This article on Fluid Mechanics and Hydraulic Machines has been written by Rohit Sachdeva. He graduated from Delhi College of Engineering (now DTU) in 2012 (a gold medalist in his batch) in Civil Engineering branch. Then he appeared in Civil Engineering (CE) paper in GATE 2017 and secured an All India Rank (AIR) of 93.

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In this blog, I will be discussing an important subject of Civil Engineering: Fluid Mechanics & Hydraulic Machines. Despite being a very vast topic, its weightage in recent years in GATE has been medium.

On the other hand, studying this topic in detail is most important for interviews for people wanting to pursue their career/further studies in Water-Resource Engineering.

However, I will be focusing how to prepare this subject from GATE point of view. The scope of this subject is very vast, and it is important that at least one round of revision be done. However, it is equally important that unnecessary time is not wasted in studying this subject in too much detail.

A rough breakup of questions of various topics in last 30 years in GATE is as follows:

An analysis of last 5 years of GATE papers reflect that FM & Machines carry 4-7 marks. Both theory & numericals are important. One round of study should be invested to understand the concepts, and then one round for revision & practicing numericals. Practicing numericals is important if one wants to solve the questions within stipulated time. There are a lot of formulas which need to be learnt; it is therefore advised to make a formula sheet for future revision. The textbook(s) to be referred are mentioned in a separate comprehensive blog which you should refer.

Time required for preparation

13-15 days (if you have 8-10 month of preparation) with 4-5 hours daily
7-8 days (if you have 4-5 months of preparation) with 8 hours daily

Let’s start our topic-wise discussion (most important concepts are bold & italics):

1. PROPERTIES OF FLUIDS (1 DAY)

This chapter explains about the different properties of fluids like density, specific weight, relative density, viscosity (Newton’s law of viscosity, dynamic and kinematic viscosity, variation of viscosity with temperature, Ostwald de Waele’s power law model), compressibility, surface tension & capillarity and difference in pressure across curved surfaces (air/soap bubble & jet).

A clear understanding of all these properties is necessary for studying this subject. Practice numerical questions from viscosity, surface tension and capillarity.

2. FLUID STATICS (3 DAYS)

This is one of the important chapters in fluid mechanics. It consists of two parts:

Pressure (units of measurement, standard atmospheric pressure, local atmospheric pressure, absolute, gauge and vacuum pressure, vapor pressure and cavitation), Pascal’s law, Hydrostatic law or Torricelli’s theorem, pressure measurement devices (piezometer, manometer, mechanical devices, transducers), Hydrostatic force or total pressure on flat plates and curved plates, concept of accelerated vessels (horizontal & vertical). Understand the concepts clearly and practice numerical questions from these topics. Give importance to questions related to pressure measurement using manometer (differential, inverted and inclined) and calculation of total pressures on different surfaces.

Buoyancy: Calculation of apparent weight, equilibrium and stability, the stability of fully submerged and floating bodies, metacenter & time period of rolling. Practice 2-3 numerical to calculate apparent weights and finding the metacentric height.

3. FLUID KINEMATICS (2 DAYS)

This chapter deals with the geometry of fluid Flow without any regard to the forces causing the flow. This is a very important chapter in GATE exam point of view.

The topics include Lagrangian & Eularian approaches to analyze fluid flow, classification of fluid flows (steady & unsteady, uniform & non-uniform), velocity of flow, acceleration (local & convective acceleration, differential equations in Cartesian and cylindrical coordinates), continuity equation, streamlines, streaklines, pathlines & timelines, Stream function, rotational & irrotational flow, velocity potential function, Cauchy-Reimann equations, flow nets, vorticity and circulation. Practice different types of numerical questions which cover all these topics. Give importance to stream functions, rotational and irrotational flow.

4. FLUID DYNAMICS (3 DAYS)

Energy equation (Bernoulli’s equation: assumptions & limitations, different forms of BE), grade lines, measurement of velocity (piezometer and pitot tube), measurement of discharge (venturimeter, orificemeter, nozzlemeter, comparison of their Cd), free liquid jet (similar to projectile motion), vortex motion (free & forced vortex motion and rotation of fluid mass in a cylinder), momentum equation, forces on pipe bends, impact of jets (on flat/curved, straight/inclined/series of plates)

This chapter is also very important for GATE exam. There have been direct theory questions from this chapter. A clear idea of these concepts is necessary to answer them. Practice numerical questions mainly from forces on pipe bends, impact of jets and measurement of discharge.

5. LAMINAR FLOW (1 DAY)

This is a small chapter. You need to know the formulae for solving numerical questions within time limit. Learn the concepts once and prepare a separate formula sheet for revising. Learn the formulae for velocity, discharge, average velocity, pressure drop, head loss & shear stress for laminar flow through pipes and for laminar flow between flat plates.

6. FLOW IN PIPES & TURBULENT FLOW (3 DAYS)

This chapter is one of the most important chapters in fluid mechanics. This chapter can be divided into two portions as follows.

Flow in pipes: This topic deals with head losses in pipes, Darcy Weisbach equation, shear velocity, minor losses (expansion, contraction, exit into reservoir, discharge from reservoir (entry), bends and fittings), hydraulic power, branching of pipes/pipe junctions (series/parallel), water hammer and flow through nozzle. Both conceptual questions and numerical questions are asked from this topic.

Turbulent flow: Velocity in turbulent flow, shear stress, the establishment of flow (laminar & turbulent), hydrodynamically smooth and rough pipes, friction factor, equivalent sand-grain roughness, ageing of pipes. Practice 2-3 numerical questions which apply these concepts.

7. CONCEPT OF BOUNDARY LAYER AND ITS GROWTH (1 DAY)

This is a small chapter that is mainly formula based. Laminar, transitional and turbulent boundary layer, boundary layer thickness, laminar B.L on a flat plate (Blasius result), wall shear stress, displacement thickness, momentum thickness, energy thickness, boundary layer separation, drag and lift are the topics in this chapter.

8. DIMENSIONAL ANALYSIS (1/2 DAY)

This is again a small topic & can be solved easily. However, questions are less common nowadays. Fourier’s concept of dimensional homogeneity, Buckingham’s-π theorem, Rayleigh’s method, Model studies & Model Laws (Reynold, Euler, Mach, Froude, Weber), dimensional similitude, Similarity (undistorted & distorted models: scale ratios) are some points to study.

9. HYDRAULIC MACHINES (1.5-2 DAYS)

This topic is vast! It is like another subject in itself; either you can skip it completely, or study the following points. Turbines & Pumps are extension of the concept of “impact of jets” on the curved surface. More important than their actual working is the comparison of 2 turbines/pumps or single turbine under different heads.

Turbines: Understand the theoretical difference b/w Pelton & Francis turbines, specific speed, unit quantities (speed, discharge, power: performance of the same turbine under different head), model-prototype relations (use of specific quantities & compare 2 turbines).

Pumps: Centrifugal pump parts, series & parallel multi-staging of pumps, priming, cavitation, specific speed, model-prototype relations (use of specific quantities & compare 2 pumps), net positive suction head (NPSH), single & double acting reciprocating pump.

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