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FE Other Disciplines practice questions

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Question 1Other Disciplines (content domain not enumerated in the source)

A simply supported steel beam spans 6 m and carries a uniformly distributed load of 10 kN/m over its full length. What is the maximum bending moment in the beam?

  1. 60 kN·m
  2. 45 kN·m Correct answer.
  3. 90 kN·m
  4. 30 kN·m

Explanation

For a simply supported beam with a uniform load w over span L, the maximum moment is wL²/8. Substituting gives 10 × 6²/8 = 360/8 = 45 kN·m at midspan.

Question 2Other Disciplines (content domain not enumerated in the source)

A 120 V source is connected across a 40 Ω resistor. What power is dissipated in the resistor?

  1. 360 W Correct answer.
  2. 0.33 W
  3. 4800 W
  4. 3 W

Explanation

Power in a resistive element can be computed as P = V²/R. With V = 120 V and R = 40 Ω, P = 14400/40 = 360 W.

Question 3Other Disciplines (content domain not enumerated in the source)

Which dimensionless group is used to characterize whether flow in a pipe is laminar or turbulent?

  1. Mach number
  2. Reynolds number Correct answer.
  3. Froude number
  4. Prandtl number

Explanation

The Reynolds number, Re = ρVD/μ, compares inertial to viscous forces and its magnitude indicates laminar, transitional, or turbulent pipe flow. Values below roughly 2100 indicate laminar flow in a circular pipe.

Question 4Other Disciplines (content domain not enumerated in the source)

In the standard Americano (USCS) unit system, which combination of base units is consistent for a force-based system?

  1. slug, foot, second Correct answer.
  2. newton, meter, second
  3. pound-mass, foot, second
  4. kilogram, meter, second

Explanation

The USCS force-based system uses the slug as the mass unit alongside the foot and second, so that force in pounds equals mass in slugs times acceleration in ft/s². The pound-mass variant is a separate gravitational convention.

Question 5Other Disciplines (content domain not enumerated in the source)

A Carnot engine operates between thermal reservoirs at 600 K and 300 K. What is its thermal efficiency?

  1. 0.25
  2. 0.50 Correct answer.
  3. 0.75
  4. 1.00

Explanation

Carnot efficiency depends only on the absolute reservoir temperatures: η = 1 − T_C/T_H. Here η = 1 − 300/600 = 0.50, or 50 percent.

Question 6Other Disciplines (content domain not enumerated in the source)

Which type of chemical bond results from the electrostatic attraction between oppositely charged ions?

  1. Hydrogen bond
  2. Ionic bond Correct answer.
  3. Metallic bond
  4. Covalent bond

Explanation

An ionic bond forms when one atom transfers electrons to another, creating cations and anions that attract electrostatically. This contrasts with sharing of electrons in covalent bonding.

Question 7Other Disciplines (content domain not enumerated in the source)

A sample of soil has a total volume of 0.05 m³ and a total mass of 90 kg. What is its bulk (wet) density?

  1. 1800 kg/m³ Correct answer.
  2. 450 kg/m³
  3. 900 kg/m³
  4. 4.5 kg/m³

Explanation

Bulk density is total mass divided by total volume: 90 kg / 0.05 m³ = 1800 kg/m³. This includes both solids and pore water.

Question 8Other Disciplines (content domain not enumerated in the source)

In engineering economics, what does the term 'sunk cost' refer to?

  1. A cost that varies directly with production level
  2. A future cost estimated for alternatives under comparison
  3. A past cost that cannot be recovered and should be ignored in future decisions Correct answer.
  4. The cost of borrowing capital over time

Explanation

A sunk cost has already been incurred and cannot be recovered, so it is irrelevant to incremental analysis of future alternatives. Good decision-making compares only future costs and benefits.

Question 9Other Disciplines (content domain not enumerated in the source)

A 2 kg block slides down a frictionless incline that makes a 30° angle with the horizontal. Taking g = 9.81 m/s², what is the component of gravitational force parallel to the incline?

  1. 19.6 N
  2. 9.81 N Correct answer.
  3. 8.50 N
  4. 17.0 N

Explanation

The component of weight along an incline is mg sin θ. Here mg = 2 × 9.81 = 19.62 N and sin 30° = 0.5, giving 9.81 N parallel to the surface.

Question 10Other Disciplines (content domain not enumerated in the source)

A steel rod 2 m long with a cross-sectional area of 500 mm² carries an axial tensile load of 50 kN. Taking E = 200 GPa, what is the elongation?

  1. 1.0 mm Correct answer.
  2. 0.1 mm
  3. 2.0 mm
  4. 0.5 mm

Explanation

Axial elongation is δ = PL/(AE). With P = 50,000 N, L = 2000 mm, A = 500 mm², and E = 200,000 N/mm², δ = (50,000 × 2000)/(500 × 200,000) = 1.0 mm.

Question 11Other Disciplines (content domain not enumerated in the source)

A horizontal pipe carries water that flows from a 150 mm diameter section into a 75 mm diameter section. If the velocity in the larger section is 1.5 m/s, what is the velocity in the smaller section?

  1. 3.0 m/s
  2. 6.0 m/s Correct answer.
  3. 1.5 m/s
  4. 0.75 m/s

Explanation

Continuity for incompressible flow requires A₁V₁ = A₂V₂. Since area scales with diameter squared, the velocity scales by (150/75)² = 4, giving V₂ = 4 × 1.5 = 6.0 m/s.

Question 12Other Disciplines (content domain not enumerated in the source)

A gas undergoes an isothermal expansion at 400 K while absorbing 8000 J of heat. Treating the gas as ideal, how much work does it do?

  1. 0 J
  2. 8000 J Correct answer.
  3. 16000 J
  4. 4000 J

Explanation

For an ideal gas, internal energy depends only on temperature, so an isothermal process has ΔU = 0. The first law then gives Q = W, so the work done equals the heat absorbed, 8000 J.

Question 13Other Disciplines (content domain not enumerated in the source)

In a vapor-compression refrigeration cycle, what is the function of the expansion (throttling) valve?

  1. It compresses vapor from low to high pressure.
  2. It raises the refrigerant pressure from the evaporator to the condenser.
  3. It drops the refrigerant pressure and temperature before it enters the evaporator. Correct answer.
  4. It removes heat from the refrigerant to the surroundings.

Explanation

The expansion valve throttles the refrigerant from condenser pressure to evaporator pressure, lowering its temperature so it can absorb heat in the evaporator. The process is essentially isenthalpic.

Question 14Other Disciplines (content domain not enumerated in the source)

A series circuit contains a 60 Ω resistor and a 30 Ω resistor connected to a 12 V source. What is the voltage drop across the 60 Ω resistor?

  1. 6 V
  2. 12 V
  3. 8 V Correct answer.
  4. 4 V

Explanation

The total resistance is 90 Ω, so the current is 12/90 = 0.133 A. The drop across 60 Ω is 0.133 × 60 = 8 V, which also follows from the voltage divider ratio 60/90.

Question 15Other Disciplines (content domain not enumerated in the source)

A reaction has an equilibrium constant K much greater than 1 at a given temperature. What does this indicate?

  1. The reaction is far endothermic.
  2. The reaction proceeds at a very high rate.
  3. Reactants are strongly favored at equilibrium.
  4. Products are strongly favored at equilibrium. Correct answer.

Explanation

For a reaction at equilibrium, a large K means the product-side activities are much greater than reactant-side activities, so products dominate. K describes thermodynamic position, not kinetic speed.

Question 16Other Disciplines (content domain not enumerated in the source)

A soil sample has a void ratio of 0.60 and a specific gravity of solids of 2.70. Taking the unit weight of water as 9.81 kN/m³, what is the saturated unit weight?

  1. 16.6 kN/m³
  2. 14.9 kN/m³
  3. 20.7 kN/m³
  4. 18.4 kN/m³ Correct answer.

Explanation

Saturated unit weight is γ_sat = (G_s + e)γ_w/(1 + e). Substituting gives (2.70 + 0.60)(9.81)/(1.60) = 32.37/1.60 ≈ 18.4 kN/m³.

Question 17Other Disciplines (content domain not enumerated in the source)

A project requires an initial investment of $50,000 and returns $15,000 per year for 5 years. At an interest rate of 8 percent, what is the present worth of the annual returns? Use the uniform series present worth factor (P/A, 8%, 5) ≈ 3.993.

  1. $75,000
  2. $29,895
  3. $59,895 Correct answer.
  4. $45,000

Explanation

The present worth of a uniform series is A × (P/A, i, n). Multiplying $15,000 by 3.993 yields approximately $59,895, which exceeds the initial cost and indicates a favorable project.

Question 18Other Disciplines (content domain not enumerated in the source)

A 5 kg mass attached to a spring of stiffness 500 N/m oscillates on a frictionless surface. What is the natural frequency of oscillation in rad/s?

  1. 0.1 rad/s
  2. 5 rad/s
  3. 100 rad/s
  4. 10 rad/s Correct answer.

Explanation

The natural angular frequency of a spring-mass system is ω = √(k/m). Here ω = √(500/5) = √100 = 10 rad/s.

Question 19Other Disciplines (content domain not enumerated in the source)

A steel specimen with a rectangular cross section 10 mm wide by 20 mm thick is loaded in tension. If the yield strength is 250 MPa, what axial load causes first yielding?

  1. 500 kN
  2. 100 kN
  3. 50 kN Correct answer.
  4. 25 kN

Explanation

The cross-sectional area is 10 mm × 20 mm = 200 mm². Yielding begins when σ = P/A reaches 250 N/mm², so P = 250 × 200 = 50,000 N = 50 kN.

Question 20Other Disciplines (content domain not enumerated in the source)

A pump delivers 0.02 m³/s of water against a total head of 25 m. Taking water density as 1000 kg/m³ and g = 9.81 m/s², what is the hydraulic power delivered to the water?

  1. 2.45 kW
  2. 4.9 kW Correct answer.
  3. 0.49 kW
  4. 49 kW

Explanation

Hydraulic power is P = ρgQH. Substituting gives 1000 × 9.81 × 0.02 × 25 ≈ 4905 W, or about 4.9 kW.

Question 21Other Disciplines (content domain not enumerated in the source)

A simply supported beam of length 4 m carries a concentrated load of 20 kN at its midspan. What is the maximum bending moment?

  1. 20 kN·m Correct answer.
  2. 10 kN·m
  3. 80 kN·m
  4. 40 kN·m

Explanation

For a simply supported beam with a central point load P, the maximum moment is PL/4. Here M = 20 × 4/4 = 20 kN·m at midspan.

Question 22Other Disciplines (content domain not enumerated in the source)

A rigid tank contains an ideal gas at 300 K and 200 kPa. The gas is heated until its temperature reaches 450 K while the volume is held constant. What is the final pressure?

  1. 133 kPa
  2. 400 kPa
  3. 300 kPa Correct answer.
  4. 150 kPa

Explanation

At constant volume, the ideal gas law reduces to P₂/P₁ = T₂/T₁. Thus P₂ = 200 × (450/300) = 300 kPa.

Question 23Other Disciplines (content domain not enumerated in the source)

A cantilever beam of length L carries a uniformly distributed load w over its entire length. What are the maximum bending moment and its location?

  1. wL²/2 at the fixed support Correct answer.
  2. wL²/12 at the fixed support
  3. wL²/2 at the free end
  4. wL²/8 at midspan

Explanation

For a cantilever with a full uniform load, the fixed-end reaction moment is wL²/2, and the bending moment decreases parabolically to zero at the free end. So the maximum occurs at the support.

Question 24Other Disciplines (content domain not enumerated in the source)

Water flows through a horizontal pipe with a sudden enlargement. Applying the energy equation with a loss coefficient based on the smaller-section velocity, which statement best describes the head change across the enlargement?

  1. Total head increases because the velocity decreases.
  2. Static pressure rises but total head decreases by the minor loss. Correct answer.
  3. Both static pressure and total head remain unchanged.
  4. Static pressure falls and velocity rises across the enlargement.

Explanation

Across a sudden enlargement the velocity decreases, so the pressure recovers according to Bernoulli, but irreversible mixing causes a minor head loss. Thus static pressure rises while total head drops by the loss term.

Question 25Other Disciplines (content domain not enumerated in the source)

A closed system undergoes a process in which 500 J of work is done on the system and 200 J of heat is transferred out of the system. Using the sign convention where heat added and work done by the system are positive, what is the change in internal energy?

  1. 700 J
  2. −300 J
  3. 300 J Correct answer.
  4. −700 J

Explanation

With Q positive into the system and W positive out of the system, the first law is ΔU = Q − W. Here Q = −200 J and W = −500 J, so ΔU = −200 − (−500) = +300 J.

Question 26Other Disciplines (content domain not enumerated in the source)

A simply supported beam of rectangular cross section has width b = 100 mm and depth h = 200 mm. What is its elastic section modulus S about the horizontal centroidal axis?

  1. 1.33 × 10^6 mm³
  2. 6.67 × 10^5 mm³ Correct answer.
  3. 3.33 × 10^5 mm³
  4. 2.00 × 10^6 mm³

Explanation

The moment of inertia about the horizontal centroidal axis is I = b·h³/12 = 100 × 200³/12 = 6.667 × 10^7 mm⁴, and the section modulus is S = I/c with c = h/2 = 100 mm. Dividing gives S = 6.667 × 10^5 mm³, which sets the bending stress as σ = M/S.

Question 27Other Disciplines (content domain not enumerated in the source)

In a Mohr's circle for plane stress, the radius of the circle equals which quantity?

  1. The von Mises equivalent stress
  2. The larger principal stress
  3. The maximum in-plane shear stress Correct answer.
  4. The average normal stress

Explanation

Mohr's circle is constructed with center at the average normal stress and radius equal to the maximum in-plane shear stress, R = sqrt[((σx − σy)/2)² + τxy²]. The principal stresses are the center plus or minus the radius, and the peak shear ordinate equals the radius itself.

Question 28Other Disciplines (content domain not enumerated in the source)

A 6061-T6 aluminum bar and a steel bar have identical lengths and cross sections and are loaded by the same axial tensile force. Taking E_al ≈ 69 GPa and E_steel ≈ 200 GPa, what is the ratio of aluminum elongation to steel elongation?

  1. About 0.12
  2. About 1.0
  3. About 2.9 Correct answer.
  4. About 0.35

Explanation

Axial elongation is δ = PL/(AE), so for equal P, L, and A the elongation is inversely proportional to E. The ratio is E_steel/E_al = 200/69 ≈ 2.9, meaning the aluminum bar stretches nearly three times as much as the steel bar.

Question 29Other Disciplines (content domain not enumerated in the source)

A steady heat flow of 1.2 kW passes through a 0.05 m thick wall of area 4 m². If the inner surface is at 90 °C and the outer surface at 10 °C, what is the thermal conductivity?

  1. 5.25 W/(m·K)
  2. 0.19 W/(m·K) Correct answer.
  3. 0.75 W/(m·K)
  4. 1.33 W/(m·K)

Explanation

Fourier's law for a plane wall gives q = kAΔT/L, so k = qL/(AΔT) = 1200 × 0.05/(4 × 80) = 0.1875 W/(m·K). This is a plausible value for an insulating or low-conductivity material.

Question 30Other Disciplines (content domain not enumerated in the source)

Which dimensionless group expresses the ratio of inertial forces to viscous forces in a flowing fluid?

  1. Nusselt number
  2. Froude number
  3. Reynolds number Correct answer.
  4. Prandtl number

Explanation

The Reynolds number Re = ρVD/μ compares inertial to viscous forces and governs laminar versus turbulent regime transitions. Its magnitude indicates which force dominates and whether the flow is likely to be stable and layered or chaotic.

Question 31Other Disciplines (content domain not enumerated in the source)

A Carnot heat engine operates between a 600 K source and a 300 K sink. What is its thermal efficiency?

  1. 1.00
  2. 0.30
  3. 0.50 Correct answer.
  4. 0.67

Explanation

For a reversible Carnot engine, efficiency is η = 1 − T_C/T_H using absolute temperatures. Substituting gives 1 − 300/600 = 0.50, so half of the heat drawn from the source becomes work.

Question 32Other Disciplines (content domain not enumerated in the source)

In a steady-flow device, 50 kW of heat is transferred to the working fluid while 20 kW of shaft work is delivered by the fluid. Neglecting kinetic and potential energy changes, what is the mass flow rate if the fluid enthalpy rises by 60 kJ/kg?

  1. 0.50 kg/s Correct answer.
  2. 1.17 kg/s
  3. 0.83 kg/s
  4. 1.50 kg/s

Explanation

The steady-flow energy balance with negligible KE and PE reduces to Q − W = ṁ(h₂ − h₁). With Q = +50 kW and W = +20 kW, the net energy into the fluid is 30 kW, so ṁ = 30/60 = 0.50 kg/s.

Question 33Other Disciplines (content domain not enumerated in the source)

A 10 Ω resistor dissipates 90 W. What is the current through it?

  1. 0.33 A
  2. 30 A
  3. 9 A
  4. 3 A Correct answer.

Explanation

Joule heating in a resistor is P = I²R, so I = sqrt(P/R) = sqrt(90/10) = 3 A. The corresponding voltage drop is IR = 30 V, which also satisfies P = V²/R.

Question 34Other Disciplines (content domain not enumerated in the source)

A transformer with 200 turns on its primary and 50 turns on its secondary is connected to a 240 V rms primary supply. What is the secondary voltage?

  1. 240 V
  2. 480 V
  3. 960 V
  4. 60 V Correct answer.

Explanation

For an ideal transformer the voltage ratio equals the turns ratio: V_s = V_p(N_s/N_p) = 240 × (50/200) = 60 V. This is a step-down transformer, so the secondary voltage is one quarter of the primary.

Question 35Other Disciplines (content domain not enumerated in the source)

An ideal operational amplifier circuit is configured as a non-inverting amplifier with R_f = 90 kΩ and R_in = 10 kΩ. What is the closed-loop voltage gain?

  1. 9
  2. 10 Correct answer.
  3. 0.10
  4. 1

Explanation

For the non-inverting configuration the gain is 1 + R_f/R_in = 1 + 90/10 = 10. The input signal appears at the inverting node through feedback, so the output is ten times the input.

Question 36Other Disciplines (content domain not enumerated in the source)

For a second-order control system with a damping ratio of 0.5, what is the percent overshoot to a unit step input?

  1. About 2%
  2. About 5%
  3. About 16% Correct answer.
  4. About 50%

Explanation

Percent overshoot is given by exp(−ζπ/sqrt(1 − ζ²)) × 100. With ζ = 0.5, the exponent is −0.5π/0.866 ≈ −1.814, giving about 0.163, or roughly 16%.

Question 37Other Disciplines (content domain not enumerated in the source)

A simply supported beam of span 6 m carries a uniformly distributed load of 8 kN/m over its entire length. What is the maximum bending moment?

  1. 18 kN·m
  2. 36 kN·m Correct answer.
  3. 24 kN·m
  4. 72 kN·m

Explanation

For a uniformly loaded simply supported beam, the maximum moment is wL²/8 at midspan. Substituting w = 8 kN/m and L = 6 m gives 8 × 36/8 = 36 kN·m.

Question 38Other Disciplines (content domain not enumerated in the source)

A particle moves along a straight line with velocity v(t) = 3t² − 2t m/s, starting from the origin at t = 0. What is its displacement at t = 2 s?

  1. 4 m Correct answer.
  2. 2 m
  3. 8 m
  4. 12 m

Explanation

Displacement is the integral of velocity: x = ∫(3t² − 2t)dt = t³ − t². Evaluating at t = 2 s gives 8 − 4 = 4 m, which is the net change in position.

Question 39Other Disciplines (content domain not enumerated in the source)

A 0.5 kg ball moving horizontally at 4 m/s strikes a wall and rebounds horizontally at 3 m/s. What is the magnitude of the impulse delivered to the ball?

  1. 0.5 N·s
  2. 2.0 N·s
  3. 7.0 N·s
  4. 3.5 N·s Correct answer.

Explanation

Impulse equals the change in momentum, and the rebound reverses direction. Taking the initial direction as positive, Δp = m(v_f − v_i) = 0.5(−3 − 4) = −3.5 N·s, so the magnitude is 3.5 N·s.

Question 40Other Disciplines (content domain not enumerated in the source)

A block of mass 2 kg rests on a horizontal surface with a coefficient of static friction of 0.30. Taking g = 9.81 m/s², what horizontal force is just sufficient to start motion?

  1. 0.60 N
  2. 5.89 N Correct answer.
  3. 1.96 N
  4. 19.62 N

Explanation

The maximum static friction force is f_s = μ_s·N, and on a horizontal surface N equals the weight mg = 19.62 N. Multiplying by 0.30 gives about 5.89 N, the threshold force needed to initiate sliding.

Question 41Other Disciplines (content domain not enumerated in the source)

In a mixture of ideal gases, the total pressure equals the sum of the partial pressures exerted by each component. This statement is known as which law?

  1. Charles's law
  2. Raoult's law
  3. Dalton's law Correct answer.
  4. Henry's law

Explanation

Dalton's law of partial pressures states that the total pressure of a non-reacting ideal gas mixture is the sum of the partial pressures of its components. Each partial pressure equals the mole fraction times the total pressure.

Question 42Other Disciplines (content domain not enumerated in the source)

A first-order reaction has a rate constant of 0.05 s⁻¹. What is its half-life?

  1. 13.9 s Correct answer.
  2. 0.035 s
  3. 20.0 s
  4. 0.69 s

Explanation

For first-order kinetics the half-life is t₁/₂ = ln 2 / k, independent of initial concentration. Substituting k = 0.05 s⁻¹ gives 0.693/0.05 ≈ 13.9 s.

Question 43Other Disciplines (content domain not enumerated in the source)

Which quantity corresponds to the pH of a solution with a hydrogen ion concentration of 1.0 × 10⁻⁴ mol/L?

  1. 10.0
  2. 1.0
  3. −4.0
  4. 4.0 Correct answer.

Explanation

pH is defined as the negative base-10 logarithm of the hydrogen ion activity, approximated here by concentration. Thus pH = −log(1.0 × 10⁻⁴) = 4.0, indicating an acidic solution.

Question 44Other Disciplines (content domain not enumerated in the source)

A municipal wastewater stream has a 5-day biochemical oxygen demand of 250 mg/L and a flow of 0.10 m³/s. What mass of oxygen is demanded per day?

  1. 25 kg/d
  2. 216 kg/d
  3. 2160 kg/d Correct answer.
  4. 21.6 kg/d

Explanation

Convert flow to liters per day: 0.10 m³/s × 1000 L/m³ × 86,400 s/d = 8.64 × 10⁶ L/d. Multiplying by 250 mg/L gives 2.16 × 10⁹ mg/d, which equals 2160 kg/d.

Question 45Other Disciplines (content domain not enumerated in the source)

A horizontal curve on a highway has a radius of 200 m. If the design speed is 80 km/h and superelevation is neglected, what minimum coefficient of side friction is required?

  1. 0.40
  2. 0.16
  3. 0.05
  4. 0.25 Correct answer.

Explanation

Convert speed to m/s: 80 km/h ≈ 22.2 m/s. With no superelevation, the friction supplies all centripetal force, so f = v²/(gR) = 493/(9.81 × 200) ≈ 0.25.

Question 46Other Disciplines (content domain not enumerated in the source)

In engineering economy, which term describes the interest rate at which the present worth of a project's cash inflows equals the present worth of its outflows?

  1. Internal rate of return Correct answer.
  2. Minimum attractive rate of return
  3. Benefit-cost ratio
  4. Payback period

Explanation

The internal rate of return is the discount rate that makes the net present value of a cash flow series equal to zero. It is found by solving for the rate, then compared with a hurdle rate to decide whether to invest.

Question 47Other Disciplines (content domain not enumerated in the source)

A project has an initial cost of $20,000 and annual net savings of $6,000 for 4 years. Using a straight-line payback analysis with no discounting, what is the payback period?

  1. 3.33 years Correct answer.
  2. 1.20 years
  3. 2.00 years
  4. 4.00 years

Explanation

Simple payback divides the initial investment by the uniform annual net cash flow: 20,000/6,000 ≈ 3.33 years. This falls within the four-year life, so the investment is recovered before the project ends.

Question 48Other Disciplines (content domain not enumerated in the source)

A rectangular channel 2 m wide carries 4 m³/s of water at a uniform depth of 1 m. What is the Froude number, and what flow regime does it indicate?

  1. 0.64, supercritical
  2. 0.64, subcritical Correct answer.
  3. 1.00, critical
  4. 1.57, supercritical

Explanation

Velocity is V = Q/(by) = 4/(2 × 1) = 2 m/s, and hydraulic depth is y = 1 m. The Froude number is Fr = V/sqrt(gy) = 2/sqrt(9.81) ≈ 0.64; since Fr < 1 the flow is subcritical.

Question 49Other Disciplines (content domain not enumerated in the source)

A 2 m wide rectangular gate is hinged at its top edge and holds back 3 m of water. Taking the density of water as 1000 kg/m³ and g = 9.81 m/s², what is the total hydrostatic force on the gate?

  1. 88.3 kN Correct answer.
  2. 58.9 kN
  3. 44.1 kN
  4. 176.6 kN

Explanation

The resultant force on a vertical rectangular area is F = ρg·y_c·A, where y_c is the depth to the centroid. Here y_c = 1.5 m and A = 6 m², so F = 1000 × 9.81 × 1.5 × 6 ≈ 88.3 kN.

Question 50Other Disciplines (content domain not enumerated in the source)

A soil sample has a total unit weight of 19 kN/m³ and a water content of 15 percent. Taking the unit weight of water as 9.81 kN/m³, what is the dry unit weight?

  1. 21.9 kN/m³
  2. 16.5 kN/m³ Correct answer.
  3. 2.85 kN/m³
  4. 19.2 kN/m³

Explanation

Dry unit weight relates to total unit weight through γ_d = γ/(1 + w), where w is expressed as a decimal. Substituting gives 19/1.15 ≈ 16.5 kN/m³, which is lower than the wet value as expected.