UPSC ESE Mechanical Engineering Fluid Mechanics Syllabus

Fluid Mechanics 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 in UPSC ESE Mechanical Engineering, not a summary of it.

1. 1

   Fluid Properties

   3 topics

   • Viscosity
   • Density
   • Surface Tension
2. 2

   Fluid Statics

   3 topics

   • Pressure Measurement
   • Buoyancy
   • Hydrostatic Forces
3. 3

   Fluid Dynamics

   3 topics

   • Continuity Equation
   • Bernoulli's Equation
   • Navier-Stokes Equations

Fluid Mechanics flashcards for UPSC ESE Mechanical Engineering

25 of 51 cards from the Fluid Mechanics deck — real questions with worked answers.

1. Define dynamic (absolute) viscosity and state its SI unit.

   Dynamic viscosity $\mu$ is the proportionality constant between shear stress and velocity gradient in Newton's law of viscosity, $\tau = \mu \frac{du}{dy}$. Its SI unit is $\mathrm{Pa\cdot s}$ (equivalently $\mathrm{N\cdot s/m^{2}}$ or $\mathrm{kg/(m\cdot s)}$).

2. State Newton's law of viscosity.

   $$\tau = \mu \frac{du}{dy}$$ where $\tau$ is shear stress, $\mu$ is dynamic viscosity, and $\frac{du}{dy}$ is the velocity gradient (rate of shear strain) perpendicular to flow.

3. Define kinematic viscosity and give its SI unit and relation to dynamic viscosity.

   Kinematic viscosity is the ratio of dynamic viscosity to density: $$\nu = \frac{\mu}{\rho}$$ Its SI unit is $\mathrm{m^{2}/s}$ (CGS unit: stokes, $1\,\mathrm{St}=10^{-4}\,\mathrm{m^{2}/s}$).

4. How do the viscosities of liquids and gases respond to an increase in temperature?

   For liquids, viscosity decreases with increasing temperature (molecular cohesion dominates). For gases, viscosity increases with increasing temperature (molecular momentum transfer dominates).

5. Classify fluids as Newtonian vs non-Newtonian based on the $\tau$ vs $\frac{du}{dy}$ relationship.

   Newtonian fluids have a linear $\tau$–$\frac{du}{dy}$ relation through the origin with constant $\mu$ (e.g. water, air). Non-Newtonian fluids have a nonlinear or non-origin relation where apparent viscosity varies (e.g. blood, paint, slurries).

6. Distinguish dilatant, pseudoplastic, and Bingham plastic fluids.

   Pseudoplastic (shear-thinning): apparent viscosity decreases with shear rate (e.g. paint). Dilatant (shear-thickening): apparent viscosity increases with shear rate (e.g. starch suspension). Bingham plastic: requires a yield stress $\tau_{0}$ before flowing, then behaves linearly: $\tau = \tau_{0} + \mu \frac{du}{dy}$ (e.g. toothpaste).

7. What is an ideal (inviscid) fluid?

   An ideal fluid is a hypothetical fluid with zero viscosity ($\mu = 0$) and is incompressible. It offers no resistance to shear, so no shear stresses develop and there is no boundary layer.

8. Give the approximate dynamic viscosity of water at $20^{\circ}\mathrm{C}$.

   Water at $20^{\circ}\mathrm{C}$ has $\mu \approx 1.0 \times 10^{-3}\,\mathrm{Pa\cdot s}$ (i.e. $1\,\mathrm{cP}$), and kinematic viscosity $\nu \approx 1.0 \times 10^{-6}\,\mathrm{m^{2}/s}$.

9. Define mass density, specific weight, and specific gravity of a fluid.

   Mass density $\rho = \frac{m}{V}$ (unit $\mathrm{kg/m^{3}}$). Specific weight $\gamma = \rho g$ (unit $\mathrm{N/m^{3}}$). Specific gravity $S = \frac{\rho}{\rho_{water}}$, a dimensionless ratio relative to water at $4^{\circ}\mathrm{C}$.

10. State the density and specific weight of water at standard conditions ($4^{\circ}\mathrm{C}$).

    $\rho_{water} = 1000\,\mathrm{kg/m^{3}}$ and specific weight $\gamma_{water} = \rho g = 1000 \times 9.81 = 9810\,\mathrm{N/m^{3}}$ (about $9.81\,\mathrm{kN/m^{3}}$).

11. Define specific volume of a fluid and give its unit.

    Specific volume is the volume per unit mass, the reciprocal of density: $$v = \frac{1}{\rho}$$ with SI unit $\mathrm{m^{3}/kg}$.

12. What is the bulk modulus of elasticity of a fluid?

    Bulk modulus $K$ measures a fluid's resistance to compression: $$K = -\frac{dp}{dV/V} = \frac{dp}{d\rho/\rho}$$ A larger $K$ means a less compressible fluid (for water $K \approx 2.2\,\mathrm{GPa}$).

13. Define surface tension and state its SI unit.

    Surface tension $\sigma$ is the tensile force per unit length acting along a liquid surface due to unbalanced cohesive molecular forces at the interface. Its SI unit is $\mathrm{N/m}$ (energy per unit area, $\mathrm{J/m^{2}}$).

14. Give the formula for the pressure inside a spherical liquid droplet.

    $$\Delta p = \frac{4\sigma}{d} = \frac{2\sigma}{r}$$ where $\sigma$ is surface tension, $d$ the diameter, and $r$ the radius. The droplet has one surface.

15. Give the excess pressure inside a soap bubble.

    $$\Delta p = \frac{8\sigma}{d} = \frac{4\sigma}{r}$$ A soap bubble has two surfaces (inner and outer), so the pressure is twice that of a droplet of the same size.

16. State the excess pressure inside a cylindrical liquid jet.

    $$\Delta p = \frac{2\sigma}{d} = \frac{\sigma}{r}$$ where $\sigma$ is surface tension and $r$ the radius of the jet.

17. Give the capillary rise/fall formula in a tube and its dependence on diameter.

    $$h = \frac{4\sigma \cos\theta}{\rho g d}$$ where $\theta$ is the contact angle and $d$ the tube diameter. Rise is inversely proportional to $d$; $\theta < 90^{\circ}$ gives a rise (wetting), $\theta > 90^{\circ}$ gives a fall (e.g. mercury).

18. What value of contact angle distinguishes capillary rise from capillary fall?

    If the contact angle $\theta < 90^{\circ}$ the liquid wets the surface and rises (e.g. water in glass). If $\theta > 90^{\circ}$ the liquid does not wet and falls/depresses (e.g. mercury in glass, $\theta \approx 130^{\circ}$).

19. State the surface tension of water in contact with air at $20^{\circ}\mathrm{C}$.

    Surface tension of water against air at about $20^{\circ}\mathrm{C}$ is approximately $\sigma \approx 0.073\,\mathrm{N/m}$ (it decreases as temperature rises).

20. State the basic hydrostatic pressure equation for a fluid at rest.

    $$p = \rho g h = \gamma h$$ The gauge pressure increases linearly with depth $h$ below a free surface; pressure is the same at all points on a horizontal plane in a connected static fluid.

21. What is the relationship between absolute, gauge, and atmospheric pressure?

    $$p_{abs} = p_{atm} + p_{gauge}$$ Gauge pressure is measured relative to atmospheric; a negative gauge pressure is a vacuum pressure: $p_{vacuum} = p_{atm} - p_{abs}$.

22. State Pascal's law.

    Pascal's law states that pressure at a point in a fluid at rest is equal in all directions (isotropic): $p_{x} = p_{y} = p_{z}$. It also implies pressure applied to a confined fluid is transmitted undiminished throughout.

23. How does a simple piezometer measure pressure, and what is its limitation?

    A piezometer is an open vertical tube tapped into the pipe; the liquid rises to a height $h$ giving gauge pressure $p = \rho g h$. Limitations: it cannot measure negative (vacuum) or gas pressures and is impractical for large pressures (very tall column).

24. For a simple U-tube manometer with a heavier gauge fluid, write the pressure at the pipe centre.

    $$p_{A} = \rho_{m} g h_{m} - \rho_{1} g h_{1}$$ where $\rho_{m}$ is the manometer (gauge) fluid density rising height $h_{m}$ and $\rho_{1}, h_{1}$ refer to the fluid in the pipe limb. Pressures are balanced about a common horizontal datum.

25. What does a differential manometer measure and write its reading for two pipes A and B.

    A differential manometer measures the pressure difference between two points. With a heavier manometer fluid: $$p_{A} - p_{B} = g\,[\rho_{m} h_{m} + \rho_{B} h_{B} - \rho_{A} h_{A}]$$ obtained by balancing pressures at the datum.

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