Engineering Mock 1

Questions on structural mechanics, fluid dynamics, and thermodynamics.

3 questions • Estimated time: 20-30 minutes

How to Use This Mock

Read each question carefully
Attempt your own answer first — spend at least 5 minutes thinking
Only reveal the model answer after you've tried
Compare your reasoning to the model answer

Structural Mechanics

A simply supported beam of length L carries a central point load P. Explain why the maximum bending stress occurs at the outer fibres of the beam, and derive an expression for this stress in terms of P, L, and the beam's second moment of area I.

Model Answer

In bending, the beam experiences a linear stress distribution through its depth: compression on one side and tension on the other, with zero stress at the neutral axis. The further a fibre is from the neutral axis, the larger the stress needed to maintain compatibility of strain.

The bending moment at mid-span for a central point load is:

M_{max} = \frac{PL}{4}

The bending stress is:

\sigma = \frac{M y}{I}

where $y$ is the perpendicular distance from the neutral axis. The maximum stress occurs at $y = c$ , the distance to the outer fibres. Thus:

\sigma_{max} = \frac{PLc}{4I}

Physically, the outer fibres undergo the largest curvature, so they must carry the most stress. This is why material is placed furthest from the neutral axis in I-beams.

Key Concepts:

Bending StressNeutral AxisSecond Moment of Area

Fluid Dynamics

Using Bernoulli’s equation, explain why the pressure at the throat of a Venturi tube is lower than the pressure in the wider section. How is this effect used to measure flow rate?

Model Answer

Bernoulli’s equation for steady, incompressible, inviscid flow along a streamline is:

p + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}

As fluid enters the narrow throat, continuity requires that velocity increases:

A_1 v_1 = A_2 v_2

Since $A_2 < A_1$ , we have $v_2 > v_1$ . The increase in velocity must be balanced by a decrease in static pressure so the total energy remains constant.

Thus the throat has a lower pressure.

To measure flow rate, the pressure difference $\Delta p = p_1 - p_2$ is recorded. Using Bernoulli and continuity:

Q = A_2 v_2 = A_2 \sqrt{\frac{2(p_1 - p_2)}{\rho (1 - (A_2/A_1)^2)}}

This makes the Venturi an accurate, low-loss flow meter.

Key Concepts:

Bernoulli’s EquationContinuityVenturi EffectFlow Measurement

Thermodynamics

Explain why the efficiency of a heat engine cannot exceed the Carnot efficiency, and discuss physically what happens as an engine attempts to approach the Carnot limit.

Model Answer

The Carnot efficiency for an engine operating between reservoirs at temperatures $T_H$ and $T_C$ is:

\eta_{Carnot} = 1 - \frac{T_C}{T_H}

It sets the upper bound for any heat engine because it is derived from the Second Law of Thermodynamics: no engine can convert heat entirely into work without producing entropy.

Real engines have unavoidable irreversibilities:

- friction

- finite temperature differences for heat transfer

- turbulence and viscous dissipation

- non-quasi-static compression/expansion

Approaching the Carnot limit requires the engine to operate quasi-statically with infinitesimal temperature differences during heat transfer. This makes the process extremely slow and power output tends to zero.

Thus, while Carnot efficiency is a theoretical maximum, real engines trade some efficiency for usable power.

Note:

Classic interview question assessing conceptual understanding of thermodynamic limits.

Key Concepts:

Carnot CycleSecond Law of ThermodynamicsEfficiencyIrreversibility

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