Float valve! Raising the sealed piston creates a vacuum beneath it. Assuming at least Atmospheric pressure is exerted on the reservoir of water beneath, water will be pushed up this pipe. Similar to the manual bicycle tire pump:

Another “Positive Displacement” Pump

Much simpler to understand is the impeller pump which can continuously drive water through. OUT IN Momentum Transfer Pumps

Industrial impeller

d P Each pump stroke of distance d and drives a volume of water forward. does an amount of work = F  d To move this much water forward (say smoothly at constant speed) against the pressure in the fluid requires a force A. equal to the weight of displaced fluid. B. P  A (fluid pressure  cross sectional area). C. equal to the atmospheric pressure.

d P Each pump stroke of distance d and drives a volume of water forward. does an amount of work = PA  d The volume of water moved by this single stroke of the pump is equal to A. P  A. B. A  d. C. P  d. So work done by pump on water = P V

Low pressure High pressure can’t depend only on the static pressure just where the pump is pushing. For every cubic foot of water pushed into the system, a cubic foot must be displaced out of the way and a cubic foot must exit out the other end! Pushing a volume of water through some elaborate plumbing system

Just like a train of interconnected cars where no car can move faster than the car ahead, or slower than the car behind even if some are going uphill, others downhill Doing work at one end of a pipe, fights any pressure variations throughout the entire system.

Unlike a train of interconnected cars pushing through a fixed volume of fluid through the entire system can mean: changes in speed for different portions of water at different points along the route! The confining pressures and the fluid speeds can vary all along the route through the plumbing!

Kinetic Energy can be USED to do work

P1P1 P2P2 Dynamic equilibrium of fluids “Steady state” flow. Pressures are not equal in all directions. Fluid is moved only as it moves an equal volume out of its way. P 1  P 2 doing work on the fluid in front of it even as work is done on it by the fluid pushing from behind.

P1P1 P2P2 Dynamic equilibrium of fluids Work done on a volume of fluid increase in its kinetic energy Work it does in moving an equivalent volume out of its way! mechanically by a pump or naturally by gravity =+ Under steady state conditions, where the work driving the flow is constant, this sum must remain constant. The normal relationship we saw when unbalanced forces acted on solid objects.

P1P1 P2P2 Dynamic equilibrium of fluids constant Kinetic Energy of volume of fluid Work it does in moving an equivalent volume out of its way! =+ mass of moving volume of fluid work done by this volume’s own pressure Constant “energy/volume”

Constant “energy/volume” A steady-state-flow carries water through an elaborate plumbing system. It slows to an almost dead crawl at points in the system where the pressure is A. exceedingly small. B. exceedingly large. C. balanced by atmospheric pressure. Water courses through pipes near the center of the system at speed v. At the open faucet where it drains, the speed of the emerging water is A. smaller than v. B. larger than v. C. the same as v. It slows to an almost dead crawl at points in the system where the pressure is A. exceedingly small. B. exceedingly large. C. balanced by atmospheric pressure.

Water flows at speed v within the pipe where the pressure is equivalent to 3 atmospheres (45 lbs/sq.in.). The pressure at the point it exits from the pipe is A. 1 atmosphere. B. 2 atmospheres. C. 3 atmospheres. D. 4 atmospheres. E. 5 atmospheres. F. 6 atmospheres. With what speed does this water exit? Only possible if narrow pipe with viscous forces slowing waterflow - See next chapter!

Constant “energy/volume” means: conditions within the pipeline conditions at pipeline exit 3 atms.1 atm. density of water = 1000 kg/m 3 = 1 g/cm 3

Density of water:  water = 1 g/cc = 1000 kg/m 3 Density of air: depends on altitude!  air = kg/m 3 = gram/cc depends on barometric pressure! depends on temperature! at sea level and 20 o C Incompressible!

The pink sphere would initially Were the walls of the container suddenly to vanish A. remain in place. B. fly out horizontally. C. be pushed down, sliding diagonally.

It’s own weight pulls it straight down. The weight of the above layer bear down along this contact point. Its also supported by contact below and the inside wall of the beaker.

And this collection of forces acting on this individual sphere all balance!

All together these forces exactly balance (cancel) the force exerted by the wall. Were it to be removed the net force would be outward!

Water pressure on the bottom surface is the total weight of the water above it

However this pressure is not just directed DOWNWARD P But outward as well

3.0 meters Swimming along the 10-foot bottom of the pool your back supports a ~3 meter column of water. With cross-sectional area A  0.75 m 2 That’s a 3  0.75 = 2.25 m 3 volume of water with a weight of  Vg = 22,050 Newtons  5000 pounds!

Bernoulli’s Equation P +  v 2 +  gh = constant 1212 When a stream of water either speeds up or flows uphill the pressure it exerts drops! When a stream of water slows or flows downhill the pressure it exerts drops! Speeding up or rising uses up energy!