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Fundamentals of Engineering Exam Review
Fluid Mechanics and Dynamics of Liquids
Dr. Nancy Moore
Fundamentals of Engineering Exam Review
We are grateful to NCEES for granting us
permission to copy short sections from the
FE Handbook to show students how to use
Handbook information in solving problems.
This information will normally appear in
these videos as white boxes.
Fundamentals of Engineering Exam Review
Other Disciplines FE SpecificationsTopic: Fluid Mechanics and Dynamics of Liquids8-12 FE exam problems
Exam Problem Numbers
A. Fluid properties (e.g., Newtonian, non-Newtonian) 73, 77
B. Dimensionless numbers (e.g., Reynolds number, Froude
number)
C. Laminar and turbulent flow 74
D. Fluid statics 75
E. Energy, impulse, and momentum equations (e.g.,
Bernoulli equation)76
F. Pipe flow and friction losses (e.g., pipes, valves, fittings,
Darcy-Weisbach equation, Hazen-Williams equation)78, 79
Fundamentals of Engineering Exam Review
Other Disciplines FE SpecificationsTopic: Fluid Mechanics and Dynamics of Liquids8-12 FE exam problems
Exam Problem Numbers
G. Open-channel flow (e.g., Manning equation, drag)
H. Fluid transport systems (e.g., series and parallel
operations)
I. Flow measurement 80
J. Turbomachinery (e.g., pumps, turbines) 91
Fundamentals of Engineering Exam Review
1. A clean glass tube is to be selected in the design of a manometer to measure the
pressure of kerosene. The specific gravity of kerosene is 0.82 and the surface
tension of kerosene is 0.025 N/m. If the capillary rise is to be limited to 1 mm, the
smallest diameter, in cm, of the glass tube should be most nearly
(A) 1.25 (B) 1.50 (C) 1.75 (D) 2.00
ℎ =4𝜎𝑐𝑜𝑠𝛽
𝛾𝑑
𝑑 =4 0.025 ൗ𝑁 𝑚 𝑐𝑜𝑠0
0.82 9.8 ൗ𝑘𝑁 𝑚31000 𝑁1 𝑘𝑁
11000
𝑚= .0124 𝑚
Fundamentals of Engineering Exam Review
2. For a body partially submerged in a fluid and at equilibrium, which of the following
is a true statement?
(A) The weight of the body is equal to the weight of the volume of fluid displaced.
(B) The weight of the body is less than the weight of the volume of fluid displaced.
(C) The weight of the body is greater than the weight of the volume of fluid
displaced.
(D)The specific gravity of the body is greater than the specific gravity of the fluid.
Since the body is at equilibrium, the weight of the body should equal the buoyancy force, which in turn is equal to the weight of the volume of fluid displaced.
Fundamentals of Engineering Exam Review
3. The hydraulic diameter of a circular pipe is equal to
(A) half its diameter.
(B) its diameter.
(C) double its diameter.
(D) π times its diameter.
𝐷ℎ =4(𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎)
𝑤𝑒𝑡𝑡𝑒𝑑 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟=4
𝜋4𝐷
2
𝜋𝐷= 𝐷
Fundamentals of Engineering Exam Review
4. When a Newtonian fluid flows under steady,
laminar conditions through a circular pipe of
constant diameter, which of the following is NOT a
correct conclusion?
(A) The shear stress at the centerline of the pipe
is zero.
(B) The maximum velocity at a section is twice the
average velocity at that section.
(C) The velocity will decrease along the length of
the pipe.
(D) The velocity gradient at the centerline of the
pipe is zero.
Fundamentals of Engineering Exam Review
5. Ethyl alcohol (specific gravity = 0.79, and viscosity = 1.19x10-3 Pa-s) is flowing
through a 25-cm diameter, horizontal pipeline. When the flow rate is 0.5 m3/min, the
Reynolds Number is most nearly
(A) 28,158 (B) 31,424 (C) 35,597 (D) 42,632
𝑉 =𝑄
𝜋4𝐷2
=0.5 ൗ𝑚
3
𝑚𝑖𝑛1𝑚𝑖𝑛60 𝑠
𝜋4.25 𝑚 2
𝑉 = 0.17 Τ𝑚 𝑠
𝑅𝑒 =𝑆𝐺𝜌𝑤𝑉𝐷
𝜇
𝑅𝑒 =0.79 1000 ൗ
𝑘𝑔𝑚3
0.17 Τ𝑚 𝑠 .25 𝑚
1.19𝑥10−3𝑃𝑎𝑠= 28214
Fundamentals of Engineering Exam Review
6. The figure shows a 10-cm diameter, horizontal pipeline with two piezometers
installed 3 m apart. Under laminar flow of lubricating oil (specific gravity = 0.92 and
viscosity = 3.8x10-1 Pa-s), the difference in piezometer readings is 12 cm. The flow
rate, in m3/min, under the above conditions is most nearly
(A) 0.02 (B) 0.09 (C) 0.14 (D) 0.21
𝑄 =𝜋𝐷4Δ𝑃𝑓
128𝜇𝐿=
𝜋 0.1 𝑚 4 1082 𝑃𝑎
128 3.8𝑥10−1𝑃𝑎𝑠 3 𝑚= 0.0023 ൗ𝑚
3𝑠
Δ𝑃 = 𝜌𝑔ℎ = 𝑆𝐺𝛾𝑤ℎ = 0.92 9.8 ൗ𝑘𝑁
𝑚30.12 𝑚 = 1.082 𝑘𝑃𝑎
Fundamentals of Engineering Exam Review
7. When fluid flow is characterized as fully turbulent, which of the following is a true
statement?
(A) Friction factor will increase with increase of Reynolds Number
(B) Friction factor will decrease with increase of Reynolds Number
(C) Friction factor is independent of Reynolds Number
(D) Friction factor is independent of relative roughness
Fundamentals of Engineering Exam Review
Fundamentals of Engineering Exam Review
7. When fluid flow is characterized as fully turbulent, which of the following is a true
statement?
(A) Friction factor will increase with increase of Reynolds Number.
(B) Friction factor will decrease with increase of Reynolds Number.
(C) Friction factor is independent of Reynolds Number.
(D) Friction factor is independent of relative roughness.
Fundamentals of Engineering Exam Review
8. The relative roughness of a new pipeline is 0.002. The flow is such that the
Reynolds Number is 20,000. If the relative roughness increases to 0.006, and the
Reynolds Number remains the same, which of the following is most likely?
(A) Friction factor will decrease.
(B) Friction factor will increase.
(C) Friction factor will remain the same.
(D) Head loss will remain the same.
Refer to the Moody diagram:For Re = 20,000 and Τ𝜀 𝐷 = 0.002, 𝑓 ≈ 0.030.For the same Reynolds number and Τ𝜀 𝐷 = 0.006, 𝑓 ≈ 0.036.Therefore, the friction factor will increase and the head loss will increase.
Fundamentals of Engineering Exam Review
9. A 20-cm in diameter pipeline with a relative roughness of 0.01 has a total length of
45 m. When water at 25ºC is pumped through it at a rate of 5 m3/min, the major
head loss, in m, is most nearly
(A) 3 (B) 10 (C) 15 (D) 20
𝑉 =𝑄
𝐴=
5 ൗ𝑚3
𝑚𝑖𝑛1 𝑚𝑖𝑛60 𝑠
𝜋40.20𝑚 2
= 2.65 Τ𝑚 𝑠
𝑅𝑒 =𝜌𝑉𝐷
𝜇=
997 ൗ𝑘𝑔
𝑚32.65 Τ𝑚 𝑠 0.20𝑚
0.00089𝑃𝑎𝑠= 593719
Therefore the flow is turbulent. From the Moody diagram, 𝑓 ≈ 0.038.
ℎ𝑓 = 𝑓𝐿
𝐷
𝑉2
2𝑔= 3.06 𝑚
Fundamentals of Engineering Exam Review
10. Consider the free jet of an incompressible fluid flowing through an orifice fitted to
a constant level tank as shown. Ignoring all losses, which of the following is a correct
statement about the magnitude of the initial velocity V of the jet?
(A) V is directly proportional to the orifice diameter.
(B) V is inversely proportional to the fluid’s density.
(C) V is proportional to the square root of the depth h.
(D) V is proportional to the square of the depth h.
𝑃1𝛾+𝑉12
2𝑔+ 𝑧1 =
𝑃2𝛾+𝑉22
2𝑔+ 𝑧2
ℎ =𝑉22
2𝑔
𝑉 = 2𝑔ℎ
Fundamentals of Engineering Exam Review
11. Considering the flow of an incompressible fluid through a horizontal pipe, which
of the following is a correct statement?
(A)The energy grade line is always parallel to the centerline of the pipeline.
(B) The energy grade line is always above the hydraulic grade line.
(C) The energy grade line is always horizontal.
(D)The energy grade line is always parallel to the hydraulic grade line.
Fundamentals of Engineering Exam Review
12. The schematic of a pumping system to pump water from a canal to an overhead
storage tank is shown. The total head loss of the system is to be 10% of the total
static head. If the pump is powered by a 5 kW motor at an efficiency of 85%, the
pumping rate, in m3/min, is most nearly
(A) 0.2 (B) 0.6 (C) 1.0 (D) 2.0
Total static head = suction lift + delivery head = (3 m) + (15 + 4)m = 22 m
Total head loss = 10% of 22 m = 2.2 m
Total head added = 22 m + 2.2 m = 24.2 m
𝑄 =ሶ𝑊𝜂
𝛾ℎ= 0.0179 ൗ𝑚
3
𝑠
Fundamentals of Engineering Exam Review
13. The drag coefficient for a car with a frontal area of 28 ft2 is 0.32. Assuming the
density of air to be 2.4x10-3 slugs/ft3, the drag force, in lbf, on this car when driven at
60 mph against a head wind of 20 mph is most nearly
(A) 37 (B) 83 (C) 148 (D) 185
Relative velocity = 60 mph + 20 mph = 80 mph = 117.3 ft/s
𝐹𝐷 =𝐶𝐷𝜌𝑉
2𝐴
2
=0.32 2.4𝑥10−3 ൘
𝑠𝑙𝑢𝑔𝑠𝑓𝑡3
117.3 ൗ𝑓𝑡
𝑠2
28𝑓𝑡2
2= 148 𝑙𝑏𝑓
Fundamentals of Engineering Exam Review
14. The figure below shows a branched pipe network. A pressure gage just
upstream of A reads 60 psi and a pressure gage just downstream of D reads 54 psi.
The flow rates, diameters, and the lengths of the two branches are as follows:Branch ABD Branch ACD
Flow rate Q 2Q
Diameter D D
Length L L
Which of the following is a true conclusion?
(A)Pressure drop in branch ACD = 4 psi
(B)Pressure drop in branch ABD = 2 psi
(C)Pressure drop in branch ACD = Pressure drop in branch ABD = 6 psi
(D)Pressure drop in branch ACD = Pressure drop in branch ABD = 3 psi
In a branched pipe network such as the one shown, the head loss is the same in each branch.
Pressure drop in branch ABD = 60 psi – 54 psi = 6 psi
Pressure drop in branch ACD = 60 psi – 54 psi = 6 psi
Fundamentals of Engineering Exam Review
15. The figure below shows a branched pipe network. The flow rates, diameters, the
friction factors, and the lengths of the two branches are as follows:
Branch ABD Branch ACD
Flow rate Q 2Q
Diameter D D
Length L L
Friction factor f1 f2Which of the following is a true conclusion?
(A) f1 = 2f2 (B) f1 = 4f2 (C) f1 = f2 (D) f1 = (1/2)f2
𝑓1𝐿
𝐷
𝑉12
2𝑔= 𝑓2
𝐿
𝐷
𝑉22
2𝑔
𝑓1𝐿
𝐷
𝑄/𝐴 2
2𝑔= 𝑓2
𝐿
𝐷
2𝑄/𝐴 2
2𝑔
Fundamentals of Engineering Exam Review
16. At a certain section in a pipeline, a reducer is used to reduce the diameter from
2D gradually to diameter D. When an incompressible fluid flows through this
pipeline, the velocity is V1 in the first section and V2 in the second section. Which of
the following is a true conclusion?
(A) V2 = 4V1 (B) V2 = 2V1 (C) V2 = (1/2)V1 (D) V2 = (1/4)V1
From continuity equation, Q = A1 V1 = A2 V2where, A1 = area before reduction =
𝜋
42𝐷 2 = 𝜋𝐷2
and A2 = area after reduction = 𝜋
4𝐷 2
Thus, 𝑉2 =𝐴1
𝐴2𝑉1 = 4𝑉1.
Fundamentals of Engineering Exam Review
17. A 5-cm diameter pipeline is delivering water from a storage tank to an open
canal. The water level in the storage tank can be assumed to be at a constant height
of 12 m above the discharge point. Ignoring all losses, the discharge, in m3/min,
under these conditions is most nearly
(A) 0.03 (B) 1.80 (C) 7.35 (D) 15.34
𝑃1𝛾+𝑉12
2𝑔+ 𝑧1 =
𝑃2𝛾+𝑉22
2𝑔+ 𝑧2
𝑉2 = 2𝑔𝑧1 = 15.34 Τ𝑚
𝑠
𝑄2 = 𝐴2𝑉2 =𝜋
4𝐷2𝑉2 = 0.0301 Τ
𝑚3𝑠
Fundamentals of Engineering Exam Review
18. An open tank contains brine to a depth of 2 m and a 3-m layer of oil on top of the
brine. Density of brine is 1,030 kg/m3 and the density of oil is 880 kg/m3. The gage
pressure (kPa) at the bottom of the tank is most nearly
(A) 4.7 (B) 20.2 (C) 25.6 (D) 46.1
In the brine layer, Δ𝑃 = 𝜌𝑔ℎ = 1030 ൗ𝑘𝑔 𝑚3 9.81 Τ𝑚
𝑠2 2𝑚 = 20209 𝑃𝑎
In the oil layer, Δ𝑃 = 𝜌𝑔ℎ = 880 ൗ𝑘𝑔 𝑚3 9.81 Τ𝑚
𝑠2 3𝑚 = 25898 𝑃𝑎
Gage pressure = 20209 Pa + 25898 Pa = 46.1 kPa
Fundamentals of Engineering Exam Review
19. A tank is filled with seawater to a depth of 12 ft. If the specific gravity of seawater
is 1.03 and the atmospheric pressure at this location is 14.8 psi, the absolute
pressure, in psi, at the bottom of the tank is most nearly
(A) 5.4 (B) 20.2 (C) 26.8 (D) 27.2
𝑃𝑔𝑎𝑔𝑒 = 𝜌𝑔ℎ = 𝑆𝐺𝛾𝑤ℎ = 1.03 62.4 ൘𝑙𝑏𝑓
𝑓𝑡312 𝑓𝑡
𝑃𝑔𝑎𝑔𝑒 = 771.3 ൘𝑙𝑏𝑓
𝑓𝑡2= 5.36 𝑝𝑠𝑖
𝑃𝑎𝑏𝑠 = 𝑃𝑎𝑡𝑚 + 𝑃𝑔𝑎𝑔𝑒 = 20.2 𝑝𝑠𝑖
Fundamentals of Engineering Exam Review
20. A Newtonian fluid flows under steady, laminar conditions through a circular pipe
of diameter 0.16 m at a volumetric rate of 0.05 m3/s. Under these conditions, the
maximum local velocity, in m/s, at a section is most nearly
(A) 2.0 (B) 2.5 (C) 3.0 (D) 5.0
𝑉 =𝑄
𝐴=
𝑄𝜋4𝐷2
= 2.49 Τ𝑚 𝑠
𝑉𝑚𝑎𝑥 = 2𝑉