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Fluid Flow

Fluid Flow. 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. Flow Rate. Streamlines can be grouped together. This corresponds to the fluid flow through an area.

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Fluid Flow

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  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 time • density 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. 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. A1 = w1d1 Use the continuity equation. v1A1 = v2A2 v1w1d1 = v2w2d2 Solve for the unknown d2. d2 = v1w1d1 / v2w2 (4.5 m/s)(40. m)(2.2 m) / (3.7m)(6.0 m/s) = 18 m Canyon

  6. Fluid Energy • The kinetic energy in a fluid is the same as for any other mass: K = ½ mv2. • The change in potential energy is: U = mgh. • The work done on a fluid is due to pressure. • Pressure acting on a volume: W = PADx = 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 density • Divide 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. FL

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

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