MTH- 486: Fluid Mechanics Instructor: Dr. Fahad Munir Abbasi Assistant Professor Department of Mathematics Comsats Institute of Information Technology Islamabad, Pakistan

Layout of lecture # 4 Summary of the previous lecture Velocity of the fluid at a point: local and particle rate of change Viscosity of a fluid Real and Ideal fluids Summary

Previously we studied… Pressure, temperature and density Flow and its types Types of flow lines Stress and stress field

Velocity of the fluid at a point MTH-486, Fluid Mechanics Lec. # 04 Fig. 1: Velocity of a particle at a point.

MTH-486, Fluid Mechanics Lec. # 04 (1) (2) (3)

MTH-486, Fluid Mechanics Lec. # 04 (4) (5) (6)

MTH-486, Fluid Mechanics Lec. # 04 (7) (8) (9) (10)

MTH-486, Fluid Mechanics Lec. # 04 (11) (12) (13)

MTH-486, Fluid Mechanics Lec. # 04

Viscosity of the fluid Viscosity of a fluid is the resistance of a fluid to its motion. Or The viscosity of a fluid is a measure of its resistance to shear or angular deformation. Or Viscosity of fluids is a physical property of fluids associated with shearing deformation of fluid particles subjected to the action of applied forces. MTH-486, Fluid Mechanics Lec. # 04

Fig. 2: Deformation of a fluid element.

MTH-486, Fluid Mechanics Lec. # 04 (1)

MTH-486, Fluid Mechanics Lec. # 04 (2) (4) (3) (5) (6)

MTH-486, Fluid Mechanics Lec. # 04 (7) (8) (9)

MTH-486, Fluid Mechanics Lec. # 04

(7)

Reason for the opposite behavior of viscosity for temperature variation in liquids and gases is that in gases the resistance to deformation is primarily due to the transfer of molecular momentum. Molecules from regions of high bulk velocity collide with molecules moving with lower bulk velocity, and vice versa. These collusions transport momentum from one region of fluid to another. Since the random molecular motions increase with increasing temperature, viscosity also increases with temperature. For liquids, where molecules are much more closely packed, resistance to deformation is primarily controlled by cohesive forces among molecules. These cohesive forces decrease with increasing temperature and hence the viscosity of liquids decreases with temperature. MTH-486, Fluid Mechanics Lec. # 04

Table. 1: Viscosities and kinematic viscosities of different fluids

Graphical representation The graphical representation of shear stress versus rate of deformation for a Newtonian fluid is a straight line which passes through the origin. The slope of the line gives the value of viscosity μ for the given fluid. MTH-486, Fluid Mechanics Lec. # 04

Note: All natural fluids including the synthetic fluids are real fluids and exhibit viscosity effects. An inviscid fluid is a fictitious fluid and does not exist in nature. However, many fluids under certain engineering applications show negligible viscosity effects and can be treated as inviscid fluids. MTH-486, Fluid Mechanics Lec. # 04

Summary Velocity of the fluid at a point: local and particle rate of change Viscosity of a fluid Real and Ideal fluids

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