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. The flow rate measure fluid movement. mass per time density times area times velocity

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.

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. 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

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:

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.

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

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