Pressure and Fluids

What’s the point? What principles govern hydraulic and pneumatic machines? Why do some things float on water?

Objectives Relate pressure, force, and area. Explain the effect of depth on the pressure within a fluid. Explain and calculate the buoyant force on an object in a fluid.

Pressure Force per unit area p = F/A Force is component perpendicular to surface Scalar quantity

Units of Pressure SI Units: N/m 2 = pascal = Pa Bar = 100,000 Pa; mbar = 100 Pa torr: Height in mm of a mercury barometer (760 torr = 1 atm) Atmosphere = atm = mean sea level pressure = 101,325 Pa = 1.01 bar lb/in 2 = psi ( psi = 1 atm)

Fluids Gases and liquids

Origin of Fluid Pressure Collision exerts a force perpendicular to surface Average pressure exerted over time and area Force

Pressure in a fluid Pascal’s Principle: pressure in a fluid is exerted uniformly in all directions throughout the fluid.

Hydraulics just another simple machine

Poll Question If a force F 1 is applied to piston 1 with area A 1, what is the pressure increase in cylinder 1? A.  p 1 = F 1 A 1. B.  p 1 = F 1 + A 1. C.  p 1 = A 1 /F 1. D.  p 1 = F 1 /A 1. 12

Poll Question If a force F 1 is applied to piston 1 with area A 1, How does force F 2 compare to F 1 ? A. F 2 = F 1. B. F 2 < F 1. C. F 2 > F 1. 12

Hydraulics Pistons have different areas Pressure p = F/A = same for both pistons F1F1 A1A1 F2F2 A2A2 = F1F1 F2F2 A1A1 A2A2 = rearranges to

Group Whiteboard Work If a force F 1 = 50 N is applied to the small piston with area A 1 = 100 cm 2, what upward force F 2 does the liquid apply to the large piston with area A 2 = 1000 cm 2 ? Remember: Pressure is the same everywhere.

Poll Question If the small piston with area A 1 is moved a distance  x 1, is the distance  x 2 that the large piston moves more or less than that? A.  x 2 =  x 1. B.  x 2 <  x 1. C.  x 2 >  x x1x1 x2x2 ?

Hydraulics are Simple Machines Volume changes  V opposite:  V = –  V 1 =  V 2 F1F1 A1A1 F2F2 A2A2 = F 1  x 1 = F 2  x 2 System does same work as done on it = VV A1A1 F1F1 VV A2A2 F2F2  V = A 1  x 1, so  x 1 =  V/A 1 ; x2 = –V/A2x2 = –V/A2 F 1,  x 1 same direction F 2,  x 2 same direction

Example Problem If the small piston with area A 1 = 100 cm 2 moves 10 cm, how far does the large piston with A 2 = 1000 cm 2 move? Remember: Volume leaving piston 1 equals volume entering piston 2.

Pressure with Depth

Poll Question As the depth beneath the surface of a fluid increases, the pressure within the fluid A.Decreases. B.Increases. C.It depends on the shape of the container. D.Fluids are incompressible, so the pressure does not change.

Pressure in a fluid Force comes from weight of fluid above Pressure increases with depth Supports weight above

Liquid Pressure Formula p =  hg p = pressure  = density of liquid h = depth under top of liquid (Valid if  is constant—liquid, not gas) h p = pressure here

Buoyancy How do things float?

Submerged in a liquid Why does it sink or float?

What forces are present?

Pressure in a fluid Pressure increases with depth Greater pressure at bottom than top of an immersed object Results in upward buoyancy force that is the (vector) sum of all pA forces

Buoyancy Force Buoyancy force = weight of fluid displaced F =  Vg  = density of fluid V= volume of fluid displaced = submerged volume of object g= 9.8 N/kg

Whiteboard Work What is the water pressure at the bottom at the deepest point of Lake Superior? Lake depth = 406 m, density of water = 1000 kg/m 3.

Buoyancy and Density If an object is more dense than the surrounding fluid, it sinks If an object is less dense than the surrounding fluid, it rises A floating object displaces exactly enough fluid to support its weight (Why? What happens if it’s too high or too low?)

Think Question Which boat (with cargo) has the greatest total volume? A. The high boat (left). B. The low boat (right). C. Both have the same total volume.

Think Question Which boat (with cargo) has the greatest volume under the water line? A. The high boat (left). B. The low boat (right). C. Both have the same submerged volume.

Poll Question Which boat (with cargo) experiences the greatest buoyancy force? A. The high boat (left). B. The low boat (right). C. Both experience the same buoyancy force.

Think Question Which boat (with cargo) has the greatest mass? A. The high boat (left). B. The low boat (right). C. Both have the same mass.

Poll Question After a boat sinks, it displaces A.more water than when it floated. B.less water than when it floated. C.the same volume and weight of water as when it floated.