Properties Of Fluids(basic)

Properties of fluids 1. Introduction

Three states of matter

Solids

Gases

Liquids

Offer permanent resistance to a deforming force.

Fluids Are capable of flowing and conform to the shape of the containing vessel and offer little resistance to change of form. When in equilibrium, fluids cannot sustain tangential or shear forces. All fluids have some degree of compressibility.

2. Properties of fluids 2.1 Density The density of a substance is that quantity of matter contained in unit volume of the substance. Mass density (ρ) It is defined as the mass (m) of the substance per unit volume. ρ=

m V

[m = W/g]

SI unit: kg/m3. 1

Typical value: The mass density of water at 4 0C is 1000 kg/m3. 2.2 Specific or unit weight (γ or w) Specific or unit weight of a substance is the weight of unit volume of the substance. For liquids, specific weight can be taken as constant for practical changes in pressure. Weight per unit volume, w = mass per unit volume × g w = ρ× g w=ρg [SI unit: Nm-3] Typical value: specific weight of water is 9.81 × 103 Nm-3 It should be noted that mass density of a body: ρ = w/g 2.3 Specific gravity of a body It is the dimensionless ratio of the weight of the body to the weight of an equal volume of a substance taken as a standard. Solids and liquids are usually referred to water (at 20 0C) as standard while gases are often referred to air free of carbon dioxide and hydrogen (at 0 0C and 1 atmosphere or 101.3 kPa pressure) as standard. Specific gravity of a substance = Weight of substance/Weight of equal volume of water = Density of substance/Density of water

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2.4 Viscosity Fluids flow under the action of forces, deforming continuously for as long as the force is applied. Deformation is caused by shearing forces F, which cut tangentially to the surface to which they are applied and cause the material originally occupying the space ABCD to deform to AB1C1D. B1

B

C1

C x

E

θ

y

A

D

If ABCD represents an element in a fluid with thickness s perpendicvular to the diagram, then the force F will act over an area A equal to BC×s. The force per unit area F/A is the shear stress τ and it is found experimentally that, in a true fluid, the rate of shear strain is directly proportionl to the shear stress. Suppose that at time t a particle E moves through a distance y from AD then, for small angles, Shear strain, Φ = x/y Rate of shear strain = x/yt = (x/t)/y = u/y, Where u = x/t is the velocity of the particle at E. Assuming that the experimental result that shear stress is proportional to shear strain, then τ = constant × u/y The term u/y is the change of velocity with y and may be written in the differential form du/dy. The constant of proportionality is known as the dynamic viscosity µ of the fluid. 3

τ = µ × du/dy This is the Newton’s Law of viscosity Kinematic viscosity, ν µ ν (nu) = ρ =

µ

µg γ = γ g

2.5 Vapour pressure When evaporation takes place within an enclosed space, the partial pressure created by the vapour molecules is called vapour pressure. 2.6 Bulk Modulus of Elasticity (K) If the force per unit area on a surface increases from p to p +δp, the relationship between change of pressure and change of volume depend on the bulk modulus of the material: Bulk Modulus = Change in pressure / Volumetric strain Where the volumetric strain is the change in volume divided by the original volume. Therefore, δp

 − δV  as δp → 0    V  dp = -V dv

K =

The concept of bulk modulus is mainly applied to liquids. Surface tension Although all molecules are in constant motion, a molecule within the body of the liquid is on average attracted equally in all directions by the other molecules surrounding it, but at the surface between liquid and air or interface between one substance and another, the upward and downward attraction are unbalanced, the surface molecules being pulled inward towards the bulk of the liquid. This causes the liquid surface to behave as if it were an elastic membrane under tension. 4

The surface tension, σ, is measured as the force acting across unit length of a line drawn in the surface. The effect of surface tension is to reduce the surface of a body of liquid to a minimum. For this reason drops of liquid tend o take spherical shape. For a small droplet, surface tension will cause an increase of internal pressure p in order to balance the surface force. Considering the forces acting on a diametral plane through a spherical drop, radius r, Force

p σ

p σ

p

Force due to internal pressure = pressure ×area = p× πr2 Force due to surface tension around the perimeter = 2πr×σ For equilibrium, p× πr2 = 2πr×σ p = 2σ/r

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In many problems with which engineers are concerned, the magnitude of surface tension forces is very small compared with the other forces acting on the fluid and may, therefore, be neglected. However, these forces can cause serious errors in hydraulic scale models through capillary effects. Capillarity Suppose that a fine tube, open at both ends, is lowered vertically into a liquid. If the liquid wets the tube, the level of liquid will rise in the tube. This means that the magnitude of the cohesion of the molecules in the liquid is lesser than the adhesion of the liquid to the walls of the tube. θ

h

For liquids that do not wet glasses, the level of the liquid would fall in the tube, e.g. mercury in glass tubes.

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h

θ

Capillarity is a serious source of error in fine gauge tubes. For example, for water in a tube of 5 mm diameter, the capillary rise will be approximately 4.5 mm, while that for mercury the corresponding figure would be – 1.4 mm. 3. Problems 1. If 6 m3 of oil weighs 47 kN, calculate its specific weight, γ, density, ρ, and specific gravity. Take specific weight of water to be 9.79 kN/m3. Solution Specific weight, γ = (47 kN)/(6 m3) = 7.833 kN/m3 Density, ρ = γ/g = (7.833N/m3)/ (9.81 m/s2) = 798 kg/m3 Specific gravity = γoil/γwater = (7.833 kN/m3)/(9.79 kN/m3) = 0.800 2. If the density of a liquid is 835 kg/m3, find its specific weight and specific gravity. [Ans: 8.20 kN/m3, 0.837] 3. What pressure must be applied to water to reduce its volume by 1.25% if the bulk modulus of elasticity is 2.19 GPa.

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