Fluid Mechanics and Hydraulics Notes for SSC JE Civil

Fluid mechanics and hydraulics is a regular and scoring subject of the SSC JE Civil paper. The questions are about the properties of the fluids, the pressure, the Bernoulli equation, the discharge over the notches and the weirs, the flow in the pipes and the open channels, and the pumps and the turbines. These fluid mechanics and hydraulics notes for SSC JE Civil give you the formulas and the standard values in simple tables, followed by 20 practice questions. Read them with the Strength of Materials and Structural Analysis Notes for SSC JE Civil, Soil Mechanics Notes for SSC JE and Transportation Engineering Notes for SSC JE notes.

Properties of Fluids

• A Newtonian fluid follows Newton's law of viscosity (water, air, oil); a non-Newtonian fluid does not (paint, blood, toothpaste). An ideal fluid has no viscosity and is incompressible.
• The viscosity of a liquid decreases with the temperature, while that of a gas increases.

Pressure and Its Measurement

• Pascal's law: the pressure applied to a fluid at rest is transmitted equally in all directions (used in the hydraulic lift and the hydraulic brake).
• Hydrostatic pressure: p = rho g h; it increases with the depth. Absolute pressure = gauge pressure + atmospheric pressure. A vacuum pressure is the negative gauge pressure.
• Standard atmospheric pressure = 101.325 kPa = 10.33 m of water = 760 mm of mercury.
• Manometers: piezometer (only for the liquids at a positive gauge pressure), U-tube manometer, differential manometer, inclined manometer (for the small pressures). Mechanical gauges: Bourdon tube gauge, diaphragm gauge. A barometer measures the atmospheric pressure.
• Total pressure on a plane surface: F = rho g A y_bar, where y_bar is the depth of the centroid. The centre of pressure h* = y_bar + I_G / (A y_bar); it always lies below the centroid. For a vertical rectangular surface with the top edge at the free surface, the force is rho g b d squared / 2 and the centre of pressure is at 2d / 3 from the top.
• The force on a curved surface has the horizontal component (the force on the vertical projection) and the vertical component (the weight of the liquid above the surface).

Buoyancy and Floatation

• Archimedes' principle: the buoyant force on a submerged or floating body = the weight of the fluid displaced.
• The buoyant force acts at the centre of buoyancy (B), the centroid of the displaced fluid. A body floats if its weight is equal to the weight of the fluid displaced.
• Metacentre (M) is the point about which the body starts to oscillate when it is tilted. The metacentric height GM = BM - BG, with BM = I / V (I is the moment of inertia of the waterline area and V is the volume displaced).
• The equilibrium of a floating body is stable if M is above G (GM positive), neutral if M coincides with G and unstable if M is below G. A submerged body is stable if G is below B.
• The relative density of a floating iceberg shows that about 90 percent of its volume is below the water.

Fluid Kinematics and Bernoulli's Equation

• Types of flow: steady and unsteady, uniform and non-uniform, laminar and turbulent, rotational and irrotational, compressible and incompressible.
• Continuity equation: Q = A1 v1 = A2 v2 (for the incompressible flow).
• Bernoulli's equation: p / (rho g) + v squared / (2 g) + z = constant. The three terms are the pressure head, velocity head (kinetic head) and datum head (potential head). The assumptions: steady, incompressible, non-viscous flow along a streamline.
• The total energy line (TEL) is above the hydraulic gradient line (HGL) by the velocity head.
• Venturimeter measures the discharge in a pipe: Q = Cd [a1 a2 / square root of (a1 squared - a2 squared)] square root of (2 g h). It has the convergent cone, the throat and the divergent cone; the loss of the head is small.
• Orifice meter is cheaper but has the more head loss; the pitot tube measures the velocity at a point: v = Cv square root of (2 g h).
• Momentum equation gives the force on the pipe bends and the jets.

Orifices, Mouthpieces and Notches

• A notch is an opening in the side of a tank; a weir is a structure over which the water flows in a channel.
• A sharp-crested weir has a thin crest; the broad-crested weir has a wide crest and is used in the irrigation channels.
• The velocity of approach increases the discharge; the end contraction decreases it.

Flow Through Pipes

• The boundary layer is the thin layer near a solid boundary where the velocity changes from zero to the free stream value.
• Siphon: a closed pipe that carries the water over a high point; its summit must not be more than about 7.6 m above the supply level, otherwise the water vapourises (cavitation).

Open Channel Flow

• In a uniform flow, the bed slope = the water surface slope = the energy line slope.
• The maximum velocity in a circular channel occurs at 0.81 of the diameter and the maximum discharge at 0.95 of the diameter.

Pumps and Turbines (Hydraulic Machines)

• Dimensional analysis: Buckingham's pi theorem: the number of the pi terms = the number of variables - the number of the fundamental dimensions.
• Model laws: the Reynolds model law (for the viscous forces: pipes and the submerged bodies) and the Froude model law (for the gravity forces: the open channels, spillways and the ships).
• Dimensions: force = M L T to the power -2; pressure = M L to the power -1 T to the power -2; viscosity = M L to the power -1 T to the power -1.

Important Questions Explained

Question 1: What is the value of the standard atmospheric pressure in kPa and in metres of water?
Answer: 101.325 kPa and 10.33 m of water.

Question 2: At what depth is the centre of pressure of a vertical rectangular surface whose top edge is at the free surface?
Answer: At 2d / 3 from the top (d is the depth of the surface).

Question 3: For what value of the Reynolds number is the pipe flow laminar?
Answer: Less than 2000.

Question 4: What is the head loss formula of Darcy-Weisbach?
Answer: hf = f L v squared / (2 g d).

Question 5: What are the dimensions of the most economical rectangular channel section?
Answer: Width b = 2 x depth d, and hydraulic radius R = d / 2.

Question 6: Which turbine is used for a high head and a low discharge?
Answer: The Pelton wheel (impulse turbine).

Question 7: What is the friction factor of a laminar flow in a pipe?
Answer: f = 64 / Re.

Quick Tips to Remember

• Learn the units: viscosity (Pa s), kinematic viscosity (square metre per second), pressure (Pa).
• Remember the Reynolds numbers 2000 and 4000 for the pipes.
• Remember that the best rectangular channel has b = 2d.
• Remember Q for the rectangular and the triangular notch with the powers 3/2 and 5/2.
• Learn the turbines in the order of the head: Pelton (high), Francis (medium) and Kaplan (low).
• Remember that the centre of pressure is always below the centroid.

Common Mistakes to Avoid

• Writing the Reynolds limit of the laminar flow as 4000.
• Mixing the dynamic viscosity (mu) and the kinematic viscosity (nu = mu / rho).
• Writing the power 5/2 for the rectangular notch (it is 3/2) and 3/2 for the triangular notch (it is 5/2).
• Writing Francis as a high head turbine.
• Taking the gauge pressure as the absolute pressure.

Quick Revision Points

• p = rho g h; p_abs = p_gauge + p_atm; 1 atm = 10.33 m water = 760 mm Hg.
• Continuity Q = A v; Bernoulli: p / rho g + v squared / 2g + z = constant.
• Re: laminar below 2000, turbulent above 4000; f = 64 / Re for the laminar flow.
• Darcy-Weisbach: hf = f L v squared / 2gd; maximum power in pipe when hf = H / 3.
• Manning: v = (1/n) R to the power 2/3 S to the power 1/2; best rectangular section b = 2d.
• Notches: rectangular (2/3) Cd L root(2g) H to the power 3/2; triangular (8/15) Cd tan(theta/2) root(2g) H to the power 5/2.
• Pelton: high head; Francis: medium; Kaplan: low head.

Practice Questions With Answers

1. What is the unit of the dynamic viscosity?
   Answer: Pa s (N s per square metre) (Poise in CGS).
2. What is the formula of the kinematic viscosity?
   Answer: mu / rho (Stoke).
3. What is the pressure at a depth h in a liquid?
   Answer: rho g h (Hydrostatic).
4. Which law explains the hydraulic lift?
   Answer: Pascal's law (Pressure transmitted equally).
5. What is the buoyant force equal to?
   Answer: The weight of the fluid displaced (Archimedes).
6. What is the condition for the stable equilibrium of a floating body?
   Answer: The metacentre should be above the centre of gravity (GM positive).
7. What is the equation of continuity?
   Answer: A1 v1 = A2 v2 (Constant discharge).
8. Which equation is the conservation of the energy of a flow?
   Answer: Bernoulli's equation (Along a streamline).
9. Which device measures the discharge in a pipe by the pressure difference?
   Answer: Venturimeter (Cd).
10. What is the value of Cc for a sharp-edged orifice?
    Answer: About 0.62 (Contraction).
11. What is the Reynolds number for a laminar flow?
    Answer: Less than 2000 (Pipe flow).
12. What is the friction factor for a laminar flow?
    Answer: 64 / Re (Hagen-Poiseuille).
13. Which equation gives the head loss in a pipe?
    Answer: Darcy-Weisbach equation (hf = fLv squared / 2gd).
14. What is the maximum efficiency of power transmission through a pipe?
    Answer: 66.7 percent (hf = H / 3).
15. Which formula is used in an open channel with the roughness coefficient n?
    Answer: Manning's formula (Chezy also).
16. What is the condition of the most economical rectangular channel?
    Answer: b = 2d (R = d / 2).
17. What is the Froude number for the critical flow?
    Answer: 1 (Fr = v / root(gD)).
18. What is the sudden change from the super-critical to the sub-critical flow called?
    Answer: Hydraulic jump (Energy loss).
19. Which turbine is used for the low head and the high discharge?
    Answer: Kaplan turbine (Axial flow).
20. Which pump must be primed before the starting?
    Answer: Centrifugal pump (Filled with water).

How to Practise This Topic

1. Write the formulas of the notches, the pipes and the channels on one page.
2. Learn the fluid properties and the units in a table.
3. Revise the hydraulic machines and the model laws the next day.
4. Attempt the practice questions without looking at the answers.
5. Solve the SSC practice papers and the previous year papers to practise the JE pattern.

Related Notes and Practice

• Strength of Materials and Structural Analysis Notes for SSC JE Civil
• Soil Mechanics Notes for SSC JE
• Transportation Engineering Notes for SSC JE
• Estimating, Costing and Valuation Notes for SSC JE
• Civil Engineering (SSC JE) Notes
• SSC practice papers

Frequently Asked Questions

What is fluid mechanics?

Fluid mechanics is the branch of science that studies the behaviour of the fluids (liquids and gases) at rest and in motion.

What is the difference between the dynamic and the kinematic viscosity?

The dynamic viscosity (mu) is the resistance of a fluid to the shear, while the kinematic viscosity (nu) is the dynamic viscosity divided by the density.

What is Pascal's law?

Pascal's law says that the pressure applied to a fluid at rest is transmitted equally in all directions.

What is Bernoulli's equation?

Bernoulli's equation says that for a steady, incompressible and non-viscous flow along a streamline, the sum of the pressure head, the velocity head and the datum head is constant.

What is the Reynolds number?

The Reynolds number is the ratio of the inertial forces to the viscous forces (Re = rho v d / mu). It decides if the flow is laminar or turbulent.

What is a venturimeter?

A venturimeter is a device fitted in a pipe to measure the discharge from the pressure difference between the inlet and the throat.

What is the difference between a notch and a weir?

A notch is an opening in the side of a tank, while a weir is a structure over which the water flows in a channel; both measure the discharge.

What is a hydraulic jump?

A hydraulic jump is the sudden rise in the water surface when a super-critical flow changes to a sub-critical flow, with a large loss of energy.

Which turbine is used for a high head?

The Pelton wheel, an impulse turbine, is used for a high head and a low discharge.

What is cavitation?

Cavitation is the formation and the collapse of the vapour bubbles in a liquid when the pressure falls below the vapour pressure, which damages the pumps and the turbines.

How many questions come from fluid mechanics in the SSC JE exam?

Usually 4 to 6 questions come from fluid mechanics and the hydraulics in the SSC JE Civil paper.

How can I prepare fluid mechanics for SSC JE?

Learn the formulas and the standard values in tables, solve the numerical problems and the previous year questions, and revise the hydraulic machines.