Physics 2 Chapter 9 Section 4

Characteristics of Fluid Flow Steady vs unsteady steady – velocity of fluid particles at any point is constant as time passes velocity at 2 different points can be different but every particle that passes the same point is the same unsteady – velocity at a point in the fluid changes with time extreme case is turbulent flow Turbulent flow – occurs when there are sharp turns or obstacles Velocity at any point changes erratically

Characteristics cont’d. Compressible vs incompressible incompressible – density stays nearly constant as pressure changes most liquids are incompressible most gases are compressible

Characteristics cont’d. Viscous vs non-viscous viscous – doesn’t flow readily ex – honey flow of viscous fluid is energy-dissipating No fluid is truly non-viscous but some come close More viscous the more energy lost

Characteristics cont’d. Rotational vs irrotational rotational – part of the fluid has rotational and translational motion Irrotational – all of the fluid has translational motion only ▲ If rotational, a paddle wheel will turn since speed changes with depth

Streamline When fluid flow is steady we use streamlines to represent the trajectories of the fluid particles Streamline – line drawn such that a tangent to the streamline at any point is parallel to the fluid velocity at that point For steady flow streamlines don’t cross

Equation of Continuity The mass flow rate has the same value at every position along a tube that has a single entry and a single exit For any 2 points along the tube ρ1A1v1 = ρ2A2v2 where ρAv = mass flow rate Put finger across garden hose and water comes out faster Explain using equation of continuity

Equation of Continuity cont’d. Mass Flow Rate= mass flow rate is the mass of a substance which passes per unit of time [ρAv] = kg/s where ρ – density of fluid A – cross sectional area of tube v – speed of fluid

Equation of Continuity cont’d. If fluid is incompressible ρ1 = ρ2 so A1v1 = A2v2 where Av is volume flow rate Volume flow rate – amount of volume passing a point per second Q = Av and [Q] = m3/s If cross sectional area of tube gets smaller, speed gets faster Ex – river gets faster as it narrows

In the condition known as atherosclerosis, a deposit forms on the arterial wall and reduced the opening through which blood can flow. In the carotid artery in the neck, the radius of the opening is 3.5 mm at an unobstructed point but is only 2mm where a deposit forms. Determine the ratio of speeds of the blood at these two locations.

The water flowing from a gharden hose fills a 2 gallon bucket (231 in3) in 30s. Find the speed of the water that leaves the hose when the hose (a) has an unobstructed opening whose radius is 0.375 in (b) has an obstructed opening reducing the area by a factor of 2 of the initial.

Volume and mass flow rates are constant for an incompressible fluid Because V2 is greater than V1 there is acceleration from the large tube to the small tube. This can only be possible with an unbalanced force which is greater in the wide tube than the narrow tube.

V2 >V1; there is acceleration from wide to narrow V2 >V1; there is acceleration from wide to narrow. Fwide > Fnarrow P= F/A; (Fn <<Fw)/(An<Aw) Pressure decreases with decreased Area.

Steady, irrotational, incompressible, non-viscous fluid Can be described at any point along its path by specifying speed, pressure, and elevation Observations – 1) if cross-sectional area drops, pressure drops, remember P= F/A 2) if rise in elevation the pressure decreases if the area stays the same

Bernoulli’s Equation P1 + 1/2 ρv12 + ρgy1 = P2 + 1/2 ρv22 + ρgy2 can be used to explain cases where fluids aren’t flowing through actual pipes ex – airplane wings are curved more on upper surface curve balls drag zone in racing Hurricanes – air rotates around an area of low pressure with speeds exceeding 180 mph and pressure drop below 950 millibars (1013 millibars is normal) Coke cans suck together Airplane wings are curved more on upper surface so air travels faster and pressure is reduced Curve balls – when given a spin air close to ball is dragged around the ball so on ½ the speed is greater and pressure is less so gets deflected that way Drag zone in racing – leader creates a partial vacuum due to air flow that follower gets pulled in t0

An aneurysm is an abnormal enlargement of a blood vessel An aneurysm is an abnormal enlargement of a blood vessel. Suppose that, because of an aneurysm, the cross-sectional area of the aorta increases to 1.7 A1. The speed of the blood (ρ= 1060 kg/m3) through a normal portion of the aorta is 0.4m/s. Assuming the aorta is horizontal, determine the amount by which the pressure in the enlarge region exceeds the normal region.