AP Physics Chp 11

• Density (mass density)

• ρ=m/V

• Solids and liquids are fairly constant at our range of temp/pressure but gases vary.

• Pressure

• P = F/A the force is perpendicular to the surface area but pressure is not a vector

• 1 Pa = 1N/m 1 atm = 101,325 Pa• bar = 105 Pa • The english system used lb/sqin = psi

• The pressure we experience now is due to the fluid above us being pulled down by gravity.

• 14.7 lb/si or 101,325 Pa is the standard at sea level

• The higher up you go the lower the pressure gets because of less fluid above you

• Thus in a static fluid

• P2 = P1 + ρgh

• ρ is the density and h is the depth in m

• We use this in constructing a barometer (measure air pressure).

• As well as manometers which measure other fluid pressure.

• Gauge pressure is the pressure compared to atmospheric pressure

• Absolute pressure is the actual pressure

• How high can a submersible pump raise water if it has a maximum pressure of 110 kPa?

• P2 = P1 + ρgh

• 110000 = 101325 Pa + (1000kg/m3)9.8m/s2(h)

• h = 0.89 m

• How much force would it have at the pump if the pipe was 2.3 cm in diameter? How much at the maximum height with the same size pipe?

• At the pump

• P = F/A • P = 110 kPa or 110000 Pa • A = πr2 r = 2.3cm/2 = 1.15cm = 0.0115m• A = π(0.0115m)2 = 0.00042m2

• F = PA = (110000 Pa)(0.00042m2) = 46 N

• At the maximum hieght

• P = F/A • P = 101325 Pa • A = πr2 r = 2.3cm/2 = 1.15cm = 0.0115m• A = π(0.0115m)2 = 0.00042m2

• F = PA = (101325 Pa)(0.00042m2) = 43 N

• Why can’t a surface mounted pump pull water up out of a well that is 12 m deep?

• P2 = P1 + ρgh

• 101325 Pa = 0 Pa + (1000kg/m3)(9.8m/s2)(h)

• h = 10 m

• Pascal’s Principle

• Any pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and enclosing walls.

• P1 = P2 if the level of the fluid is equal at each point otherwise we add ρgh as needed

• F1/A1 = F2/A2 useful in hydraulic jacks

• Arcimedes’ Principle

• Fluids apply a buoyant force on any object partially or totally submerged in it with a magnitude equal to the weight of the displaced fluid.

• Fb = Wfluid

• Fb = ρgV

• Why do supertankers float?

• The supertanker’s design displaces enough water/salt water such that Fg = Fb

• Why will filling a ship to its limit in Boston create problems when it tries to go to Panama?

• As fluid enters a tube that is open on both ends the mass of the fluid going in has to be equal to the mass coming out.

• A1v1 = A2v2 continuity equation

• How does this explain the effect on kinking a hose?

• Bernoulli’s Equation

• P1 + 1/2pv12 + pgh1 = P2 + 1/2pv2

2 + pgh2

• When the fluid isn’t moving this gives the pressure equation P = Po + pgh

• This equation is used often to explain the affects of moving air like wind over a roof.

• What is the pressure above the roof sheeting if the wind is blowing 32 m/s and there is no wind inside your attic space. Assume the height difference is negligible. Density of air is 1.29 kg/m3.

• P1 + 1/2pv12 + pgh1 = P2 + 1/2pv2

2 + pgh2

• P1 + ½(1.29 kg/m3)(32m/s)2 = 101325 Pa

• P1 = 100004 Pa