GATE Mechanical Engineering Fluid Mechanics and Thermal Sciences Syllabus

Fluid Mechanics and Thermal Sciences syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Fluid Mechanics and Thermal Sciences in GATE Mechanical Engineering, not a summary of it.

1. 1

   Fluid Mechanics

   15 topics

   • Fluid properties
   • Fluid statics
   • Forces on submerged bodies
   • Stability of floating bodies
   • Control-volume analysis of mass, momentum and energy
   • Fluid acceleration
   • Differential equations of continuity and momentum
   • Bernoulli’s equation
   • Dimensional analysis
   • Viscous flow of incompressible fluids
   • Boundary layer
   • Elementary turbulent flow
   • Flow through pipes
   • Head losses in pipes, bends and fittings
   • Basics of compressible fluid flow
2. 2

   Heat-Transfer

   19 topics

   • Modes of heat transfer
   • One dimensional heat conduction
   • Resistance concept and electrical analogy
   • Heat transfer through fins
   • Unsteady heat conduction
   • Lumped parameter system
   • Heisler's charts
   • Thermal boundary layer
   • Dimensionless parameters in free and forced convective heat transfer
   • Heat transfer correlations for flow over flat plates and through pipes
   • Effect of turbulence
   • Heat exchanger performance
   • LMTD and NTU methods
   • Radiative heat transfer
   • Stefan-Boltzmann law
   • Wien's displacement law
   • Black and grey surfaces
   • View factors
   • Radiation network analysis
3. 3

   Thermodynamics

   9 topics

   • Thermodynamic systems and processes
   • Properties of pure substances
   • Behavior of ideal and real gases
   • Zeroth and first laws of thermodynamics
   • Calculation of work and heat in various processes
   • Second law of thermodynamics
   • Thermodynamic property charts and tables
   • Availability and irreversibility
   • Thermodynamic relations
4. 4

   Applications

   4 topics

   • Power Engineering
     • Air and gas compressors
     • Vapour and gas power cycles
     • Concepts of regeneration and reheat
   • I.C. Engines
     • Air-standard Otto cycle
     • Diesel cycle
     • Dual cycle
   • Refrigeration and air-conditioning
     • Vapour and gas refrigeration and heat pump cycles
     • Properties of moist air
     • Psychrometric chart
     • Basic psychrometric processes
   • Turbomachinery
     • Impulse and reaction principles
     • Velocity diagrams
     • Pelton-wheel, Francis and Kaplan turbines
     • Steam and gas turbines

Fluid Mechanics and Thermal Sciences flashcards for GATE Mechanical Engineering

21 of 50 cards from the Fluid Mechanics and Thermal Sciences deck — real questions with worked answers.

1. Define dynamic viscosity and state Newton's law of viscosity for a Newtonian fluid.

   Dynamic (absolute) viscosity $\mu$ relates shear stress to velocity gradient: $$\tau = \mu \frac{du}{dy}$$ where $\tau$ is shear stress and $\frac{du}{dy}$ is the velocity gradient (rate of shear strain). SI unit of $\mu$ is $\text{Pa·s}$.

2. What is kinematic viscosity and how does it relate to dynamic viscosity?

   Kinematic viscosity $\nu$ is the ratio of dynamic viscosity to density: $$\nu = \frac{\mu}{\rho}$$ Its SI unit is $\text{m}^{2}/\text{s}$ (CGS unit: stokes).

3. Define surface tension and give the pressure inside a spherical droplet, a soap bubble, and a liquid jet.

   Surface tension $\sigma$ is the tensile force per unit length along a liquid surface. Excess pressures: droplet $\Delta p = \frac{4\sigma}{d}$; soap bubble (two surfaces) $\Delta p = \frac{8\sigma}{d}$; liquid jet/cylinder $\Delta p = \frac{2\sigma}{d}$, where $d$ is the diameter.

4. Give the capillary rise/depression formula and state when rise vs depression occurs.

   $$h = \frac{4\sigma \cos\theta}{\rho g d}$$ where $\theta$ is the contact angle. Rise occurs for wetting liquids ($\theta < 90^\circ$, e.g. water in glass); depression occurs for non-wetting liquids ($\theta > 90^\circ$, e.g. mercury).

5. Define bulk modulus of elasticity and its relation to compressibility.

   Bulk modulus $$K = -\frac{dp}{dV/V} = \rho \frac{dp}{d\rho}$$ Compressibility $\beta = \frac{1}{K}$. A higher $K$ means the fluid is less compressible.

6. State the basic hydrostatic pressure variation equation and pressure at depth $h$ in a static incompressible fluid.

   $$\frac{dp}{dz} = -\rho g$$ For constant density, gauge pressure at depth $h$ below the free surface is $$p = \rho g h$$

7. What is the difference between absolute, gauge, and vacuum pressure?

   $$p_{abs} = p_{atm} + p_{gauge}$$ Gauge pressure is measured relative to atmospheric pressure. Vacuum (negative gauge) pressure exists when $p_{abs} < p_{atm}$, so $p_{vac} = p_{atm} - p_{abs}$.

8. For a plane submerged surface, where does the total hydrostatic force act and what is its magnitude?

   Magnitude $F = \rho g \bar{h} A$, acting at the centroid depth $\bar{h}$. It acts at the centre of pressure, located below the centroid at depth $$h_{cp} = \bar{h} + \frac{I_G \sin^{2}\theta}{\bar{h} A}$$ where $I_G$ is the second moment of area about the centroidal axis.

9. State Archimedes' principle and the expression for buoyant force.

   A body immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid: $$F_B = \rho_{fluid}\, g\, V_{displaced}$$ The force acts through the centroid of the displaced volume (centre of buoyancy).

10. Define metacentre and metacentric height, and give the formula for $GM$.

    The metacentre $M$ is the point where the buoyancy line of action intersects the body's axis when slightly tilted. Metacentric height $$GM = \frac{I}{V} - BG$$ where $I$ is the second moment of the waterplane area, $V$ the displaced volume, and $BG$ the distance between centre of buoyancy and centre of gravity.

11. State the stability conditions for a floating body in terms of metacentric height.

    Floating body: stable if $M$ lies above $G$ ($GM > 0$), unstable if $M$ below $G$ ($GM < 0$), neutral if $M$ coincides with $G$ ($GM = 0$). For a fully submerged body, stability requires $B$ (centre of buoyancy) above $G$.

12. State the Reynolds Transport Theorem in words and symbols.

    It relates the rate of change of an extensive property $N$ of a system to the control volume: $$\frac{dN_{sys}}{dt} = \frac{\partial}{\partial t}\int_{CV} \eta\,\rho\,dV + \int_{CS} \eta\,\rho\,(\vec{V}\cdot\hat{n})\,dA$$ where $\eta = N/m$ is the intensive property.

13. Write the steady-flow continuity equation for a control volume with one inlet and one outlet.

    $$\rho_1 A_1 V_1 = \rho_2 A_2 V_2$$ For incompressible flow ($\rho$ constant): $$A_1 V_1 = A_2 V_2 = Q$$

14. State the linear momentum equation for a steady-flow control volume.

    The net external force equals the net rate of momentum outflow: $$\sum \vec{F} = \int_{CS} \vec{V}\,\rho\,(\vec{V}\cdot\hat{n})\,dA = \dot{m}(\vec{V}_{out} - \vec{V}_{in})$$ for uniform single inlet/outlet.

15. Write the steady-flow energy equation (per unit weight) between two points including head loss.

    $$\frac{p_1}{\rho g} + \frac{V_1^{2}}{2g} + z_1 + h_{pump} = \frac{p_2}{\rho g} + \frac{V_2^{2}}{2g} + z_2 + h_{turbine} + h_L$$

16. Distinguish local (temporal) and convective acceleration; write total acceleration in a flow field.

    $$\vec{a} = \underbrace{\frac{\partial \vec{V}}{\partial t}}_{\text{local}} + \underbrace{(\vec{V}\cdot\nabla)\vec{V}}_{\text{convective}}$$ Local acceleration is the time change at a point; convective acceleration arises from spatial velocity variation.

17. Write the x-component of acceleration of a fluid particle in Cartesian coordinates.

    $$a_x = \frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} + w\frac{\partial u}{\partial z}$$

18. Write the differential continuity equation (general and incompressible forms).

    General: $$\frac{\partial \rho}{\partial t} + \nabla\cdot(\rho \vec{V}) = 0$$ Incompressible: $$\nabla\cdot\vec{V} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$$

19. State the Navier–Stokes equation (vector form) for an incompressible Newtonian fluid.

    $$\rho\frac{D\vec{V}}{Dt} = -\nabla p + \rho \vec{g} + \mu \nabla^{2}\vec{V}$$ The terms represent inertia, pressure gradient, body force, and viscous diffusion respectively.

20. What is the Euler equation of motion along a streamline?

    For inviscid flow: $$\frac{1}{\rho}\frac{\partial p}{\partial s} + V\frac{\partial V}{\partial s} + g\frac{\partial z}{\partial s} = 0$$ Integrating this along a streamline (steady, incompressible) yields Bernoulli's equation.

21. State Bernoulli's equation and list the assumptions behind it.

    $$\frac{p}{\rho g} + \frac{V^{2}}{2g} + z = \text{constant along a streamline}$$ Assumptions: steady, incompressible, inviscid (frictionless), flow along a streamline, no shaft work or heat transfer.

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