Fluid dynamics Two fluid rates Fluid speed: Fluid flow rate (Volume flow rate): m3/sec past any point: Conservation of fluid volume Assume incompressible fluid (constant density)
Fluid dynamics “Continuity Equation”:
Sources of fluid pressure change 1. Friction between tube and fluid Friction causes a drop in pressure along the tube as fluid flows. Friction increases as radius _________ and length _____________ As friction grows, pressure at inlet must ___________ to keep the same flow Blood pressure example: clogged arteries
Sources of fluid pressure change 2. Changes in height
Sources of fluid pressure change 3. Speed changes (Bernoulli effect) Near a change in diameter, pressure is largest where speed is _______ Why? Water in small area moves ________________. A net force must _________________ the water, so pressure must be greater _______________. Demo: air over manometer
Bernoulli’s equation (combine height and speed effects, ignore friction) or P1 – P2 = This pressure change is on top of any frictional pressure drop effect.
Water flows from the little pipe into the big pipe Water flows from the little pipe into the big pipe. Ignore any friction or height change. R= 6 cm R = 2cm P1. The pressure in the right side is ______ than on the left greater than same as less than P2. The volume flow rate Q on the right is ______ on the left.
Water flows from the little pipe into the big pipe Water flows from the little pipe into the big pipe. Ignore any friction or height change. R= 6 cm R = 2cm P3. The ratio of the velocity on the right vs on the left is (vright/vleft) =______ A. 1/9 B. 1/3 C. 1 D. 3 E. 9
The faucet of radius r2=0. 5 cm puts water out at 15 liters/minute The faucet of radius r2=0.5 cm puts water out at 15 liters/minute. The pressure at the opening of the faucet is about 1atm. The water main (r1=6 cm), is 3 meters below the faucet. What is the pressure at the main?
Torricelli’s theorem: If a tank is open at the top, and wide enough so that the top of the fluid is essentially motionless, then the speed of water flowing out a hole at depth h is that of a ball dropped a height h. Siphons
Water from a hole in a tank makes an arc due to horizontal v Water from a hole in a tank makes an arc due to horizontal v. If a larger hole is made at the same depth, the flow will have (P4)___________ A. bigger arc B. bigger Q (vol/sec) C. bigger arc and J
A blood platelet drifts along with the flow of blood through an artery that is partially blocked by deposits. As the platelet moves from the narrow region to the wider region, it experiences (P5)_________ A. an increase in pressure. B. no change in pressure. C. a decrease in pressure. Vascular flutter
The fascinating Bernoulli effect Squealing balloons Vocal cords, trumpet lips Cars passing on freeway, boats in harbors, trucks and motorcycles Demos: Blowing on paper, Ball over blower, Venturi blower, funnel, metal plate and wood cylinder
The fascinating Bernoulli effect Cars passing on freeway, boats in harbors, trucks and motorcycles
How wings, sails work air deflection (Newton’s 3rd law)explanation Bernoulli explanation Note: my blue arrows correcting the diagrams…deflection!
Curve balls spin direction ball moves to right or “air moves to left”
Frisbees Scientific American, April 1999
Frisbees Scientific American, April 1999 Why do we need to spin it?