Fluids In Motion

Fluids In Motion

1. Fluids

   • Fluids are incompressible, its density won't change
   • Fluids are dynamic and occur lot of things inside them
     • When its flow easy it has low viscosity and when the flow is harder, they have higher viscosity, that why we pretend fluids have no viscosity
   • Also they have a laminar flow and has no viscosity
     • There is the mass flow rate, that means, mass is always going to be the same, this is because of the equation of continuity
       • To find mass flow rate, we need to know about density, area and velocity
         • So in any point of the movement fluid through something, the area by the fluids velocity will be the same in any other point
           • So in any point of the movement fluid through something, the area by the fluids velocity will be the same in any other point

2. Bernoulli's Principle

   • The higher a fluids velocity is through a pipe, the lower the pressure in the pipe walls and vice versa.
     • P + ½ p v^2 + p g y = constant.
   • Conservation of energy
     • As a fluid flows through a pipe, it won't win or lose energy.
       • When we talk about fluids, we refer to them with density rather than in mass.
         • Bernoulli transforms the conservation of energy laws into a special form useful for fluids.

3. Torricelli’s Theorem

   • The velocity of a fluid coming out of the spout is the same as the velocity of a single droplet of fluid that falls from the height of a surface of the fluid in the container.
     • P[top] + ½ pv^2 [top] + pgy [top] = P [spout] + ½ pv^2 [spout]+ pgy [spout]
       • Pressure at both points (top and spout) are the same. They both have atmospheric pressure.
         • They even out from the formula:
           • ½ pv^2 [top] + pgy [top] = ½ pv^2 [spout]+ pgy [spout]
             • ½ pv^2 [top] + pgy [top] = ½ pv^2 [spout]+ pgy [spout]
               • Top Kinetic energy density + Top potential energy = Spout Kinetic energy density + Spout potential energy
                 • Top of barrel has larger area → Velocity basically zero:
                   • Kinetic energy density is 0 on top.
                     • pgy [top] =½ pv^2 [spout] + pgy [spout]
                       • Top potential energy = Spout Kinetic energy density + Spout potential energy