FE Other Disciplines (NCEES Fundamentals of Engineering) — All Questions

What is the gauge pressure at a depth of 10 m in water (density 1000 kg/m^3, g = 9.81 m/s^2)?

• a.100 kPa
• b.981 kPa
• c.9.81 kPa
• d.98.1 kPa✓

Hydrostatic pressure p = rho·g·h = 1000 x 9.81 x 10 = 98,100 Pa = 98.1 kPa. Pressure increases linearly with depth and is independent of the container's shape.

Incompressible water flows through a pipe. If the cross-sectional area is reduced to half, what happens to the flow velocity?

• a.It doubles✓
• b.It halves
• c.It quadruples
• d.It stays the same

By the continuity equation A1·V1 = A2·V2, velocity is inversely proportional to area for incompressible flow. Halving the area doubles the velocity so that volumetric flow rate is conserved.

Water flows at 3 m/s through a circular pipe of 0.1 m diameter. What is the volumetric flow rate?

• a.0.03 m^3/s
• b.0.0236 m^3/s✓
• c.0.236 m^3/s
• d.0.0079 m^3/s

Flow rate Q = A·V. The area A = (pi/4)·D^2 = (pi/4)(0.1)^2 = 0.00785 m^2. Then Q = 0.00785 x 3 = 0.0236 m^3/s. Continuity ties cross-sectional area and velocity to discharge.

In pipe flow, flow is generally considered laminar when the Reynolds number is below approximately what value?

• a.4,000
• b.2,100✓
• c.500,000
• d.10

For flow in a circular pipe, laminar flow generally persists below Re of about 2,100; transitional and turbulent flow occur at higher values. The Reynolds number Re = rho·V·D/mu compares inertial to viscous forces.

What is the specific weight of water at standard conditions (density 1000 kg/m^3, g = 9.81 m/s^2)?

• a.1000 N/m^3
• b.981 N/m^3
• c.9.81 kN/m^3✓
• d.98.1 kN/m^3

Specific weight gamma = rho·g = 1000 x 9.81 = 9810 N/m^3 = 9.81 kN/m^3. Specific weight is weight per unit volume, distinct from density (mass per unit volume).

What is the gauge pressure at the bottom of a 5 m deep tank of oil with specific gravity 0.8 (g = 9.81 m/s^2)?

• a.4.9 kPa
• b.39.2 kPa✓
• c.392 kPa
• d.49.1 kPa

Hydrostatic pressure p = SG·rho_water·g·h = 0.8 x 1000 x 9.81 x 5 = 39,240 Pa = 39.2 kPa. Using water (SG = 1) would wrongly give 49.1 kPa; the fluid's specific gravity scales the result.

A manometer shows a mercury column height of 0.2 m (mercury SG = 13.6). What pressure does this represent (g = 9.81 m/s^2)?

• a.26.7 kPa✓
• b.1.96 kPa
• c.2.72 kPa
• d.267 kPa

p = rho·g·h = (13.6 x 1000) x 9.81 x 0.2 = 26,683 Pa = 26.7 kPa. Mercury's high density (SG 13.6) makes it compact for measuring large pressures; using water would give only 1.96 kPa.

Water discharges from a small opening 5 m below the free surface of a large tank. What is the ideal exit velocity (g = 9.81 m/s^2)?

• a.9.9 m/s✓
• b.98.1 m/s
• c.49.1 m/s
• d.19.8 m/s

By Torricelli's theorem (from Bernoulli), v = sqrt(2·g·h) = sqrt(2 x 9.81 x 5) = sqrt(98.1) = 9.9 m/s. Forgetting the square root gives the incorrect 98.1.

Water (density 1000 kg/m^3) flows at 2 m/s through a duct of cross-sectional area 0.01 m^2. What is the mass flow rate?

• a.20 kg/s✓
• b.0.02 kg/s
• c.2 kg/s
• d.200 kg/s

Mass flow rate m_dot = rho·A·V = 1000 x 0.01 x 2 = 20 kg/s. This is the continuity equation expressed in mass terms; leaving out density yields the volumetric rate 0.02 m^3/s instead.

Water (density 1000 kg/m^3, viscosity 1x10^-3 Pa·s) flows at 2 m/s in a 0.05 m diameter pipe. What is the Reynolds number?

• a.100,000✓
• b.100
• c.10,000
• d.1,000

Re = rho·V·D/mu = (1000 x 2 x 0.05)/(1x10^-3) = 100/0.001 = 100,000. This far exceeds ~2100, so the flow is turbulent. Re is the ratio of inertial to viscous forces.

An object of volume 0.02 m^3 is fully submerged in water (density 1000 kg/m^3, g = 9.81 m/s^2). What is the buoyant force on it?

• a.196.2 N✓
• b.1,962 N
• c.19.6 N
• d.98.1 N

By Archimedes' principle, buoyant force F_b = rho·g·V_displaced = 1000 x 9.81 x 0.02 = 196.2 N. It equals the weight of the displaced fluid and is independent of the object's own weight.

A vertical rectangular gate 2 m wide and 3 m tall has its top edge at the water surface. What is the total hydrostatic force on it (rho = 1000 kg/m^3, g = 9.81 m/s^2)?

• a.88.3 kN✓
• b.44.1 kN
• c.176.6 kN
• d.58.9 kN

Resultant force F = rho·g·h_c·A, where h_c is the depth to the centroid (1.5 m) and A = 2 x 3 = 6 m^2. F = 1000 x 9.81 x 1.5 x 6 = 88,290 N = 88.3 kN.

For a vertical rectangular gate 3 m tall with its top edge at the free surface, at what depth does the resultant hydrostatic force act (center of pressure)?

• a.1.5 m
• b.1.0 m
• c.2.0 m✓
• d.3.0 m

For a surface with its top at the free surface, the center of pressure is at 2/3 of the height = (2/3)(3) = 2.0 m. It lies below the centroid (1.5 m) because pressure increases with depth.

A fluid has dynamic viscosity 1x10^-3 Pa·s and density 1000 kg/m^3. What is its kinematic viscosity?

• a.1x10^-6 m^2/s✓
• b.1x10^3 m^2/s
• c.1x10^-3 m^2/s
• d.1 m^2/s

Kinematic viscosity nu = mu/rho = (1x10^-3)/1000 = 1x10^-6 m^2/s. It is the dynamic viscosity normalized by density and appears in the Reynolds number.

In a horizontal pipe of constant elevation, when the fluid speeds up as it enters a narrower section, what happens to the static pressure?

• a.Decreases✓
• b.Increases
• c.Drops to zero
• d.Stays constant

By Bernoulli's equation, along a horizontal streamline p + (1/2)rho·V^2 is constant, so higher velocity means lower static pressure. This inverse pressure-velocity relationship underlies venturi and airfoil behavior.

Water flows at 2 m/s through a 0.1 m diameter pipe 100 m long with a Darcy friction factor of 0.02. What is the head loss due to friction (g = 9.81 m/s^2)?

• a.0.41 m
• b.4.08 m✓
• c.40.8 m
• d.2.04 m

Darcy-Weisbach: h_f = f·(L/D)·(V^2/2g) = 0.02 x (100/0.1) x (2^2/(2 x 9.81)) = 0.02 x 1000 x 0.204 = 4.08 m. Head loss scales with the square of velocity.

What is the hydraulic diameter of a square duct with side length 0.2 m?

• a.0.05 m
• b.0.10 m
• c.0.40 m
• d.0.20 m✓

Hydraulic diameter D_h = 4A/P = 4(0.2^2)/(4 x 0.2) = 4(0.04)/0.8 = 0.20 m. For a square duct D_h equals the side length; it lets non-circular ducts use pipe-flow relations.

A volumetric flow rate of 0.1 m^3/s passes through a pipe of diameter 0.2 m. What is the average flow velocity?

• a.6.37 m/s
• b.1.59 m/s
• c.0.50 m/s
• d.3.18 m/s✓

V = Q/A, with A = (pi/4)D^2 = (pi/4)(0.2)^2 = 0.0314 m^2. V = 0.1/0.0314 = 3.18 m/s. Using diameter instead of area in the denominator is a common error.

A pump delivers water at 0.05 m^3/s against a head of 20 m (rho = 1000 kg/m^3, g = 9.81 m/s^2). What is the ideal hydraulic power required?

• a.9.81 kW✓
• b.4.9 kW
• c.98.1 kW
• d.0.98 kW

Hydraulic power P = rho·g·Q·H = 1000 x 9.81 x 0.05 x 20 = 9810 W = 9.81 kW. Actual shaft power is higher because pump efficiency is below 100%.

A body with drag coefficient 0.4 and frontal area 2 m^2 moves through air (density 1.2 kg/m^3) at 30 m/s. What is the drag force?

• a.216 N
• b.432 N✓
• c.43.2 N
• d.864 N

Drag force F_D = (1/2)·C_d·rho·V^2·A = 0.5 x 0.4 x 1.2 x 30^2 x 2 = 432 N. Drag grows with the square of velocity, so doubling speed quadruples drag.

A liquid has a density of 850 kg/m^3. What is its specific gravity (reference water = 1000 kg/m^3)?

• a.8.5
• b.0.85✓
• c.850
• d.1.18

Specific gravity SG = rho_fluid/rho_water = 850/1000 = 0.85. It is a dimensionless ratio; a value below 1 means the fluid is lighter than water and will float on it.

A pressure gauge reads 150 kPa. If atmospheric pressure is 101.3 kPa, what is the absolute pressure?

• a.150 kPa
• b.251.3 kPa✓
• c.48.7 kPa
• d.101.3 kPa

Absolute pressure = gauge pressure + atmospheric pressure = 150 + 101.3 = 251.3 kPa. Gauge pressure is measured relative to atmosphere; absolute is measured from a perfect vacuum.

In a hydraulic press, a 100 N force is applied to a small piston of area 0.01 m^2. What force is produced on the large piston of area 0.1 m^2?

• a.10,000 N
• b.10 N
• c.1,000 N✓
• d.100 N

By Pascal's principle, pressure is equal throughout: p = 100/0.01 = 10,000 Pa. Output force = p·A_large = 10,000 x 0.1 = 1,000 N. Force multiplies by the area ratio (10x).

Incompressible water flows at 2 m/s in a 0.1 m diameter pipe that narrows to 0.05 m diameter. What is the velocity in the narrow section?

• a.1 m/s
• b.8 m/s✓
• c.16 m/s
• d.4 m/s

Continuity A1·V1 = A2·V2 with area proportional to D^2 gives V2 = V1·(D1/D2)^2 = 2 x (0.1/0.05)^2 = 2 x 4 = 8 m/s. Velocity scales with the square of the diameter ratio, not linearly.

What is the velocity head of water flowing at 10 m/s (g = 9.81 m/s^2)?

• a.1.02 m
• b.51.0 m
• c.5.10 m✓
• d.10.2 m

Velocity head = V^2/(2g) = 10^2/(2 x 9.81) = 100/19.62 = 5.10 m. It is the kinetic-energy term of Bernoulli's equation expressed as an equivalent column height.

What is the pressure head corresponding to a water pressure of 98.1 kPa (rho = 1000 kg/m^3, g = 9.81 m/s^2)?

• a.10 m✓
• b.5 m
• c.100 m
• d.1 m

Pressure head = p/(rho·g) = 98,100/(1000 x 9.81) = 10 m. Pressure head expresses pressure as an equivalent height of the fluid column.

Water (surface tension 0.072 N/m, contact angle ~0) rises in a glass tube of radius 0.001 m. What is the approximate capillary rise (rho = 1000 kg/m^3, g = 9.81 m/s^2)?

• a.7.3 mm
• b.29.4 mm
• c.14.7 mm✓
• d.1.5 mm

Capillary rise h = 2·sigma·cos(theta)/(rho·g·r) = 2 x 0.072/(1000 x 9.81 x 0.001) = 0.144/9.81 = 0.0147 m = 14.7 mm. Rise is inversely proportional to tube radius.

What is the density of air modeled as an ideal gas at 101.3 kPa and 300 K (R = 287 J/kg·K)?

• a.1.00 kg/m^3
• b.2.35 kg/m^3
• c.1.18 kg/m^3✓
• d.0.85 kg/m^3

Ideal gas law rho = p/(R·T) = 101,300/(287 x 300) = 101,300/86,100 = 1.18 kg/m^3. Temperature must be absolute (kelvin).

For fully developed laminar pipe flow at a Reynolds number of 1600, what is the Darcy friction factor?

• a.0.016
• b.0.032
• c.0.080
• d.0.040✓

For laminar flow, f = 64/Re = 64/1600 = 0.040. This exact relation applies only below Re ~2100; turbulent flow requires the Moody chart or Colebrook equation.

A solid body of specific gravity 0.6 floats freely in water. What fraction of its volume is submerged?

• a.60%✓
• b.6%
• c.100%
• d.40%

For a floating body, the submerged fraction equals the ratio of densities: rho_body/rho_fluid = 0.6, so 60% is submerged. This follows from equating weight and buoyant force.

Open-channel flow moves at 3 m/s at a depth of 1 m. What is the Froude number (g = 9.81 m/s^2)?

• a.0.31
• b.0.96✓
• c.9.4
• d.3.0

Froude number Fr = V/sqrt(g·y) = 3/sqrt(9.81 x 1) = 3/3.13 = 0.96. Since Fr < 1 the flow is subcritical. Fr compares inertial to gravitational forces in free-surface flow.

Water (density 1000 kg/m^3) flows at 4 m/s with a static pressure of 100 kPa. What is the stagnation (total) pressure?

• a.100 kPa
• b.116 kPa
• c.108 kPa✓
• d.104 kPa

Stagnation pressure = static + dynamic = p + (1/2)rho·V^2 = 100,000 + 0.5 x 1000 x 4^2 = 100,000 + 8,000 = 108 kPa. The dynamic term is the pressure recovered when flow is brought to rest.

Pipe flow at a Reynolds number of about 3000 is best described as:

• a.Supersonic
• b.Laminar
• c.Turbulent
• d.Transitional✓

Between roughly Re 2100 and 4000, pipe flow is transitional, intermittently switching between laminar and turbulent behavior. Below ~2100 it is laminar; above ~4000 it is fully turbulent.

What height of a water column produces a pressure of 50 kPa (rho = 1000 kg/m^3, g = 9.81 m/s^2)?

• a.0.51 m
• b.5.1 m✓
• c.10.2 m
• d.2.5 m

From p = rho·g·h, h = p/(rho·g) = 50,000/(1000 x 9.81) = 5.1 m. This converts a pressure into an equivalent water-column height, as read on a manometer.

By how much does hydrostatic pressure in water increase per meter of depth (rho = 1000 kg/m^3, g = 9.81 m/s^2)?

• a.0.98 kPa/m
• b.1.0 kPa/m
• c.9.81 kPa/m✓
• d.98.1 kPa/m

The pressure gradient in a static fluid is dp/dz = rho·g = 1000 x 9.81 = 9810 Pa/m = 9.81 kPa/m. Pressure grows linearly with depth regardless of container shape.

Water flows from an orifice 2 m below the free surface of a large open tank. What is the ideal jet velocity (g = 9.81 m/s^2)?

• a.19.6 m/s
• b.39.2 m/s
• c.3.13 m/s
• d.6.26 m/s✓

Torricelli's theorem: v = sqrt(2·g·h) = sqrt(2 x 9.81 x 2) = sqrt(39.24) = 6.26 m/s. It comes from applying Bernoulli's equation between the surface and the orifice.

Pipe flow has a Reynolds number of 1500. The flow regime is:

• a.Choked
• b.Turbulent
• c.Laminar✓
• d.Transitional

Re = 1500 is below the ~2100 threshold, so the flow is laminar, dominated by viscous forces with smooth, orderly streamlines and no cross-mixing.

A Newtonian fluid with dynamic viscosity 1x10^-3 Pa·s experiences a velocity gradient of 100 s^-1 near a wall. What is the shear stress?

• a.0.01 Pa
• b.0.1 Pa✓
• c.10 Pa
• d.1 Pa

Newton's law of viscosity: tau = mu·(du/dy) = 1x10^-3 x 100 = 0.1 Pa. Shear stress is proportional to the velocity gradient, with viscosity as the proportionality constant.

A gauge pressure of -20 kPa indicates that the absolute pressure is:

• a.Above atmospheric
• b.Equal to absolute zero
• c.Below atmospheric✓
• d.Equal to atmospheric

A negative gauge pressure means the absolute pressure is below atmospheric, i.e., a partial vacuum. Absolute pressure = atmospheric + gauge = 101.3 + (-20) = 81.3 kPa, still positive.

For steady incompressible flow through a pipe with a single inlet and outlet, the continuity principle requires that:

• a.Mass in exceeds out
• b.Mass out exceeds in
• c.Mass in equals mass out✓
• d.Flow depends only on pressure

Conservation of mass for steady flow requires mass flow in to equal mass flow out. For incompressible flow this also means the volumetric flow rate Q is constant along the pipe.

A pump must deliver 8 kW of hydraulic power but operates at 80% efficiency. What shaft (brake) power is required?

• a.10 kW✓
• b.12.5 kW
• c.6.4 kW
• d.8 kW

Brake power = hydraulic power/efficiency = 8/0.8 = 10 kW. Efficiency below 100% means the input shaft power always exceeds the useful hydraulic power delivered to the fluid.

A pipe fitting has a minor loss coefficient K = 1.5. What head loss does it add at a flow velocity of 3 m/s (g = 9.81 m/s^2)?

• a.0.69 m✓
• b.1.38 m
• c.0.23 m
• d.0.46 m

Minor loss h_L = K·V^2/(2g) = 1.5 x 3^2/(2 x 9.81) = 1.5 x 0.459 = 0.69 m. Fittings, valves, and bends add losses proportional to the velocity head.

The hydrostatic paradox states that pressure at the bottom of a static liquid depends:

• a.On the liquid volume
• b.Only on depth and density✓
• c.On the container shape
• d.On the surface area

Hydrostatic pressure p = rho·g·h depends only on depth and fluid density (and g), not on the container's shape or the total volume it holds. Two differently shaped vessels filled to the same depth share the same bottom pressure.

Water flows at 4 m/s through a channel of cross-sectional area 0.05 m^2. What is the volumetric flow rate?

• a.0.2 m^3/s✓
• b.2.0 m^3/s
• c.0.4 m^3/s
• d.0.02 m^3/s

Volumetric flow rate Q = A·V = 0.05 x 4 = 0.2 m^3/s. Discharge is the product of cross-sectional area and average velocity.