Nalluri And Featherstone's Civil Engineering Hydraulics (eBook)

Essential Theory with Worked Examples

Martin Marriott (Autor)

eBook Download: EPUB

2016 | 6. Auflage
John Wiley & Sons (Verlag)
978-1-118-91566-0 (ISBN)

Infos

An update of a classic textbook covering a core subject taught on most civil engineering courses. Civil Engineering Hydraulics, 6th edition contains substantial worked example sections with an online solutions manual. This classic text provides a succinct introduction to the theory of civil engineering hydraulics, together with a large number of worked examples and exercise problems. Each chapter contains theory sections and worked examples, followed by a list of recommended reading and references. There are further problems as a useful resource for students to tackle, and exercises to enable students to assess their understanding. The numerical answers to these are at the back of the book, and solutions are available to download from the book's companion website.

Martin Marriott is a chartered civil engineer with degrees from the Universities of Cambridge, London (Imperial College) and Hertfordshire. He has wide professional experience in the UK and overseas with major firms of consulting engineers, and many years of experience as a lecturer in higher education. He has an academic management role in the School of Architecture, Computing and Engineering at the University of East London.

Textauszug

Chapter 1
Properties of Fluids

1.1 Introduction

A fluid is a substance which deforms continuously, or flows, when subjected to shear stresses. The term fluid embraces both gases and liquids; a given mass of liquid will occupy a definite volume whereas a gas will fill its container. Gases are readily compressible; the low compressibility, or elastic volumetric deformation, of liquids is generally neglected in computations except those relating to large depths in the oceans and in pressure transients in pipelines.

This text, however, deals exclusively with liquids and more particularly with Newtonian liquids (i.e. those having a linear relationship between shear stress and rate of deformation).

Typical values of different properties are quoted in the text as needed for the various worked examples. For more comprehensive details of physical properties, refer to tables such as Kaye and Laby (1995) or internet versions of such information.

1.2 Engineering units

The metre–kilogram–second (mks) system is the agreed version of the international system (SI) of units that is used in this text. The physical quantities in this text can be described by a set of three primary dimensions (units): mass (kg), length (m) and time (s). Further discussion is contained in Chapter 9 regarding dimensional analysis. The present chapter refers to the relevant units that will be used.

The unit of force is called newton (N) and 1 N is the force which accelerates a mass of 1 kg at a rate of 1 m/s2 (1 N = 1 kg m/s2).

The unit of work is called joule (J) and it is the energy needed to move a force of 1 N over a distance of 1 m. Power is the energy or work done per unit time and its unit is watt (W) (1 W = 1 J/s = 1 N m/s).

1.3 Mass density and specific weight

Mass density (ρ) or density of a substance is defined as the mass of the substance per unit volume (kg/m3) and is different from series specific weight (γ), which is the force exerted by the earth’s gravity (g) upon a unit volume of the substance (γ = ρg: N/m3). In a satellite where there is no gravity, an object has no specific weight but possesses the same density that it has on the earth.

1.4 Relative density

Relative density (s) of a substance is the ratio of its mass density to that of water at a standard temperature (4°C) and pressure (atmospheric) and is dimensionless.

For water, ρ = 103 kg/m3, γ = 103 × 9.81 ≃ 104 N/m3 and s = 1.

1.5 Viscosity of fluids

Viscosity is that property of a fluid which by virtue of cohesion and interaction between fluid molecules offers resistance to shear deformation. Different fluids deform at different rates under the action of the same shear stress. Fluids with high viscosity such as syrup deform relatively more slowly than fluids with low viscosity such as water.

All fluids are viscous and ‘Newtonian fluids’ obey the linear relationship

(1.1)

where τ is the shear stress (N/m2), du/dy the velocity gradient or the rate of deformation (rad/s) and μ the coefficient of dynamic (or absolute) viscosity (N s/m2 or kg/(m s)).

Kinematic viscosity (ν) is the ratio of dynamic viscosity to mass density expressed in metres squared per second.

Water is a Newtonian fluid having a dynamic viscosity of approximately 1.0× 10-3 N s/m2 and kinematic viscosity of 1.0 × 10−6 m2/s at 20°C.

1.6 Compressibility and elasticity of fluids

All fluids are compressible under the application of an external force and when the force is removed they expand back to their original volume, exhibiting the property that stress is proportional to volumetric strain.

(1.2)

The negative sign indicates that an increase in pressure causes a decrease in volume.

Water with a bulk modulus of 2.1 × 109 N/m2 at 20°C is 100 times more compressible than steel, but it is ordinarily considered incompressible.

1.7 Vapour pressure of liquids

A liquid in a closed container is subjected to partial vapour pressure due to the escaping molecules from the surface; it reaches a stage of equilibrium when this pressure reaches saturated vapour pressure. Since this depends upon molecular activity, which is a function of temperature, the vapour pressure of a fluid also depends upon its temperature and increases with it. If the pressure above a liquid reaches the vapour pressure of the liquid, boiling occurs; for example, if the pressure is reduced sufficiently, boiling may occur at room temperature.

The saturated vapour pressure for water at 20°C is 2.45 × 103 N/m2.

1.8 Surface tension and capillarity

Liquids possess the properties of cohesion and adhesion due to molecular attraction. Due to the property of cohesion, liquids can resist small tensile forces at the interface between the liquid and air, known as surface tension (σ: N/m). If the liquid molecules have greater adhesion than cohesion, then the liquid sticks to the surface of the container with which it is in contact, resulting in a capillary rise of the liquid surface; a predominating cohesion, in contrast, causes capillary depression. The surface tension of water is 73 × 10−3 N/m at20°C.

The capillary rise or depression h of a liquid in a tube of diameter d can be written as

(1.3)

where θ is the angle of contact between liquid and solid.

Surface tension increases the pressure within a droplet of liquid. The internal pressure p balancing the surface tensional force of a small spherical droplet of radius r is given by

(1.4)

Worked examples

Example 1.1

The density of an oil at 20°C is 850 kg/m3. Find its relative density and kinematic viscosity if the dynamic viscosity is 5 × 10−3 kg/(m s).

Solution:

Example 1.2

If the velocity distribution of a viscous liquid (μ = 0.9 N s/m2) over a fixed boundary is given by u = 0.68 y - y2, in which u is the velocity (in metres per second) at a distance y (in metres) above the boundary surface, determine the shear stress at the surface and at y = 0.34 m.

Solution:

Hence, (du/dy)y=0 = 0.68 s-1 and (du/dy)y=0.34m = 0.

From Equation 1.1,

and at y = 0.34m, τ = 0.

Example 1.3

At a depth of 8.5 km in the ocean the pressure is 90/,MN/m2. The specific weight of the sea water at the surface is 10.2 kN/m3 and its average bulk modulus is 2.4 × 106 kN/m2. Determine (a) the change in specific volume, (b) the specific volume and (c) the specific weight of sea water at 8.5 km depth.

Solution:

Defining specific volume as 1/ γ (m3/kN), the specific volume of sea water at the surface = 1/10.2 = 9.8 × 10−2/, m3/kN.

References and recommended reading

1. Kaye, G. W. C. and Laby, T. H. (1995) Tables of Physical and Chemical Constants, 16th edn, Longman, London. http://www.kayelaby.npl.co.uk
2. Massey, B. S. and Ward-Smith, J. (2012) Mechanics of Fluids, 9th edn, Taylor & Francis, Abingdon, UK.

Problems

1. 1. (a) Explain why the viscosity of a liquid decreases while that of a gas increases with an increase of temperature.
   2. (b) The following data refer to a liquid under shearing action at a constant temperature. Determine its dynamic viscosity.

   du/dy (s−1)

   0

   0.2

   0.4

   0.6

   0.8

   τ (N/m2)

   0

   0

   1.9

   3.1

   4.0

2. A 300 mm wide shaft sleeve moves along a 100 mm diameter shaft at a speed of 0.5 m/s under the application of a force of 250 N in the direction of its motion. If 1000 N of force is applied, what speed will the sleeve attain? Assume the temperature of the sleeve to be constant and determine the viscosity of the Newtonian fluid in the clearance between the shaft and its sleeve if the radial clearance is estimated to be 0.075 mm.
3. A shaft of 100 mm diameter rotates at 120 rad/s in a bearing 150 mm long. If the radial clearance is 0.2 mm and the absolute viscosity of the lubricant is 0.20 kg/(m s), find the power loss in the bearing.
4. A block of dimensions 300 mm × 300 mm × 300 mm and mass 30 kg slides down a plane inclined at 30° to the horizontal, on which there is a thin film of oil of viscosity 2.3 × 10−3 N s/m2. Determine the speed of the block if the film thickness is estimated to be 0.03 mm.
5. Calculate the capillary effect (in millimetres) in a glass tube of 6 mm diameter when immersed in (i) water and (ii) mercury, both liquids being at 20°C. Assume σ to be 73 × 10−3 N/m for water and 0.5 N/m for mercury. The contact angles for water and mercury are 0 and 130°, respectively.
6. Calculate the internal...

Produkt-Details

• Erscheint lt. Verlag: 10.3.2016
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Bauingenieur- u. Bauwesen • Bauwesen • bed load • Bernoulli • boundary layer • Buckingham • Buoyancy • capillarity • Cavitation • characteristic curves • Civil Engineering & Construction • Coastal engineering • Colebrook-White • Cost benefit analysis • Culvert • Curvilinear Flow • Darcy • density • Dimensional Analysis • displacement thickness • Elasticity • Energy Dissipation • Environmental Engineering • Equilibrium • Floating • flood alleviation • flood routing • flow measurement • flow nets • Fluid Flow • Gradient Method • Hardy Cross • head balance • Head loss • Hydraulic Jump • hydraulic models • Hydrologie • Hydrologie im Bauwesen • Hydrology (Civil Engineering) • hydrostatics • Laminar • Manometer • mean sea level • metacentric height • Momentum • Moody diagram • Open channel flow • pipe networks • pipe resistance • Poiseuille • pressure transients • project appraisal • quantity balance • Regime • reservoir routing • sediment transport • Shields diagram • Similitude • SI units • Spillways • stability • Stilling Basin • streamline • Streamlines • surface tension • surge • Surges • Suspended load • sustainability • Tractive Force • Tsunami • Umwelttechnik • unsteady flow • vapour pressure • viscosity • Vortices • Water Hammer
• ISBN-10: 1-118-91566-6 / 1118915666
• ISBN-13: 978-1-118-91566-0 / 9781118915660