Fluid Mechanics and Dynamics of Liquids Dr. Nancy Moore...Topic: Fluid Mechanics and Dynamics of...

Fundamentals of Engineering Exam Review

Fluid Mechanics and Dynamics of Liquids

Dr. Nancy Moore


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.

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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


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


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


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.


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


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.


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


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


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


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.


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.


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


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


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.


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


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


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


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


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.


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


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


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


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

Fluid Mechanics and Dynamics of Liquids Dr. Nancy Moore...Topic: Fluid Mechanics and Dynamics of...

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