Fluids

• A fluid is a material that flows. Unlike a solid, in which the atoms occupy fixed positions, the particles of a fluid can move relative to one another. Liquids or gases are considered as fluids but plasma can display fluid behaviour
• Liquids and gases expand much more than solids when they are heated, so a fixed mass of a fluid occupies a bigger volume than the solid form so its density is reduced
• The density of a material is the mass per unit volume of that material and is a measure of how compact a substance is. It is used by the formula: D = m/V
• The weight of the atmosphere produces an air pressure of about 1.0 x 10^5 Pa at the Earth's surface
• In a column of fluid of height h, density ρ and area of cross-section A. Pressure at the base = Weight of Column / Area = mg/A = Vρg/A. Volume of the column = Ah so p = hρg
• For large values of h, gases compress in the lower regions. This means that the Earth's atmosphere has a lower density at higher altitudes and its pressure is therefore not directly proportional to height above Earth
• Upthrust is a buoyancy force that is present in water and it enables objects to float or sink. It is a consequence of the water pressure being greater below an immersed object than above it.
• Upthrust is equal to the weight of the displaced fluid. It is shown through the formula: ρVg where it is Density multiplied by the volume of displaced fluid multiplied by the gravitational field strength
• Archimedes' Principle states that when a body is totally or partially immersed in a fluid, it experiences an upthrust equal to the weight of fluid displaced
• An object will float in a fluid if the upthrust - that is, the weight of the fluid it displaces is equal to its weight
• Streamlines represent the velocity of a fluid at each point within it. They can be drawn as arrowed lines that show the paths taken by small regions of the fluid
• Laminar flow occurs when adjacent layers of fluid do not cross each other. For laminar flow there are no abrupt changes in speed or direction; the velocity at a point is constant
• If the air swirls around and forms vortices(circular/spiral method of air) or eddy current. The streamlines are no longer continuous and the flow is said to be turbulent
• For turbulent flow occurs when layers of fluid cross each other, resulting in the formation of vortices or eddy currents
• Laminar flow is an important consideration in fluid motion. The uplift on an aeroplane's wings is dependent on laminar flow, and passengers experience a rocky flight when met with turbulent conditions
• The viscosity of a fluid relates to its stickiness and its resistance to flow. Viscosity can be described in terms of the resistance between adjacent layers in laminar flow. The viscosities of liquids can be compared by observing their rates of flow through a glass tube. A simple device called a Redwood viscometer can be used
• In the 19th century, Poiseuille a French Physician showed that the rate of flow of a liquid in a uniform tube depended on the pressure per unit length across the tube, the viscosity of the liquid and the fourth power of the radius of the table
• Stokes' law states that for a sphere moving through a fluid, the viscous drag acting on it is given by the equation F=6πrηv, provided that the movement of the fluid relative to the sphere is laminar
• When a sphere is released and allowed to fall freely in a fluid, it is subjected to three forces: its weight (W), the upthrust (U), the viscous drag (F). Initially, a resultant force, FR = W - (U+F) will make the sphere accelerate downward. As the velocity of the sphere increases, the viscous drag increases according to Stokes' law until (U+F) = W. The resultant force then becomes zero and the sphere continues to fall at constant velocity known as terminal velocity
• A body moving through a fluid reaches its terminal velocity when the resultant of all the forces acting upon the body is zero
• By measuring the terminal velocity of a sphere falling through a fluid it is possible to determine the coefficient of viscosity of the fluid. For a sphere of radius r and density ρ, falling through a fluid of density ρf and viscosity η with a terminal velocity v
• It is through the equation: U + F = W where U = Weight of displaced fluid = mfg = Vρfg = 4/3 πr^3ρfg. F = Viscous Drag = 6πrηv. W = Weight of Sphere = msg = Vρsg = 4/3 πr^3ρsg. It can be written as 4/3πr^3ρfg + 6πrηv = 4/3 πr^3ρsg. Which gives the viscosity as: η = 2( ρs - ρf)gr^2/9V
• Viscosity is temperature dependent as in most liquids as temperature increases, the viscosity of liquid decreases. In gases, as temperature increases, the viscosity of gas increases. The reason that viscosity varies differently with temperature in liquids as opposed to gases, arises from the fact that the frictional forces between layers are formed by different means in them