1. Fluid Flow

2. Streamline  Motion studies the paths of objects.  Fluids motion studies many paths at once.  The path of a single atom in the fluid is called a streamline.

3. Flow Rate  Streamlines can be grouped together.  This corresponds to the fluid flow through an area.  The flow rate measure fluid movement. mass per timemass per time density times area times velocitydensity times area times velocity

4. Conservation of Mass  Like other matter, fluids cannot be created or destroyed.  The mass into a tube must flow out at the same rate.  This is called the continuity equation.  For constant density it only requires the area and velocity.

5. Canyon  A river flows in a channel that is 40. m wide and 2.2 m deep with a speed of 4.5 m/s.  The river enters a gorge that is 3.7 m wide with a speed of 6.0 m/s.  How deep is the water in the gorge?  The area is width times depth.  A 1 = w 1 d 1  Use the continuity equation.  v 1 A 1 = v 2 A 2  v 1 w 1 d 1 = v 2 w 2 d 2  Solve for the unknown d 2.  d 2 = v 1 w 1 d 1 / v 2 w 2  (4.5 m/s)(40. m)(2.2 m) / (3.7m)(6.0 m/s) = 18 m

6. Fluid Energy  The kinetic energy in a fluid is the same as for any other mass: K = ½ mv 2.  The change in potential energy is: U = mgh.  The work done on a fluid is due to pressure. Pressure acting on a volume: W = PA  x = PV.Pressure acting on a volume: W = PA  x = PV.  From the work energy principle:

7. Bernoulli’s Equation  The volume element is somewhat arbitrary in a moving fluid. Mass divided by volume is densityMass divided by volume is density Divide by volume and separate states on each endDivide by volume and separate states on each end  Bernoulli’s equation is equivalent to conservation of energy for fluids.

8. Lift  If the height doesn’t change much, Bernoulli becomes:  Where speed is higher, pressure is lower.  Speed is higher on the long surface of the wing – creating a net force of lift. FLFL

9. Venturi Tube  A venturi meter uses continuity and Bernoulii’s equation to measure flow. next