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Fluids. AP Physics B. Fluids. A fluid is anything that can flow Liquids Gases. Density review. r = m / V r : density (kg/m 3 ) m: mass (kg) V: volume (m 3 ) r is the Greek letter “rho”; it is NOT a P! Capital P is pressure. Lowercase p is momentum (you’ll learn later).
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Fluids AP Physics B
Fluids • A fluid is anything that can flow • Liquids • Gases
Density review • r = m / V • r : density (kg/m3) • m: mass (kg) • V: volume (m3) • r is the Greek letter “rho”; it is NOT a P! Capital P is pressure. Lowercase p is momentum (you’ll learn later). • You should remember how to do density calculations from Chemistry; review if you don’t! We don’t have time.
Pressure • P = F / A • P : pressure (Pa) • F : force (N-Newton) • A : area (m2) • Pressure unit: pascal (1 Pa = 1 N/m2) • A lot of times, the force a fluid exerts is the weight of the fluid…
What is weight? • Weight is the pull of gravity on a mass • Weight is a force • We can sometimes replace the F with mg • g = 9.8 m/s2 (this is a constant)
Observations of Fluids • Exerts pressures in all directions • Pressure is always to surfaces • If it were parallel, it would flow • The force on a surface caused by pressure is always perpendicular to every surface at every location
Atmospheric pressure • Usually at about 101000 Pa • Differences in Patm cause winds Low Patm inside eye of a hurricane contributes to the severe winds & the development of the storm surge.
Pressure of a Liquid • P = rgh (How do you get this formula?) • P : pressure (Pa) • r : density (kg/m3) • g : acceleration constant (9.8 m/s2) • h : height of liquid column (m) • This is often called hydrostatic pressureif the liquid is water. It does NOT include atmospheric pressure! • It is also sometimes called gauge pressure, since a diver’s pressure gauge obviously never includes Patm! • How would we get absolute pressure?
AP Objective!!! • No matter the shape of the container…. Pressure at equal depths within a uniform liquid is the same
Just to be sure you got it… Gauge pressure measures the pressure of the fluid….. is measured in exclusion ofPatm. It does NOT include Patm.
Pascal’s Principle • Pressure exerted on a fluid is transmitted evenly throughout the fluid • Hydraulic lifts • Pressurein = Pressureout
Archimedes’ Principle • The buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by that object • Apparent weight = weight of object – Fbuoy • Remember: r is always the fluid! • When do objects float? Fraction of floating object submerged in water
Fluid Flow • Hydrodynamics—fluid dynamics • Types of flow • Laminar (smooth) • Turbulent (friction) • Mass flow rate Because the same fluid enters A1as A2, flow rate is equal So…. r1A1v1 = r2A2v2 (equation of continuity)
Equation of Continuity • Because density usually stays same for a fluid throughout, we can cancel density • A1v1 = A2v2 • Av: volume rate of flow • Volume rate of flow can also be and has units of m3/s • Fluids move fast in broad tubes; slowly in narrow areas
Bernoulli’s Principle • High velocity, low pressure • Low velocity, high pressure • Study in law of conservation of energy • Assumes no energy loss as fluids travel along a path P1 + ½ r1v12+ r1gy1 = P2 + ½ r2v22+ r2gy2 You can have 2 points anywhere along a flow & a lot of times P doesn’t change
Torricelli’s Theorem • Top is usually open to atmosphere so there’s no flow, v = zero • Both ends open to atmosphere so P1 = P2
