(a) A submarine can be assumed to have cylindrical shape with rounded nose. Assuming its length to be 55 m and diameter 6·0 m, determine the total power required to overcome boundary friction if it propels at the velocity of 8·0 m/s in sea water at 2

Question

(a) A submarine can be assumed to have cylindrical shape with rounded nose. Assuming its length to be 55 m and diameter 6·0 m, determine the total power required to overcome boundary friction if it propels at the velocity of 8·0 m/s in sea water at 20°C. Take mass density of sea water at 20°C as 1030 kg/m³ and kinematic viscosity of sea water at 20°C as 1 × 10⁻⁶ m²/s. (15 marks)

(b) For the beam shown in the figure below
(i) Compute the support reactions.
(ii) Write the shear force (V) and bending moment (M) value(s) at salient points as indicated in the table.

| x | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| V |   |   |   |   |   |   |
| M |   |   |   |   |   |   |

(iii) Draw the shear force diagram (SFD) indicating the nature of graph.
(iv) Draw the bending moment diagram (BMD) indicating the nature of graph.

Sign conventions for SFD and BMD are as follows:

+V

+M

25 kN/m

50 kN

40 kN

A

B

•C

•D

•E •F

300 kN-m

0.5 m

1 m

2 m

1.5 m

0.5 m 0.5 m (25 marks)

(c) Size of a rectangular simply supported beam is restricted to 300 mm × 500 mm (overall). The effective span of the beam is 5 m. The beam is subjected to an imposed load of 64 kN/m. Design the beam using M 20 grade of concrete and Fe 415 grade of steel. Take effective cover as 40 mm and width of supporting wall as 250 mm. The stress in the reinforcement can be derived from the stress-strain curve given below. Use limit state method of design.

Eₛ = 200000 N/mm² (20 marks)

UPSC Answer Check · Accepted Answer

Solve all three parts systematically, allocating approximately 25% time to part (a) on boundary layer power calculation, 40% to part (b) on SFD and BMD analysis with complete diagrams, and 35% to part (c) on limit state design of the RCC beam. Begin with clear identification of given data for each part, show all formulae with IS code references where applicable, present step-by-step calculations, and conclude with final answers in proper units.
- Part (a): Calculate Reynolds number to determine flow regime, select appropriate drag coefficient for cylindrical body, compute wetted surface area, and apply boundary layer drag formula to find power required
- Part (b)(i): Compute support reactions using equilibrium equations (ΣV=0, ΣM=0) considering UDL, point loads and applied moment
- Part (b)(ii)-(iv): Calculate SF and BM values at all salient points (A-F), complete the table, and draw SFD/BMD with proper sign conventions indicating linear/parabolic nature of curves
- Part (c): Check for limiting moment of resistance, calculate design moment, determine required steel area using limit state equations, check for minimum and maximum reinforcement, and provide detailing
- Apply correct IS 456:2000 provisions for limit state design in part (c) including partial safety factors and stress block parameters
- Use proper units throughout (kN, kNm, mm, N/mm²) and maintain consistency in calculations

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	12	Correctly identifies turbulent flow regime using Re in (a), applies proper drag coefficient for streamlined cylinder; uses correct sign conventions and equilibrium principles in (b); applies IS 456:2000 limit state philosophy with correct stress-strain relationship and neutral axis depth limits in (c)	Minor errors in flow regime identification or drag coefficient selection; some confusion in sign conventions for SFD/BMD; partial understanding of limit state method with minor errors in safety factors or stress block	Fundamental conceptual errors such as using laminar flow assumption, incorrect equilibrium setup, or working stress method instead of limit state; major errors in identifying nature of curves
Numerical accuracy	20%	12	Accurate Reynolds number (Re ≈ 4.4×10⁷), correct power ≈ 1.2-1.4 MW in (a); precise reactions (RA≈77.5 kN, RB≈117.5 kN) and all SF/BM values correct in (b); correct limiting moment check, accurate steel area calculation with proper rounding in (c)	Minor arithmetic errors (2-5% deviation) in final answers; one or two incorrect values in SF/BM table; small errors in moment calculation or steel area with partially correct final answer	Major calculation errors (>10% deviation), incorrect order of magnitude for power, completely wrong reactions, or failure to check for limiting moment leading to unsafe design
Diagram quality	20%	12	Clear, scaled SFD and BMD with all salient points marked, proper indication of linear/constant/parabolic nature, values written at key points, and correct sign conventions; neat free body diagram for reactions	Diagrams present but lacking proper scale or missing some values; nature of curves indicated but not consistently; minor errors in sign representation	Missing diagrams, incorrect shapes (e.g., straight line where parabola required), no indication of nature of curves, or completely wrong sign conventions throughout
Step-by-step derivation	20%	12	Complete derivation showing Re calculation → Cd selection → drag force → power in (a); clear section-wise SF and BM equations in (b); systematic check for Xu,max, calculation of Mu,lim, then Mu,req, and steel area with formula reference in (c)	Some steps skipped but logical flow maintained; missing intermediate calculations for some sections; partial derivation of limit state equations	No derivation shown, only final answers written; or completely wrong sequence of steps; missing critical checks like limiting moment verification
Practical interpretation	20%	12	Comments on high power requirement for submarine propulsion and relevance of streamlined shape in (a); identifies critical section for design and maximum BM location in (b); provides practical detailing (bar diameter, spacing, anchorage) and notes on deflection check in (c)	Brief mention of practical significance without elaboration; standard design conclusion without specific detailing; minimal interpretation of results	No practical interpretation, purely mathematical exercise; fails to identify that beam is singly reinforced or doubly reinforced; no mention of serviceability or durability considerations

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