 kN c. 0.75 kN d. 0.80 kN Hydraulic Dam Situation 38: The vertical face of a trapezoidal concrete dam (S = 2.40) supports water to a depth of 16 m. Uplift pressure at the base of the dam varies from full hydrostatic pressure at the heel to zero at the toe. The total height of the dam is 18 m. Upper base width is 1.50 m, and the bottom base width is unknown. 982. Which of the following most nearly gives the minimum safe bottom base of the dam if the factor of safety against overturning is 1.60? a. 13.15 m b. 12.03 m c. 11.06 m d. 10.40 m 983. Which of the following most nearly gives the factor safety against sliding if the coefficient of friction between the soil and the base of the dam is 0.75 using the calculated base in the previous question? a. 1.15 b. 1.25 c. 1.05 d. 1.00 984. Which of the following most nearly gives the maximum stress that is likely to occur at the toe of the dam? a. 159.90 kPa b. 34.38 kPa c. 284.60 kPa d. 65.20 kPa Thin-walled Pressure Vessels Situation 39: An open cylindrical wood stave tank having a a diameter of 2 m and height of 4 m is full of water. The upper and lower ends of the tank are held by hoops. 985. Which of the following most nearly gives the tensile force on the upper end hoop? a. 52.32 kN b. 39.24 kN c. 26.16 kN d. 78.48 kN 986. Which of the following most nearly gives the tensile force on the lower end hoop?

a. 52.32 kN b. 39.24 kN c. 26.16 kN d. 78.48 kN 987. If the lower end hoop remains on its position, at what distance should the other hoop be placed from the upper end of the tank so that both hoops will experience the same amount of tensile force? a. 2.67 m b. 1.67 m c. 1.98 m d. 2.98 m Relative Equilibrium Vertical Translation 988. An unbalanced vertical force of 60 lb upward accelerates 1.55 ft3 of water. If the water is 3 ft deep in a cylindrical tank, which of the following most nearly gives the force acting on the bottom of the tank? a. 156.72 lb b. 187.27 lb c. 131.04 lb d. 116.33 lb Horizontal translation 989. An open tank 30 ft long by 4 ft wide by 4 ft deep is filled with 3.25 ft of oil (S 0.822). It is accelerated uniformly from rest to 45 ft/s along its length. Which of the following most nearly gives the shortest time in which the tank may be accelerated without spilling any oil? a. 27.95 sec b. 30.42 sec c. 23.70 sec d. 25.81 sec Rotation Situation 40: A vertical cylindrical tank 3 m in diameter and 5 m high is full of water. 990. Which of the following most nearly gives the angle with the vertical that the tank must be titled so that 10 m3 of water is spilled? a. 43.320 b. 33.690 0 c. 46.68 d. 56.310 991. IF the tank is to be rotated about its axis, which of the following most nearly gives the required angular velocity so that the water profile just touches the bottom of the container? a. 63.05 rpm b. 26.39 rpm c. 6.60 rpm d. 49.07 rpm 992. If the tank is to be rotated about its axis, which of the following most nearly gives the required angular velocity so that there is no water with

0.80 m from the center of the bottom of the tank? a. 7.81 rpm b. 16.82 rpm c. 74.58 rpm d. 50.94 rpm Orifice Falling Head Situation 41: The water in a vertical cylindrical tank is lowered by an orifice from elevation 3 m to elevation 2.50 m in 70 seconds. The orifice is located at the bottom of the tank with elevation 0 m. 993. When the water level is initially at elevation 3 m, which of the following most nearly gives the time required discharging half of its contents? a. 182.58 sec b. 205.82 sec c. 215.72 sec d. 235.31 sec 994. When the water level is initially at elevation 3 m, which of the following most nearly gives the time required to discharge all the contents? a. 713.06 sec b. 803.40 sec c. 850.72 sec d. 629.60 sec 995. IF the tank is accelerated upward at 12 m/s2, which of the following most nearly gives the time required to discharge all the contents when the water level is initially at elevation 3 m? a. 400.15 sec b. 309.34 sec c. 440.53 sec d. 538.82 sec Weir Falling head Situation 42: A V-notch weir is located at one end of a tank having a horizontal square section 12 m x 12 m. The intial head of the water is 1.80 m and it takes 77 seconds to discharge 144 m3 of water. The coefficient of discharge is 0.60. 996. Which of the following most nearly gives the vertex angle of the weir? a. 72.390 b. 81.780 0 c. 77.04 d. 87.800 997. Which of the following most nearly gives the initial discharge over the weir? a. 5.33 m3/s b. 5.84 m3/s c. 4.47 m3/s d. 4.90 m3/s 998. Which of the following most nearly gives the instantaneous discharge after 77 seconds?

a. 0.64 m3/s b. 0.70 m3/s c. 0.59 m3/s d. 0.77 m3/s Pipe Flow Major Losses in Pipes Situation 43: Water is pumped through a 500 mm diameter circular pipe which is 800 m long at a velocity of 2 m/s. 999. Which of the following most nearly gives the head loss using Darcy-Weisbach equation if f = 0.02? a. 6.25 m b. 5.62 m c. 6.52 m d. 5.26 m 1000. Which of the following most nearly gives the head loss using Manning’s formula the n = 0.013? a. 8.56 m b. 7.56 m c. 7.65 m d. 8.65 m Reynolds Number Situation 44: Medium fuel oil having an absolute viscosity of 6.55 x 10-5 ft2/s flows in a steel pipe 4, 100 ft long at a maximum rate of 0.210 cfs. 1001. Which of the following most nearly gives the head loss using Hazen-Williams formula if C = 110? a. 7.34 m b. 7.43 m c. 6.34 m d. 6.43 m 1002. Which of the following most nearly gives the minimum diameter of the pipe required to keep the flow in laminar condition? a. 1.95 ft b. 2.03 ft c. 1.88 ft d. 2.16 ft 1003. Using the diameter obtained in the previous problem, which of the following most nearly gives the friction factor of the pipe? a. 0.032 b. 0.042 c. 0.051 d. 0.059 1004. Which of the following most nearly gives the head loss in the pipe? a. 0.0025 ft b. 0.0047 ft c. 0.0036 ft d. 0.0050 ft Laminar And Turbulent Flow in Pipes Situation 45: An oil with  = 900 kg/m3 and v = 0.0002 m2/s flows upward through a 10 m long pipe segment inclined at 400 with the horizontal. The pressures at the upstream and downstream end of the pipe are 350 kPa and 250 kPa

respectively. The diameter of the pipe is 60 mm. Assume the flow is laminar. 1005. Which of the following most nearly gives the head loss along the pipe segment? a. 4.90 m b. 3.77 m c. 6.10 m d. 5.35 m 1006. Which of the following most nearly gives the discharge? a. 2.08 m/s b. 2.95 m/s c. 3.37 m/s d. 2.70 m/s 1007. Which of the following most nearly gives the Reynolds Number? a. 855 b. 810 c. 824 d. 1.011 Pipe Networks Situation 46: The total head loss from A to E in the pipe system shown in the figure below is 15 m. Assume f = 0.02 for all pipes. Useful properties of the pipes are given in the following table: 1

2

3

Pipe 1 2 3 4 5

Length (m) 450 600 360 480 540

5

4

Diameter (m) 600 500 450 450 600

1008. Which of the following most nearly gives the discharge in pipe 1? a. 0.677 m3/s b. 0.608 m3/s 3 c. 0.896 m /s d. 0.485 m3/s 1009. Which of the following most nearly gives the discharge in pipe 2? a. 0.561 m3/s b. 0.301 m3/s 3 c. 0.411 m s d. 0.553 m3/s 1010. Which of the following most nearly gives the discharge in pipe 3? a. 0.335 m3/s d. 0.267 m3/s 3 c. 0.125 m /s d. 0.486 m3/s Pumps and Turbines Situation 47: Water is pumped at the rate of 20 m3/s from the reservoir and out through the steel pipe, which has a constant diameter of 1.50 m. HazenWilliams constant is 100.

1011. which of the following most nearly gives the total head loss? a. 22.57 m b. 42.10 m c. 35.62 m d. 48.74 m El. 140 m El. 100 m

300 m P

El. 95 m

5 m suction line

1012. Which of the following most nearly gives the power that must be supplied to the water? a. 22,701.86 hp b. 13,556.18 hp c. 18,171.83 hp d. 16,935.59 hp 1013. Which of the following most nearly gives the pressure at the suction line? a. -18.68 kPa b. -19.35 kPa c. -17.51 kPa d. -16.75 kPa Reservoir Problems Two Reservoir Problems Situation 48: The total flow from reservoir A in the figure is 0.394 m3/s and the discharge from pipe 4 is 0.254 m3/s. El. 43 m A 1 2

El. B 3 4 El. 14 m

Pipe 1 2 3 4

Length (m) 3,500 4,600 4,500

Diameter (mm) 430 450 400 500

Friction Factor 0.020 0.020 0.018 0.019

1014. Which of the following most nearly gives the velocity of flow along pipe 2? a. 1.34 m/s b. 1.81 m/s c. 4.89 m/s d. 3.62 m/s

1015. Which of the following most nearly gives the required length of pipeline 1? a. 3,933.16 m b. 6,108.72 m c. 3,762.09 m d. 4,985.22 m 1016. Which of the following most nearly gives the elevation of water surface in reservoir B? a. 15.47 m b. 14.76 m c. 16.35 m d. 18.20 m Three Reservoir Problems Situation 49: The design of a city water supply system is shown in the figure. Reservoir A needs to supply 0.0938 m3/s to lower reservoir B and C. Pipe 1 is 300 m diameter and 900 m long, pipe 2 is 200 mm diameter and 387 m long, and pipe 3 is 200 mm diameter and 700 m long. The roughness coefficient for all pipes is 0.011. A El. 150 m B 2

1

El. 140 m 3 C

1017. Which of the following most nearly gives the flow rate in pipe 2? a. 0.0684 m3/s b. 0.0500 m3/s c. 0.0391 m3/s d. 0.0566 m3/s 1018. Which of the following most nearly gives the flow rate in pipe 3? a. 0.0254 m3/s b. 0.0438 m3/s c. 0.0547 m3/s d. 0.0372 m3/s 1019. Which of the following most nearly gives the elevation of water surface in reservoir A to supply the needed flow rate? a. 160.00 m b. 145.40 m c. 155.96 m d. 147.11 m Open Channel Flow Manning’s Formula Situation 50: A trapezoidal channel with uniform flow has a normal depth of 2 m. The base width is 5 m and the sides slope at 2H:1V. Manning’s n can be taken as 0.015 and the bed slope is 0.001. 1 3

10 m

10 m 1 2

5m

2.50 m

4m

1020. Which of the following most nearly gives the velocity? a. 2.50 m/s b. 3.15 m/s c. 3.73 m/s d. 2.75 m/s 1021. Which of the following most nearly gives the discharge? a. 44.99 m/s b. 55.29 m/s c. 67.65 m/s d. 36.07 m/s 1022. If the channel in the above problem were to be designed for flooding it may have a section as shown in the figure. When the flow goes over the top of the trapezoidal channel it moves to the “flood plains” so the section allows for a lot more discharge to be carried. IF the flood channels are 10 m wide, have side slopes of 3:1, and Manning’s n of 0.035, calculate the discharge for a flood level of 4 m. a. 243.76 m3/s b. 114.50 m3/s c. 267.21 m3/s d. 160.36 m3/s Non Uniform Flow Situation 51: A rectangular flume of planed timber (n = 0.012) is 5 ft wide and carries 60 cfs of water. The bed slope is 0.0006. At a certain section the depth is 3 ft and at another section the depth is 2.50 ft. 1023. Which of the following most nearly gives the slope of the energy line between the two sections? a. 0.00088 b. 0.00065 c. 0.00033 d. 0.00042 1024. Which of the following most nearly gives the distance between the two sections? a. 1,376.43 ft b. 1,542.16 ft c. 1,400.70 ft d. 1,321.70 ft 1025. Which of the following most nearly gives the head loss between the two sections? a. 1.06 ft b. 0.89 ft c. 1.18 ft d. 1.23 ft Alternate Depths of Flow in Open Channels Critical Flow Situation 52: Water flows at a depth of 6ft in a trapezoidal concrete-lined channel having a side slope of 2:1 and base width of 6 ft. Use n = 0.012.

1026. Which of the following most nearly gives the slope if the flow rate is 663 cfs? a. 0.0006 b. 0.0004 c. 0.0005 d. 0.0003 1027. Which of the following most nearly gives the critical depth? a. 4.57 ft b. 5.32 ft c. 6.09 ft d. 2.65 ft 1028. Which of the following most nearly gives the critical velocity? a. 5.98 ft/s b. 8.01 ft/s c. 7.49 ft/s d. 9.58 ft/s Efficient Sections Situation 53: water flows in a trapezoidal channel whose bottom width is 2.50 m. One side of the channel is vertical and the other is inclined at 450. The slope of the channel is 0.002 and n = 0.011. 1029. Which of the following most nearly gives the depth of flow for most efficient section? a. 1.576 m b. 1.768 m c. 1.845 m d. 1.621 m 1030. Using the depth obtained in the previous problem, which of the following most nearly gives the value of the hydraulic radius? a. 0.884 m b. 0.811 m c. 0.923 m d. 0.788 m 1031. Which of the following most nearly gives the rate of flow? a. 17.97 m3/s b. 18.97 m3/s c. 24.33 m3/s d. 22.40 m3/s Hydraulic Jump Situation 54: A hydraulic jump occurs in an efficient triangular channel carrying 8 m3/s on a slope of 0.006. The depth after the jump is 2.96 m. 1032. Which of the following most nearly gives the depth before the jump? a. 0.952 m b. 0.843 m c. 0.654 m d. 0.732 m 1033. Which of the following most nearly give the loss of energy in the jump? a. 3.17 m b. 5.40 m c. 4.31 m d. 2.56 m 1034. Which of the following most nearly gives the loss of the power in the jump?

a. 243.06 kW c. 424.29 kW

b. 196.38 kW d. 338.37 kW...