The pressure at any point in a fluid acts equally in all directions. Also, the force due to the fluid pressure always acts perpendicularly to any surface the fluid is in contact with.

Atmospheric pressure= 1.013 x 10⁵ Pa (measured at sea level). This can be approximated as 101 kPa.

Gauge Pressure Pressure gauges measure the pressure over and above atmospheric pressure. This is called gauge pressure.

Absolute Pressure To get the absolute pressure at a point, one must add the atmospheric pressure to the gauge pressure. For example, if gauge pressure is 100 kPa, the absolute pressure at that point is the sum of 100 kPa and 101 kPa, or 201 kPa.

Manometer A U-shaped tube partially filled with liquid used to measure pressure. The pressure is equal to the difference in height of the two levels of the liquid according to P = P_atm + rgh.

r(H₂O) = 1000 kg/m³

Sometimes densities are given in g/cm³. To convert to the SI unit of kg/m³ simply multiply by 1000.

Density Lab - Float or Sink: You find out!"

Specific Gravity The ratio of the density of that substance to the density of water at 4.0°. It has no units.

substance	density, kg/m3	substance	density, kg/m3
aluminum	2700	iron and steel	7800
copper	8900	lead	11300
mercury	13600	ethyl alcohol	790

1. Pascal’s principle - any change in pressure at any point in a fluid is transmitted unchanged throughout the fluid. Or, pressure applied to a confined fluid increases the pressure throughout the fluid by the same amount.
   F₁/A₁ = F₂/A₂
   This is the basis for squeezing a tube of toothpaste, hydraulic brakes, and for the Heimlich maneuver.

   Hydrostatic pressure - pressure due to a fluid’s depth

   P = r g h

   where r is density of fluid in kg/m³

   h is the height (depth) of fluid

   Pressure increases with depth. The pressure at any depth depends only upon that depth and not upon any horizontal dimension. For example, Hoover Dam holds back Lake Mead which is 700 ft deep. The bottom of Hoover Dam must withstand the same pressure if it were only holding back a few thousand gallons of water 700 ft deep. Also, the pressure at equal depths within a fluid is the same.

   Archimede’s principle - an object immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. A fluid provides some support for any object placed in it. The upward force on an object placed in a fluid is called the buoyant force.

   F_B = r g V

   where r is the density of the fluid in kg/m³

   V is the volume of the displace fluid

   F_B is the buoyant force (The buoyant force occurs because the pressure in a fluid increases with depth. The upward force on the bottom surface of a submerged object is greater than the downward pressure on its top surface.)

   • If an solid floats partially submerged in a liquid, the volume of liquid displaced is less than the volume of the object. According to Archimedes Principle, the weights of the object and its displaced fluid are the same. The fractional part of an object that is submerged is equal to the ratio of the density of the solid to the density of the liquid in which is floats (for example, about 90% of an iceberg is submerged because the density of the ice is about 90% that of sea water).
   • An object floats when the buoyant force is equal to its weight.
   • Objects submerged in a fluid appear to weigh less than they do when outside the fluid.

Applet demonstrating buoyant force

Lift on an airplane wing

There are two type of fluid flow, streamline (laminar) and turbulant flow. If the slow is smooth (layers of fluid slide by each other smoothly), the flow is said to be steamlined, or laminar. Above a certain speed (which depends upon many factors), a flow becomes turbulent. Turbulent flow is characterized by the formation of eddies.

Viscosity Internal friction in a fluid.

Mass Flow Rate the ratio of the mass of a fluid that passes a certain point in a certain interval of time (or, Dm/Dt)

Volume Rate of Flow the ratio of the volume of a fluid that passes a certain point in a certain interval of time (or, DV/Dt). In SI units, this is m³/sec (or the same thing as the product of area, A, and velocity, v.)

Bernoulli's Equation Where the velocity of a fluid is high, the pressure is low; where the velocity is low, the pressure is high. Bernoulli's equation is an expression of the law of conservation of energy.

Torricelli's theorem A liquid leaves a spigot at the bottom os a reservoir with the same speed that a freely falling object falling through the same height.

AP Multiple Choice Questions   Fluid questions were added to the AP B test beginning in 2002.

• Be able to determine the buoyant force acting on an object when given the weight in air and the weight in the fluid.
• Be able to recognize that the pressure acting on the bottom of a container is due to the weight of the fluid above it.
• Recognize that high velocity fluid has low pressure. Predict the consequences of low pressure due to high velocity fluid.

AP Free Response Questions   Fluid questions were added to the AP B test beginning in 2002.

• All the ones that have occurred since 2002 have dealt with either a fluid-based laboratory exercise or with fluids at rest.
• Be able to calculate gauge pressure.
• Be able to calculate absolute pressure.
• Be able to calculate pressure.
• Kinematics is frequently integrated into fluid problems.

Thermal Energy Notes

Thermal Energy Sample Problems

States of Matter Sample Problems

Thermal Energy Homework

States of Matter Homework

AP Fluids Objectives

AP Fluids Problems