GATE Civil Engineering Water Resources Engineering Syllabus

Water Resources Engineering syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Water Resources Engineering in GATE Civil Engineering, not a summary of it.

1. 1

   Fluid Mechanics

   8 topics

   • Properties of fluids
   • Fluid statics
   • Continuity, momentum and energy equations and their applications
   • Potential flow
   • Laminar and turbulent flow
   • Flow in pipes, pipe networks
   • Concept of boundary layer and its growth
   • Concept of lift and drag
2. 2

   Hydraulics

   9 topics

   • Forces on immersed bodies
   • Flow measurement in channels and pipes
   • Dimensional analysis and hydraulic similitude
   • Channel Hydraulics - Energy-depth relationships
   • Specific energy
   • Critical flow
   • Hydraulic jump
   • Uniform flow
   • Gradually varied flow and water surface profiles
3. 3

   Hydrology

   13 topics

   • Hydrologic cycle
   • Precipitation
   • Evaporation
   • Evapo-transpiration
   • Watershed
   • Infiltration
   • Unit hydrographs
   • Hydrograph analysis
   • Reservoir capacity
   • Flood estimation and routing
   • Surface run-off models
   • Groundwater hydrology - steady state well hydraulics and aquifers
   • Application of Darcy’s Law
4. 4

   Irrigation

   6 topics

   • Types of irrigation systems and methods
   • Crop water requirements - Duty, delta, evapo-transpiration
   • Gravity Dams and Spillways
   • Lined and unlined canals
   • Design of weirs on permeable foundation
   • Cross drainage structures

Water Resources Engineering flashcards for GATE Civil Engineering

24 of 52 cards from the Water Resources Engineering deck — real questions with worked answers.

1. Define a fluid and state how it differs from a solid in terms of shear stress response.

   A fluid is a substance that deforms continuously under the action of any applied shear stress, however small. Unlike a solid (which resists shear with a finite static deformation), a fluid cannot sustain shear at rest and keeps deforming as long as the shear acts.

2. State Newton's law of viscosity and give the formula.

   Shear stress is proportional to the rate of angular (velocity) deformation: $$\tau = \mu \frac{du}{dy}$$ where $\mu$ is the dynamic viscosity and $\frac{du}{dy}$ is the velocity gradient normal to the flow.

3. Distinguish dynamic viscosity from kinematic viscosity, including their relation and SI units.

   Dynamic viscosity $\mu$ (units $\mathrm{Pa\cdot s}$ or $\mathrm{N\cdot s/m^{2}}$) relates shear stress to velocity gradient. Kinematic viscosity $\nu = \dfrac{\mu}{\rho}$ (units $\mathrm{m^{2}/s}$) is viscosity per unit density.

4. What is surface tension, and what is the gauge pressure inside a spherical droplet and a soap bubble?

   Surface tension $\sigma$ is the tensile force per unit length acting on a liquid surface. For a droplet (one surface): $p = \dfrac{4\sigma}{d}$. For a soap bubble (two surfaces): $p = \dfrac{8\sigma}{d}$, where $d$ is diameter.

5. Give the capillary rise formula and state when rise versus depression occurs.

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

6. Define bulk modulus of elasticity and relate it to compressibility.

   Bulk modulus $K = -\dfrac{dp}{dV/V} = \dfrac{dp}{d\rho/\rho}$ measures resistance to volumetric compression. Compressibility is its reciprocal, $\beta = \dfrac{1}{K}$.

7. What is vapour pressure and how does it relate to cavitation?

   Vapour pressure is the pressure at which a liquid boils (vaporizes) at a given temperature. Cavitation occurs when the local flow pressure drops to or below the vapour pressure, forming vapour bubbles that later collapse and cause damage.

8. State the basic hydrostatic pressure variation equation for an incompressible fluid.

   $$\frac{dp}{dz} = -\rho g \quad\Rightarrow\quad p = p_0 + \rho g h$$ Pressure increases linearly with depth $h$ below the free surface.

9. State Pascal's law for pressure at a point in a static fluid.

   At any point in a fluid at rest, the pressure is the same in all directions (intensity of pressure is independent of direction): $p_x = p_y = p_z$.

10. Give the magnitude and location of the total hydrostatic force on a vertical plane surface submerged in a liquid.

    Magnitude: $F = \rho g \bar{h} A$, where $\bar{h}$ is the depth of the centroid. The centre of pressure lies below the centroid at $$h_{cp} = \bar{h} + \frac{I_G}{A\bar{h}}$$ where $I_G$ is the second moment of area about the centroidal axis.

11. State Archimedes' principle and the condition for floating equilibrium.

    Archimedes' principle: a submerged or floating body experiences an upward buoyant force equal to the weight of fluid displaced. For floating: weight of body $=$ weight of displaced fluid, $W = \rho g V_{disp}$.

12. Define metacentre and metacentric height, and give the formula for metacentric height.

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

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

    Stable equilibrium: $M$ above $G$, i.e. $GM > 0$. Unstable: $M$ below $G$, $GM < 0$. Neutral: $M$ coincides with $G$, $GM = 0$.

14. State the continuity equation for one-dimensional steady incompressible flow.

    $$A_1 V_1 = A_2 V_2 = Q = \text{constant}$$ The volumetric flow rate (discharge) is conserved between sections.

15. Write the general (differential) continuity equation for incompressible flow.

    $$\nabla \cdot \vec{V} = \frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$$

16. State Bernoulli's equation and list its key assumptions.

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

17. State the linear momentum equation (impulse-momentum principle) for steady flow.

    The net external force equals the rate of change of momentum: $$\sum \vec{F} = \rho Q (\vec{V}_2 - \vec{V}_1)$$

18. Define velocity potential function and state what its existence implies about the flow.

    The velocity potential $\phi$ is a scalar such that $u = -\dfrac{\partial \phi}{\partial x}$, $v = -\dfrac{\partial \phi}{\partial y}$. Its existence implies the flow is irrotational.

19. Define stream function and state two of its key properties.

    The stream function $\psi$ satisfies $u = \dfrac{\partial \psi}{\partial y}$, $v = -\dfrac{\partial \psi}{\partial x}$. Properties: (1) it exists for any 2-D incompressible flow (continuity automatically satisfied); (2) the difference $\psi_2 - \psi_1$ between two streamlines equals the discharge between them. Lines of constant $\psi$ are streamlines.

20. For irrotational, incompressible 2-D flow, what equation do both $\phi$ and $\psi$ satisfy, and how do their lines relate?

    Both satisfy the Laplace equation: $\nabla^{2}\phi = 0$ and $\nabla^{2}\psi = 0$. The equipotential lines ($\phi = $ const) and streamlines ($\psi = $ const) intersect orthogonally, forming a flow net.

21. Define the Reynolds number and give the critical values distinguishing laminar and turbulent flow in a pipe.

    $$Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu}$$ In pipes: laminar for $Re < 2000$, transitional for $2000 < Re < 4000$, and turbulent for $Re > 4000$.

22. For fully developed laminar flow in a circular pipe (Hagen-Poiseuille), give the velocity profile shape, the mean-to-max velocity ratio, and the friction factor.

    The velocity profile is parabolic. The mean velocity is half the maximum: $V_{avg} = \dfrac{1}{2}V_{max}$. The Darcy friction factor is $f = \dfrac{64}{Re}$.

23. State the Hagen-Poiseuille equation for discharge in laminar pipe flow.

    $$Q = \frac{\pi \Delta p\, R^{4}}{8 \mu L} = \frac{\pi \Delta p\, D^{4}}{128 \mu L}$$

24. Compare laminar and turbulent flow with respect to velocity profile and head loss dependence on velocity.

    Laminar: smooth, ordered layers, parabolic profile, head loss $\propto V$. Turbulent: chaotic mixing with eddies, flatter (logarithmic) profile, head loss $\propto V^{1.75\text{ to }2}$.

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