Lecture 2 Properties of Fluids Units and Dimensions 1

Engenharia do Ambiente Mecânica dos Fluidos Ambiental The elemental volume must be much larger than the free random path of a molecule. 2/19

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Density Dimensions and Units Dimensions Units: SIC.G.SGravitational (MK p S) kg m -3 g cm -3 UMM m -3 3

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Specific Weight, Dimensions and Units Dimensions Units: SIC.G.SGravitational (MK p S) N m -3 dine cm -3 (gcms -2 )cm -3 (10 -3 kg*10 -2 ms -2 )(10 -2 m) -3 dine cm -3 = 10 Nm -2 = 1 kgm -2 kg m -3 4

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Other properties Temperature, is a measure of molecule kinetic energy, Specific Gravity (dimensionless) SIC.G.SGravitational (MK p S) kkk 5

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Viscosity When a fluid is sheared, it begins to move at a strain rate inversely proportional to a property called its coefficient of viscosity,. 6

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Viscosity is responsible for the shear stress which opposes to the relative movement of elemental fluid volumes. Is null if there is no velocity gradient, so it destroys gradients, i.e. generates momentum diffusion. 7

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Viscosity Units SIC.G.SGravitational (MK p S) N m -2 s=kgm -1 s -1 (Poiseuille) dine cm -2 s = gcm -1 s -1 (Poise=10 Poiseuille) kg m -2 s=kgm -1 s -1 8

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Kinematic Viscosity SIC.G.SGravitational (MK p S) m 2 s -1 cm 2 s -1 m 2 s -1 9

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Flow between two plates 10

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Viscosity variability Varies much with temperature and weekly with pressure. In liquids: – Decreases with temperature, In gases: – Increases with temperature. 11

Engenharia do Ambiente Mecânica dos Fluidos Ambiental No Slip Condition 12

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Surface Tension Exists because intermolecular attraction forces between liquid molecules are higher than between the liquid molecules and air. Is responsible for drop formation and for pressure increase inside the drop. 13

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Spherical droplet Surface tension decreases with temperature. This is why solubility increases with temperature. 14

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Capilarity 15

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Summary We have seen the main fluid properties, their dimensions and units. Viscosity is relevant only when there is movement and velocity gradients are present. In the next lecture we will see properties of the flow field. 16

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Velocity, momentum, kinetic energy Momentum is the Force applied to a volume multiplied by the action time. A small force acting for long can generate big momentum. 17

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Dimensions consistency/homogeneity In one equation all terms must have the same dimensions. In Fluid mechanics this norm is usually respected. In many empirical laws (often in natural sciences) it is not, being a source of errors. Manning formula for friction is a tricky example of a non-homogeneous formula. 18

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Other properties computed from velocity 19

Engenharia do Ambiente Mecânica dos Fluidos Ambiental Momentum and kinetic energy Momentum is often called impulse 20