Fluid Mechanics is 4 to 6 questions on the 110-question FE Civil exam, and it is the area where a small setup error costs the most. A manometer sign, a centroid depth measured to the wrong surface, or a velocity head dropped from the energy equation all produce answers that appear in the option list.
These free practice problems follow the same pattern as the exam: a short scenario, a figure, and four numeric choices. Solutions show the control volume or datum chosen, the equation as it appears in the handbook, and the unit conversion step, because most fluids errors on the FE are unit errors in disguise.
Exam weight: NCEES lists Fluid Mechanics at 4-6 questions (4-6%) of the 110-question FE Civil exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Fluid Mechanics
NCEES splits Fluid Mechanics into four areas across its 4 to 6 questions: fluid properties, fluid statics, energy and impulse-momentum, and flow measurement. Statics questions ask for hydrostatic force on a gate or dam wall and the location of its center of pressure, manometer pressure differences, and buoyancy or stability of a floating body. These are geometry problems as much as fluids problems.
The energy side runs from continuity and the Bernoulli equation to the full energy equation with pump head, turbine head, and friction loss from Darcy-Weisbach and the Moody diagram or Hazen-Williams. Momentum questions want the force on a pipe bend or a jet striking a vane. Flow measurement covers venturi meters, orifices, pitot tubes, and weirs, each with its own discharge coefficient.
5 Free Fluid Mechanics Practice Problems
Each problem below comes from the PECivilClick FE Civil question bank and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1
Which property is primarily responsible for a liquid forming droplets instead of a continuous stream at a small leak?
A) Viscosity
B) Compressibility
C) Surface tension
D) Density
Answer: C) Surface tension
Step 1 – Identify given information: A liquid leaks from a small opening and forms droplets instead of a continuous stream. We must identify which fluid property is responsible.
Step 2 – Recall fluid property definitions: From the FE Handbook, the key fluid properties are:
- Viscosity: resistance to shear deformation
- Compressibility: volume change under pressure
- Surface tension \( \sigma \): force per unit length at the liquid-air interface that minimizes surface area
- Density: mass per unit volume
Step 3 – Apply concept: Surface tension creates a cohesive film at the free surface. This force acts to minimize the surface area of the liquid, pulling it into spherical droplets (the shape with the minimum surface-area-to-volume ratio). The internal pressure of a droplet is given by \( \Delta p = \frac{2\sigma}{r} \).
Step 4 – Answer: The correct answer is (C) Surface tension.
(A) Viscosity resists flow but does not cause droplet formation.
(B) Compressibility relates to volume change under pressure and is negligible for liquids.
(D) Density affects weight but not the tendency to form droplets.
Problem 2
An oil has specific gravity \( SG = 0.92 \) and kinematic viscosity \( \nu = 4.5 \times 10^{-4}\,\mathrm{m}^2/\mathrm{s} \). What is its dynamic viscosity \( \mu \) (Pa·s)?
A) 0.041
B) 0.21
C) 0.41
D) 4.1
Answer: C) 0.41
Step 1 – Find density from specific gravity:
\(\rho = SG \times 1000 = 0.92 \times 1000 = 920 \text{ kg/m}^3\)
Step 2 – Dynamic viscosity from kinematic:
\(\mu = \rho
u = 920 \times 4.5 \times 10^{-4} = 0.414 \text{ Pa}\cdot\text{s}\)
Correct answer: (C)
Problem 3
A rectangular gate \( 1.2\,\mathrm{m} \) wide and \( 2.0\,\mathrm{m} \) tall is vertical in water. The top edge is \( 0.5\,\mathrm{m} \) below the surface. Where is the center of pressure measured below the surface?
A) 1.17 m
B) 1.50 m
C) 1.72 m
D) 2.17 m
Answer: C) 1.72 m
Step 1 – Identify given information:
| Parameter | Value |
|---|---|
| Gate width \( b \) | \( 1.2 \text{ m} \) |
| Gate height \( h \) | \( 2.0 \text{ m} \) |
| Top edge depth | \( 0.5 \text{ m} \) |
Step 2 – Center of pressure formula: From the FE Handbook:
\( y_{cp} = \bar{h} + \frac{I_g}{A\bar{h}} \)
Step 3 – Substitute and solve:
Centroid depth: \( \bar{h} = 0.5 + 2.0/2 = 1.5 \text{ m} \)
Second moment of area: \( I_g = \frac{bh^3}{12} = \frac{1.2(2)^3}{12} = 0.8 \text{ m}^4 \)
Area: \( A = 1.2 \times 2 = 2.4 \text{ m}^2 \)
\( y_{cp} = 1.5 + \frac{0.8}{2.4 \times 1.5} = 1.5 + 0.222 = 1.72 \text{ m} \)
This matches option (C) 1.72 m.
Step 4 – Answer: The correct answer is (C) 1.72 m. The center of pressure is always below the centroid for a submerged surface. The offset \( I_g/(A\bar{h}) \) decreases as the surface is placed deeper.
Problem 4
A fluid has dynamic viscosity \( \mu = 0.015\,\mathrm{Pa{\cdot}s} \) and density \( \rho = 850\,\mathrm{kg/m}^3 \). What is its kinematic viscosity \( \nu \) (m\(^{2}\)/s)?
A) 1.8\(\times\)10^-6
B) 1.8\(\times\)10^-5
C) 1.8\(\times\)10^-4
D) 1.8\(\times\)10^-3
Answer: B) 1.8\(\times\)10^-5
Step 1 – Identify given information:
| Parameter | Value |
|---|---|
| Dynamic viscosity \( \mu \) | \( 0.015 \text{ Pa}\cdot\text{s} \) |
| Density \( \rho \) | \( 850 \text{ kg/m}^3 \) |
Step 2 – Kinematic viscosity formula: From the FE Handbook:
\(
u = \frac{\mu}{\rho} \)
Step 3 – Substitute and solve:
\(
u = \frac{0.015}{850} = 1.76 \times 10^{-5} \text{ m}^2\text{/s} \)
Step 4 – Answer: The correct answer is (B) \( 1.8 \times 10^{-5} \) m\(^{2}\)/s. The other options differ by orders of magnitude, which is a common trap when dealing with scientific notation in viscosity problems.
Problem 5
Which set of units is correct for kinematic viscosity \( \nu \)?
A) m\(^{2}\)/s
B) Pa·s
C) kg/m\(^{3}\)
D) N/m
Answer: A) m\(^{2}\)/s
Step 1 – Identify given information: We need to determine the correct SI units for kinematic viscosity \(
u \).
Step 2 – Kinematic viscosity definition: From the FE Handbook, kinematic viscosity is defined as:
\(
u = \frac{\mu}{\rho} \)
where \( \mu \) = dynamic viscosity (Pa·s) and \( \rho \) = density (kg/m\(^{3}\)).
Step 3 – Derive units:
\(
u = \frac{[\text{Pa}\cdot\text{s}]}{[\text{kg/m}^3]} = \frac{\text{kg/(m}\cdot\text{s)}}{\text{kg/m}^3} = \frac{\text{m}^2}{\text{s}} \)
Step 4 – Answer: The correct answer is (A) m\(^{2}\)/s.
(B) Pa·s are units of dynamic viscosity \( \mu \), not kinematic.
(C) kg/m\(^{3}\) are units of density \( \rho \).
(D) N/m are units of surface tension \( \sigma \).
Using the FE Reference Handbook for Fluid Mechanics
The Fluid Mechanics section is dense, so navigate by figure rather than by search term. The hydrostatic force diagram with the center of pressure offset, the Moody diagram, and the table of loss coefficients for fittings are the three pages you will open most. Note that open-channel flow and pipe networks sit in the Water Resources section, not here.
Four Mistakes That Cost Points
- Using the centroid depth where the center of pressure belongs Resultant hydrostatic force uses the depth to the centroid of the surface, but its line of action acts lower, at the center of pressure offset by I divided by y-bar times A. Moment questions about a gate hinge fail whenever the force is applied at the centroid.
- Applying Bernoulli where energy is lost Bernoulli assumes no friction, no pump, and no turbine. The moment a problem mentions pipe length, roughness, fittings, or a pump, you need the full energy equation with head loss terms. Sudden expansions and exits also remove energy that Bernoulli alone will not account for.
- Mixing gauge and absolute pressure Manometer and hydrostatic problems are almost always gauge pressure, but property questions involving gas density, vapor pressure, or cavitation need absolute. Adding or omitting one atmosphere changes the answer by a factor the distractors are built around, so decide which reference you are on before writing an equation.
- Forgetting that momentum is a vector Force on a pipe bend requires x and y components summed separately, then combined. Reversing the sign on the outlet velocity is the usual error, because the momentum flux leaves the control volume while the inlet enters it. Sketch the control volume and label positive directions before substituting numbers.
Frequently Asked Questions
How many fluid mechanics questions are on the FE Civil exam?
NCEES assigns 4 to 6 of the 110 questions to Fluid Mechanics. Water Resources and Environmental Engineering is a separate and larger area, but it leans on the same energy equation and friction loss tools, so time spent here pays off twice. Treat fluids as foundation work rather than as an isolated five-question block.
Do I have to read the Moody diagram on screen?
Yes, and it is worth practicing. On the computer-based exam you read the friction factor off the on-screen chart, which is harder than using a printed copy. Compute the Reynolds number and relative roughness first, then locate the curve. For fully turbulent flow at high roughness the factor flattens out and precise reading matters less.
What units cause the most trouble in FE fluids problems?
Pressure and density in US customary units. Pounds per square inch versus pounds per square foot costs a factor of 144, and slugs versus pounds-mass costs a factor of 32.2. Write every quantity in a consistent set before substituting, and check that your final head comes out in feet and your force in pounds.
Are the fluid mechanics questions conceptual or numerical?
Mostly numerical, with a few conceptual items on fluid properties such as viscosity, surface tension, and the difference between laminar and turbulent behavior. The numerical ones are short by design, since the whole exam averages under three minutes per question. If a fluids problem is taking five minutes, you have probably picked the wrong equation.
Keep Going
Work through the other FE Civil knowledge areas with more free practice problems, review the full FE Civil exam topic breakdown, or plan your preparation with our FE exam study guide and study timeline.