Fluid Mechanics Chapter 8

Fluids Ability to flow Ability to change shape Both liquids and gases Only liquids have definite volume

Density

Buoyancy Buoyant force upward force exerted on objects partially or completely submerged in a fluid Apparent weight weight of object immersed in fluid W apparent = W o – F b = W o – W f

Archimedes Principle The upward buoyant force is equal to the weight of the fluid displaced by the object. When an object is floating: Buoyant force = object weight W f = m f x g m f = ρ f x V f W f = ρ f x V f x g Buoyant force

Relationships If buoyant force is: greater than weightobject floats equal to weightobject is suspended less than weightobject sinks

Submerged Objects Can use ratios to develop a useful equation F b = ρ f x V f x g W o = ρ o x V o x g F b /W o = ρ f /ρ o

Example An object has a weight of 6.5 N. When the object is complete immersed in water, it was a weight of 5.3 N. What is the density of the object? 5.4 x 10 3 kg/m 3

Example An empty balloon has a mass of kg and is filled with hydrogen with a density of kg/m 3. The filled balloon has a radius of 0.45 m. What is the buoyant force acting on the balloon if the density of air is 1.29 kg/m 3 ?

Fluid Pressure P = F/A SI unit is Pascal (Pa) = N/m 2 101,325 Pa = 1 atm

Pascal’s Principle Pressure in a closed container is transmitted equally to every point of the fluid and to the walls of the container. P 1 = P 2 F 1 /A 1 = F 2 /A 2

Example A car weighing N sits on a large piston with an area of 0.90 m 2. If the small piston of the hydraulic lift has an area of 0.20 m 2, what force must be applied to the small piston to support the car?

Pressure varies with fluid depth P = F/A P = P 0 + ρgh

Example Water is to be pumped from the Fox River to the top of the Leo Frigo Memorial bridge which is 62 m tall. What gauge pressure is needed in the water line on the Fox River to raise the water to this height?

Fluids in Motion Laminar – smooth fluid flow; all parts pass a point along the same smooth path Turbulent – irregular fluid flow; eddy currents and unpredictable flow patterns

Ideal Fluid Ideal fluid fluid with no internal friction or viscosity and is incompressible Do not lose KE to friction as they flow Steady flow; non-turbulent

Viscosity – amount of internal friction within a fluid; high viscosity flows more slowly

Principles Mass is conserved Flow rate into a pipe equals flow rate out A 1 V 1 = A 2 V 2

Example Water flows through a 2.0 m diameter pipe at a speed of 2.0 m/s. The pipe narrows to 0.50 m diameter. 1.What is the flow rate of the water? 2.What is the speed of the water in the narrow section of the pipe?

Bernoulli’s Principle Fluid pressure is related to speed of flow Acceleration caused by unbalanced forces (pressure difference) The pressure in a fluid decreases as the fluid’s velocity increases.

Newtonian vs. Non Newtonian Newtonian fluid Viscosity does not vary with flow (shear stresses) Non Newtonian fluid Viscosity does vary with flow (shear stresses) Non Newtonian fluid (ooblek)