Fluid Flow Streamline Motion studies the paths of

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? Ø The area is width times depth. Ø A 1 = w 1 d 1 Ø Use the continuity equation. Ø v 1 A 1 = v 2 A 2 Ø v 1 w 1 d 1 = v 2 w 2 d 2 Ø Solve for the unknown d 2. Ø d 2 = v 1 w 1 d 1 / v 2 w 2 Ø (4. 5 m/s)(40. m)(2. 2 m) / (3. 7 m)(6. 0 m/s) = 18 m

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 = 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.