Fluid Mechanics Concepts

Fluid Mechanics ConceptFluid at RestFluid in MotionArchimedes EurekaAnything that flowsFluids can be liquid or gasSolving for DensityDensity = m/v; measured in kg/m^3If an object or fluid is made out of heavier atoms or molecules, then it’s going to have a higher density.Pressure = F/A; Measured in Pascals (Pa)Average air pressure at sea level is 101,325 PaSolving for the pressure at a given depth Pressure = density x gravity x heightChange in Pressure = density x gravity x change in heightThe water in the pool is one of the examples of a confined fluid.Blaise Pascal/ Pascal Principle“If you apply pressure to a confined fluid, the pressure in every part of the fluid increases by that amount.”The input of your force is doubled on your output.The bigger difference in area, the more extra force you get.Measuring the pressureManometers BarometersU shaped tube with a fluid insideIf you measured the difference in fluid height directly, you'd get what's known as gauge pressure. TO GET THE ABSOLUTE PRESSURE:P = P0 + density (g) (∆h) gauge pressure P0 = Atmospheric Pressure Long vertical tube filled with mercury. Mercury is used because it is a very dense liquid which means the air pressure supports a much shorter column so barometers can be smaller.Standard P0 = 76cmNOTE: If the air pressure goes up, so does the level of the mercury and vice versa.Lived in Greece in the third century BCE.He discovered that when you put something in a fluid, the fluids volume increases by the amount of the object's volume.Buoyant Force (FB)Counteracting the force of gravityArchimedes PrincipleThere’s a buoyant force pushing upward on object in water, and its equal to the weight of the water that the object displaced.King HieronF_B = m_F gm_F = mass of displace fluidsailing vessel, 50x bigger than a standard warshipa gift for Ptolemy (named Syracusia)Syracusia-Pitch from France-Ropes from Spain-Beams of pine and fir from Mt.EtnaComponentsProblem: Will it sink?-Ship’s Bow ‘180pound stone missiles-Top deck 8 towers-flower lined promenade-sheltered swimming & bathhouse w/ heated water-a library-temple to the goddess Aphrodite-gymnasium400 tons of grain = 10000 jars of picked fish74 tons of water600 tons of woolIt carried a thousand of people w/ 600 soldiers, w/ 20 hoursAn object partially immersed in a fluid is buoyed up by a forceFORCE=WEIGHT Of the fluid2000 tons of water= it barely float4000 tons of water=it would float1000 tons of water=it wouldn’t floatBathtub, explains why a steel can float as easyWooden rowboatLow ViscosityThe fluid flows easily, like water.High ViscosityThe fluids that don't flow as easily, like honey.Mass Flow RateIt is always going to be the same everywhere in the pipe.Equation of ContinuityThe mass flow rate at one point in the pipe will be equal to the mass flow rate at any other point.Δm1/Δt = Δm2/ΔtBernoulli's PrincipleThe higher a fluid's velocity is through a pipe, the lower the pressure on the pipe's walls, and vice versa.Pressure times volumeP + 1/2 p v^2 + pgy = a constantKinetic energy densityKE = 1/2 mv^2. Bernoulli divided this form of energy by volume, to get half the fluid's density, times its velocity squared.Potential energy comes from gravitySo when you look at his equation piece by piece, you can see that Bernoulli was really just putting conservation of energy into a special form that would be useful for fluids.Torricelli's TheoremUses conservation of energy to find the velocity of fluid flowing from a small spout in a container.The velocity of the fluid coming out of the spout is the same as the velocity of a single droplet of fluid that falls from the height of the surface of the fluid in the container.The pressure that pushing the fluid out of the spout gives it the same velocity that it would get from the force of gravity.Members: Mista, Lara Denesse; Narbay, Shanin; Pulido, Abigail; Millanes, Lameye; Reverente, Genevieve 12-STEM
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