Fluid Mechanics

• Fluid


  Substances that can flow and change its shape since its particles can move around with respect to one another
• Particles in solids are fixed in a lattice, resulting in their definite shape, hence this is not a fluid
• Liquids and gases are fluids since their particles can move freely
• Density


  The mass per unit volume
• Density is represented by the Greek letter, rho, not p
• The SI unit for density is kg/cm3
• Objects made of the same material have the same density, regardless of their mass and volume
• Calculating the mass and weight of air in a room

  1. Find the volume of the room

  2. Use the density formula to calculate the mass

  3. Use the weight formula to calculate the weight
• Pressure


  The force per unit area
• The SI unit for pressure is the pascal (Pa), named after the scientist Blaise Pascal
• Atmospheric pressure


  The pressure of the earth's atmosphere, which varies with weather changes and with elevation
• The normal atmospheric pressure at sea level (an average value) is 1 atmosphere (atm) which is equal to 101,325 Pa
• Pressure in a liquid


  The fluid's pressure pushes on the walls of the surrounding container, as well as on all parts of the fluid itself
• The pressure a liquid exerts depends on the depth, and increases with depth because of gravity
• Liquid pressure formula


  p = p0 + ρgh
• When you increase the pressure at the fluid's surface, the pressure at any depth increases by the same amount. This is known as Pascal's law
• Calculating the density of gasoline in a tank

  1. Use the liquid pressure formula

  2. Rearrange to solve for density
• Buoyancy


  The upward force exerted by a fluid that counteracts the downward force of an object
• Archimedes' principle


  Objects submerged in a fluid will experience an upward buoyant force equal in magnitude to the weight of the fluid being displaced
• Buoyant force can be expressed as the gravitational force of the displaced fluid, which is equal to the mass of the displaced fluid times acceleration due to gravity
• A floating object displaces fluid based on its mass, while a sinking object displaces fluid based on its volume
• Buoyant force formula


  B = ρgv
• Calculating the buoyant force on a block in water

  Use the buoyant force formula with the given values
• Continuity equation


  A1v1 = A2v2
• The continuity equation describes the relationship between the area and velocity of a fluid flow
• Calculating the velocity of water in a pipe with different cross-sectional areas

  Use the continuity equation to solve for the unknown velocity
• Bernoulli's principle


  A quantity involving the pressure p, flow speed v, and height h has the same value anywhere in a flow tube, assuming steady flow in an ideal fluid
• Bernoulli's equation


  p1 + ρgh1 + ½ρv1 2 = p2 + ρgh2 + ½ρv2 2
• Calculating the pressure at one end of a Z-shaped pipe

  Use Bernoulli's equation with the given values to solve for the unknown pressure