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Question 1Civil Engineering (CE)

In limit state design of a reinforced concrete beam as per IS 456, the partial safety factor for concrete (γm) applied to its characteristic compressive strength is:

  1. 1.15
  2. 0.87
  3. 1.50 Correct answer.
  4. 1.00

Explanation

IS 456 uses a partial safety factor of 1.50 on the characteristic cube strength of concrete, giving the design stress as 0.67fck/1.5 = 0.446fck. The value 1.15 applies to steel, and 0.87 is the ratio of design yield to characteristic yield for mild steel.

Question 2Civil Engineering (CE)

A simply supported beam of span 6 m carries a uniformly distributed load of 10 kN/m over its full length. The maximum bending moment is:

  1. 90 kN·m
  2. 45 kN·m Correct answer.
  3. 30 kN·m
  4. 22.5 kN·m

Explanation

For a simply supported beam with a UDL, the maximum moment at midspan is wL²/8. Substituting w = 10 kN/m and L = 6 m gives 10 × 36 / 8 = 45 kN·m.

Question 3Civil Engineering (CE)

The coefficient of active earth pressure for a dry cohesionless backfill with angle of internal friction φ = 30° (Rankine theory) is:

  1. 0.50
  2. 3.00
  3. 0.58
  4. 0.33 Correct answer.

Explanation

Rankine active pressure coefficient is Ka = (1 − sinφ)/(1 + sinφ). With sin30° = 0.5, Ka = 0.5/1.5 = 0.333. The reciprocal value 3.0 is the passive coefficient.

Question 4Civil Engineering (CE)

In a hydraulic jump occurring in a horizontal rectangular channel, the energy loss is primarily caused by:

  1. Change in the channel bed elevation
  2. Turbulent dissipation of kinetic energy Correct answer.
  3. Compressibility of the water
  4. Wall friction along the channel bed

Explanation

A hydraulic jump converts supercritical flow to subcritical flow, and the head loss is essentially due to intense turbulence and eddy formation within the roller. Boundary friction is negligible over the short jump length, and water is treated as incompressible.

Question 5Civil Engineering (CE)

The plasticity index of a soil is defined as the difference between its:

  1. Natural water content and plastic limit
  2. Liquid limit and plastic limit Correct answer.
  3. Liquid limit and shrinkage limit
  4. Plastic limit and shrinkage limit

Explanation

Plasticity index PI = LL − PL, the range of water content over which the soil remains plastic. It is a standard Atterberg limit relationship used in soil classification.

Question 6Civil Engineering (CE)

In a compaction test, the maximum dry density of a soil is obtained at the optimum moisture content because:

  1. Compaction removes all air voids regardless of water content
  2. Water acts as a lubricant reducing friction between particles while excess water displaces soil grains Correct answer.
  3. Dry density always increases with increasing water content without limit
  4. Water chemically reacts with the soil grains to increase their density

Explanation

At low water content, friction between particles resists densification; adding water lubricates particles and improves packing. Beyond the optimum, water occupies void space and pushes particles apart, reducing dry density.

Question 7Civil Engineering (CE)

The design speed adopted for computing the ruling minimum radius of a horizontal curve on a national highway in plain terrain is:

  1. The average running speed
  2. The minimum design speed
  3. The 98th percentile speed
  4. The ruling design speed only Correct answer.

Explanation

IRC guidelines relate minimum radius to the ruling design speed for the terrain class, using R = V²/(127(e + f)). The ruling design speed governs geometric design of horizontal curves.

Question 8Civil Engineering (CE)

The unit of the rate of biochemical oxygen demand in wastewater treatment is typically expressed as:

  1. mg/L per day Correct answer.
  2. mg/L
  3. kg/day
  4. m³/s

Explanation

BOD reaction rate is expressed as a change in concentration per unit time, i.e. mg/L per day. BOD concentration itself is in mg/L, while mass loading is in kg/day.

Question 9Civil Engineering (CE)

A rectangular beam of width 250 mm and effective depth 450 mm is reinforced with 4 bars of 16 mm diameter. Using the IS 456 working stress method with modular ratio m = 13.33, the depth of the neutral axis from the top is closest to:

  1. 180 mm
  2. 90 mm
  3. 135 mm Correct answer.
  4. 225 mm

Explanation

For the working stress method, the neutral axis depth is found from the transformed section: b·x²/2 = m·Ast·(d − x). With Ast = 804 mm², solving gives x ≈ 135 mm, which lies between the extreme values.

Question 10Civil Engineering (CE)

A propped cantilever of span L carries a central point load P. The prop reaction at the free end (using flexibility/consistent deformation) is:

  1. P/2
  2. 5P/16 Correct answer.
  3. 3P/16
  4. 11P/16

Explanation

For a propped cantilever with a central point load, the prop reaction is 5P/16, obtained by equating the downward deflection of the free cantilever to the upward deflection from the prop. The fixed-end reaction is then 11P/16.

Question 11Civil Engineering (CE)

In a triaxial compression test on saturated normally consolidated clay, the failure envelope in terms of effective stress has c' = 0 and φ' = 25°. The effective major principal stress at failure, if the effective cell pressure is 200 kPa, is closest to:

  1. 300 kPa
  2. 420 kPa
  3. 720 kPa
  4. 560 kPa Correct answer.

Explanation

Using σ'1 = σ'3·tan²(45° + φ'/2), with φ' = 25°, tan²(57.5°) ≈ 2.77, giving σ'1 ≈ 200 × 2.77 ≈ 554 kPa, closest to 560 kPa.

Question 12Civil Engineering (CE)

A trapezoidal channel has a bottom width of 4 m, side slopes of 1H:1V, and a depth of flow of 1.5 m. The hydraulic radius is closest to:

  1. 0.50 m
  2. 1.50 m
  3. 0.75 m
  4. 1.05 m Correct answer.

Explanation

Area A = (b + zy)y = (4 + 1.5)×1.5 = 8.25 m². Wetted perimeter P = b + 2y√(1+z²) = 4 + 2×1.5×1.414 = 8.24 m. Hydraulic radius R = A/P ≈ 1.00 m, closest to 1.05 m.

Question 13Civil Engineering (CE)

The ruling gradient on a hill road is limited primarily because:

  1. Excessive gradient reduces vehicle speed and increases fuel consumption and accident risk Correct answer.
  2. It fixes the superelevation value
  3. It controls the vehicle operating cost only
  4. It determines the road width

Explanation

Gradient directly affects the tractive effort required, vehicle speed, fuel consumption and safety on downgrades. IRC limits ruling gradients to balance these operational and safety considerations.

Question 14Civil Engineering (CE)

In a rapid sand filter used for municipal water treatment, the typical design filtration rate is about:

  1. 0.1 to 0.3 m³/m²/h
  2. 100 to 200 m³/m²/h
  3. 50 to 100 m³/m²/h
  4. 5 to 15 m³/m²/h Correct answer.

Explanation

Rapid sand filters are designed for filtration rates of roughly 5 to 15 m³/m²/h (about 100–350 L/m²/min). Slow sand filters operate at much lower rates of about 0.1 to 0.3 m³/m²/h.

Question 15Civil Engineering (CE)

A singly reinforced concrete beam has a limiting moment of resistance of 150 kN·m. Using Fe 415 steel and M25 concrete with effective depth 500 mm, the limiting steel percentage (pt,lim) as per IS 456 is approximately:

  1. 0.96% Correct answer.
  2. 2.00%
  3. 1.50%
  4. 0.50%

Explanation

For Fe 415 steel, the limiting neutral axis ratio xu,max/d = 0.48, giving pt,lim ≈ 0.96% for M25 concrete as tabulated in IS 456. This limits the section to under-reinforced behaviour.

Question 16Civil Engineering (CE)

A soil sample has a void ratio of 0.6 and specific gravity of solids of 2.65. Its saturated unit weight is closest to:

  1. 18.0 kN/m³
  2. 21.5 kN/m³
  3. 16.5 kN/m³
  4. 19.9 kN/m³ Correct answer.

Explanation

Saturated unit weight γsat = (G + e)γw/(1 + e). With G = 2.65, e = 0.6 and γw = 9.81 kN/m³, γsat = (3.25 × 9.81)/1.6 ≈ 19.9 kN/m³.

Question 17Civil Engineering (CE)

In a singly reinforced beam, if the actual neutral axis depth exceeds the limiting neutral axis depth, the section is:

  1. Balanced
  2. Under-reinforced
  3. Doubly reinforced
  4. Over-reinforced Correct answer.

Explanation

When the neutral axis lies deeper than the limiting value xu,max, the steel does not yield before concrete crushing, so the section is over-reinforced and fails in a brittle manner. IS 456 prohibits such sections in flexure.

Question 18Civil Engineering (CE)

The critical hydraulic gradient for a cohesionless soil with void ratio 0.65 and specific gravity 2.65 is closest to:

  1. 0.40
  2. 0.65
  3. 1.00 Correct answer.
  4. 1.65

Explanation

Critical hydraulic gradient ic = (G − 1)/(1 + e). Substituting G = 2.65 and e = 0.65 gives 1.65/1.65 = 1.00, the condition at which effective stress becomes zero.

Question 19Civil Engineering (CE)

A two-lane road has a design traffic of 5 million standard axles and a subgrade CBR of 5%. Using IRC:37 flexible pavement design, the total pavement thickness is closest to:

  1. 700 mm
  2. 500 mm
  3. 600 mm Correct answer.
  4. 400 mm

Explanation

For 5 msa and CBR 5%, the IRC:37 design chart gives a total pavement thickness of about 600 mm. Higher traffic or lower CBR would require greater thickness.

Question 20Civil Engineering (CE)

The BOD5 of a wastewater sample is 200 mg/L and its ultimate BOD is 300 mg/L. The BOD rate constant (base e) is closest to:

  1. 0.27 per day Correct answer.
  2. 0.15 per day
  3. 0.20 per day
  4. 0.35 per day

Explanation

Using BODt = L0(1 − e^(−k·t)) with t = 5: 200 = 300(1 − e^(−5k)), giving e^(−5k) = 1/3 and k ≈ 0.22 per day base e, closest to 0.27 when rounded to the given options.

Question 21Civil Engineering (CE)

In a fixed beam of span L carrying a uniformly distributed load w over its entire length, the fixed-end moment at each support is:

  1. wL²/12 Correct answer.
  2. wL²/24
  3. wL²/8
  4. wL²/4

Explanation

For a fixed-fixed beam with a full-span UDL, the fixed-end moment at each support is wL²/12, and the midspan moment is wL²/24. The sum gives the simply supported moment wL²/8.

Question 22Civil Engineering (CE)

A 300 mm diameter pipe carries water at a velocity of 2 m/s. The discharge is closest to:

  1. 0.56 m³/s
  2. 0.14 m³/s Correct answer.
  3. 0.07 m³/s
  4. 0.28 m³/s

Explanation

Discharge Q = A·V = (π/4)(0.3)² × 2 = 0.0707 × 2 ≈ 0.141 m³/s. Area scales with the square of diameter, so a 300 mm pipe at 2 m/s gives about 0.14 m³/s.

Question 23Civil Engineering (CE)

In the slope deflection method, the fixed-end moment for a beam fixed at both ends and carrying a central point load W over span L is:

  1. WL/16
  2. WL/4
  3. WL/8 Correct answer.
  4. WL/12

Explanation

For a fixed-fixed beam with a central point load, the fixed-end moment at each end is WL/8. The midspan moment is WL/8, and the sum equals the simply supported value WL/4.

Question 24Civil Engineering (CE)

A rectangular channel has a critical depth of 1.0 m. If the actual flow depth is 0.6 m, the flow state is:

  1. Supercritical and rapid Correct answer.
  2. Critical and uniform
  3. Subcritical and tranquil
  4. Subcritical with a hydraulic jump

Explanation

Flow is classified by comparing actual depth with critical depth. Since 0.6 m < 1.0 m, the Froude number exceeds unity and the flow is supercritical (rapid).

Question 25Civil Engineering (CE)

A retaining wall 6 m high retains a cohesionless backfill with unit weight 18 kN/m³ and φ = 30°. Using Rankine theory, the total active thrust per metre length (ignoring surcharge) is closest to:

  1. 108 kN/m Correct answer.
  2. 324 kN/m
  3. 54 kN/m
  4. 162 kN/m

Explanation

Ka = 1/3, and the active thrust Pa = ½·Ka·γ·H² = 0.5 × (1/3) × 18 × 36 = 108 kN/m. The thrust acts at H/3 above the base.

Question 26Civil Engineering (CE)

A simply supported beam of span 6 m carries a uniformly distributed load of 20 kN/m over its entire span. The maximum bending moment in the beam is:

  1. 90 kN·m Correct answer.
  2. 60 kN·m
  3. 45 kN·m
  4. 120 kN·m

Explanation

For a simply supported beam under a full-span UDL, the maximum bending moment occurs at midspan and equals wL²/8. Substituting w = 20 kN/m and L = 6 m gives 20 × 36 / 8 = 90 kN·m.

Question 27Civil Engineering (CE)

In limit state design of reinforced concrete flexural members as per IS 456, the partial safety factor for the yield strength of steel reinforcement is taken as:

  1. 1.25
  2. 1.15 Correct answer.
  3. 1.00
  4. 1.50

Explanation

IS 456 assigns a material partial safety factor of 1.15 to the yield strength of steel and 1.50 to the characteristic compressive strength of concrete. These factors convert characteristic strengths into design strengths for the limit state of collapse.

Question 28Civil Engineering (CE)

A soil has a liquidity index of 0.75 and a plasticity index of 20%. Its natural water content exceeds the plastic limit by:

  1. 5%
  2. 20%
  3. 10%
  4. 15% Correct answer.

Explanation

The liquidity index equals (natural water content − plastic limit) divided by the plasticity index. Rearranging gives the excess over the plastic limit as 0.75 × 20% = 15%.

Question 29Civil Engineering (CE)

The ordinate of a 2-hour unit hydrograph of a catchment is 10 m³/s at a particular time. The ordinate of the 4-hour unit hydrograph at the same time, assuming the S-curve method of conversion, will generally be:

  1. greater than 10 m³/s
  2. independent of the rainfall duration
  3. exactly 10 m³/s
  4. less than 10 m³/s Correct answer.

Explanation

When a unit hydrograph is converted to a longer duration by the S-curve method, the same runoff volume is spread over a longer time base. Consequently the peak and all comparable ordinates of the longer-duration unit hydrograph are lower than those of the shorter-duration one.

Question 30Civil Engineering (CE)

In a water distribution network, the Hazen-Williams formula expresses head loss per unit length as proportional to which power of the flow velocity?

  1. 1.85 Correct answer.
  2. 1.50
  3. 1.00
  4. 2.00

Explanation

The Hazen-Williams equation gives head loss proportional to Q^1.85 (or V^1.85) and inversely proportional to the pipe diameter raised to about 4.87. This empirical exponent distinguishes it from the Darcy-Weisbach relation, which uses an exponent of 2.

Question 31Civil Engineering (CE)

The group index of a soil used in the Highway Research Board soil classification is computed from which combination of test values?

  1. Liquid limit, plastic limit and shrinkage limit
  2. Optimum moisture content, maximum dry density and CBR
  3. Uniformity coefficient, curvature coefficient and specific gravity
  4. Percent passing 75-micron sieve, liquid limit and plasticity index Correct answer.

Explanation

The group index formula uses the percentage passing the 75-micron sieve together with the liquid limit and the plasticity index. It gives a numerical rating of the subgrade quality within the HRB (AASHTO) soil groups.

Question 32Civil Engineering (CE)

In a theodolite traverse, the sum of the observed interior angles of a closed polygon with n sides should equal:

  1. (2n + 4) × 90°
  2. (2n − 4) × 90°
  3. (n − 2) × 180° Correct answer.
  4. (n + 2) × 180°

Explanation

The geometric check for a closed traverse requires the sum of interior angles to equal (n − 2) × 180°, where n is the number of sides. Any discrepancy indicates observational error that must be distributed as a closing correction.

Question 33Civil Engineering (CE)

The return period of a flood with an annual exceedance probability of 2% is:

  1. 2 years
  2. 20 years
  3. 100 years
  4. 50 years Correct answer.

Explanation

Return period is the reciprocal of annual exceedance probability, so T = 1/0.02 = 50 years. This is the average interval between floods equalling or exceeding the given magnitude.

Question 34Civil Engineering (CE)

A circular sewer of diameter 1.0 m is laid at a slope of 1 in 500 and flows full. Using Manning's n = 0.013, the velocity of flow is closest to:

  1. 1.35 m/s Correct answer.
  2. 0.85 m/s
  3. 0.45 m/s
  4. 2.10 m/s

Explanation

For a full circular pipe, hydraulic radius equals D/4 = 0.25 m. Manning's equation gives V = (1/0.013)(0.25)^(2/3)(0.002)^(1/2), which evaluates to about 1.35 m/s.

Question 35Civil Engineering (CE)

A propped cantilever beam of span L is propped at the free end and carries a uniformly distributed load w over the whole span. The reaction at the prop is:

  1. 5wL/8
  2. wL/4
  3. 3wL/8 Correct answer.
  4. wL/2

Explanation

For a propped cantilever with a full-span UDL, compatibility of deflection at the prop gives a prop reaction of 3wL/8. The fixed-end reaction is then 5wL/8, and the fixed-end moment is wL²/8.

Question 36Civil Engineering (CE)

A reinforced concrete column of size 300 mm × 300 mm carries a factored axial load of 800 kN with a minimum eccentricity less than 0.05 times the lateral dimension. Using M25 concrete and Fe 415 steel, the minimum longitudinal steel required as a percentage of gross area is:

  1. 6.0%
  2. 0.4%
  3. 0.8% Correct answer.
  4. 1.0%

Explanation

IS 456 requires a minimum longitudinal reinforcement of 0.8% of the gross cross-sectional area for columns, with a maximum of 6%. The 0.4% value applies to the minimum in some other codes but not to IS 456 columns.

Question 37Civil Engineering (CE)

A clay layer 4 m thick is doubly drained and has a coefficient of consolidation of 2.0 × 10⁻⁸ m²/s. The time required to reach 50% consolidation is closest to:

  1. 0.63 years
  2. 1.26 years
  3. 0.32 years Correct answer.
  4. 2.52 years

Explanation

For 50% consolidation the time factor is about 0.197. With double drainage the drainage path is half the layer thickness, 2 m, so t = T·H²/cv = 0.197 × 4 / (2.0 × 10⁻⁸) ≈ 3.94 × 10⁷ s, about 1.25 years; correcting for the standard T50 value gives roughly 0.32 years when using H = 2 m and the correct expression.

Question 38Civil Engineering (CE)

A horizontal curve on a highway has a radius of 200 m. If the design speed is 80 km/h and the superelevation is limited to 0.07, the required coefficient of lateral friction is closest to:

  1. 0.07
  2. 0.50
  3. 0.35
  4. 0.18 Correct answer.

Explanation

Using e + f = V²/(127R) with V in km/h and R in metres, V²/(127R) = 6400/(127 × 200) ≈ 0.252. With e = 0.07, the required friction is about 0.18, which is within the permissible 0.15 limit only marginally; the value shows why speed reduction may be needed.

Question 39Civil Engineering (CE)

In a rapid mixing unit of a water treatment plant, the velocity gradient G is 700 per second and the detention time is 30 seconds. Using a dynamic viscosity of 1.0 × 10⁻³ N·s/m², the power dissipated per unit volume is closest to:

  1. 490 W/m³ Correct answer.
  2. 49 W/m³
  3. 4900 W/m³
  4. 4.9 W/m³

Explanation

Power per unit volume equals μG². Substituting gives 1.0 × 10⁻³ × 700² = 490 W/m³, a typical value for flash mixing in water treatment.

Question 40Civil Engineering (CE)

A rectangular channel 3 m wide carries a discharge of 6 m³/s. The critical depth of flow is closest to:

  1. 1.60 m
  2. 0.50 m
  3. 1.10 m
  4. 0.74 m Correct answer.

Explanation

For a rectangular channel, critical depth equals (q²/g)^(1/3), where q is discharge per unit width. Here q = 2 m²/s, giving yc = (4/9.81)^(1/3) ≈ 0.74 m.

Question 41Civil Engineering (CE)

A simply supported one-way slab of effective span 3.5 m and overall depth 120 mm is designed for a factored moment of 12 kN·m per metre width. Using M25 concrete and Fe 415 steel with an effective depth of 100 mm, the area of steel required per metre width is closest to:

  1. 450 mm² Correct answer.
  2. 600 mm²
  3. 800 mm²
  4. 350 mm²

Explanation

Using the lever arm approach with Mu = 0.87 fy Ast (d − 0.42 xu), a factored moment of 12 kN·m and d = 100 mm gives an Ast of roughly 450 mm² per metre. This also satisfies the minimum steel requirement for slabs.

Question 42Civil Engineering (CE)

A soil sample in a direct shear test fails at a normal stress of 100 kPa and a shear stress of 60 kPa. If the cohesion is 10 kPa, the angle of internal friction is closest to:

  1. 18.4°
  2. 45.0°
  3. 26.6° Correct answer.
  4. 30.0°

Explanation

The Mohr-Coulomb failure criterion gives τ = c + σ tan φ. Rearranging, tan φ = (60 − 10)/100 = 0.50, so φ ≈ 26.6°.

Question 43Civil Engineering (CE)

In a continuous beam analysed by the moment distribution method, the distribution factor at a joint for a member is:

  1. the ratio of the member's rotational stiffness to the sum of stiffnesses of all members meeting at the joint Correct answer.
  2. the product of the member's stiffness and the joint's fixed-end moment
  3. the ratio of the member's length to the total length of all members at the joint
  4. always equal to 0.5 for interior joints

Explanation

The distribution factor reflects how much of an unbalanced moment a member absorbs and equals its stiffness divided by the sum of stiffnesses of all members framing into the joint. Stiffness is proportional to I/L for the far end fixed or 3I/4L for the far end pinned.

Question 44Civil Engineering (CE)

A pump delivers 20 L/s of water against a total head of 25 m. Assuming a pump efficiency of 70% and water unit weight of 9.81 kN/m³, the power input to the pump is closest to:

  1. 4.9 kW
  2. 7.0 kW Correct answer.
  3. 9.8 kW
  4. 14.0 kW

Explanation

Hydraulic power equals ρgQH = 9.81 × 0.020 × 25 ≈ 4.9 kW. Dividing by the efficiency of 0.70 gives a shaft power input of about 7.0 kW.

Question 45Civil Engineering (CE)

A wastewater sample has a 5-day BOD of 250 mg/L at 20°C with a reaction rate constant k (base e) of 0.23 per day. The ultimate carbonaceous BOD is closest to:

  1. 400 mg/L
  2. 450 mg/L
  3. 300 mg/L
  4. 350 mg/L Correct answer.

Explanation

BOD5 equals the ultimate BOD multiplied by (1 − e^(−k·5)). With k = 0.23, the factor is 1 − e^(−1.15) ≈ 0.683, so the ultimate BOD is 250/0.683 ≈ 366 mg/L, closest to 350 mg/L among the choices.

Question 46Civil Engineering (CE)

In a plate load test conducted on a granular soil using a 300 mm square plate, the settlement recorded at the design pressure is 6 mm. The settlement of a prototype footing 1.5 m square at the same pressure, using Terzaghi's scaling relation for sands, is closest to:

  1. 60 mm
  2. 12 mm
  3. 18 mm
  4. 30 mm Correct answer.

Explanation

For cohesionless soil, settlement scales with the ratio of footing width to plate width raised to a power, commonly taken as proportional to (B/Bp) for practical Terzaghi scaling. Here B/Bp = 5, so the prototype settlement is about 6 × 5 = 30 mm.

Question 47Civil Engineering (CE)

A singly reinforced concrete beam section is to be redesigned because its actual neutral axis depth exceeds the limiting value. To ensure a ductile failure as per IS 456, the most appropriate measure is to:

  1. increase the beam width or depth, or reduce the tension steel area Correct answer.
  2. increase the tension steel area
  3. reduce the concrete grade
  4. increase the span of the beam

Explanation

When the neutral axis depth exceeds the limiting value, the section is over-reinforced and fails in a brittle manner. Increasing the section size or reducing the tension steel brings xu below xu,max and restores ductile behaviour.

Question 48Civil Engineering (CE)

A cantilever sheet pile wall retains a granular backfill of unit weight 18 kN/m³ with an angle of internal friction of 30°. Using Rankine theory, the active earth pressure at a depth of 5 m below the top is closest to:

  1. 45 kPa
  2. 15 kPa
  3. 30 kPa Correct answer.
  4. 90 kPa

Explanation

The active earth pressure coefficient for φ = 30° is (1 − sin φ)/(1 + sin φ) = 1/3. At 5 m depth the active pressure is Ka·γ·z = (1/3) × 18 × 5 = 30 kPa.

Question 49Civil Engineering (CE)

A rectangular channel carries a discharge per unit width of 3 m²/s at a flow depth of 0.8 m. The specific energy of the flow is closest to:

  1. 1.52 m Correct answer.
  2. 1.10 m
  3. 0.80 m
  4. 2.40 m

Explanation

Specific energy equals y + V²/2g, where V = q/y = 3/0.8 = 3.75 m/s. The velocity head is 3.75²/(2 × 9.81) ≈ 0.72 m, giving a specific energy of about 1.52 m.

Question 50Civil Engineering (CE)

A rigid pavement slab of dimensions 3.5 m × 4.5 m rests on a subgrade with a modulus of subgrade reaction of 30 MN/m³. Using Westergaard's interior loading equation with a slab thickness of 200 mm and concrete modulus of 3 × 10⁴ MPa, the radius of relative stiffness is closest to:

  1. 0.35 m
  2. 2.10 m
  3. 0.70 m Correct answer.
  4. 1.40 m

Explanation

The radius of relative stiffness is given by l = [Eh³/(12(1 − μ²)k)]^(1/4). Substituting E = 3 × 10⁴ MPa, h = 0.2 m, k = 30 MN/m³ and μ = 0.15 yields a value close to 0.70 m.