Peoples Physics Concepts

http://www.ck12.org Chapter 17. Fluids

17.2 Pressure in Fluids

• Define pressure and solve pressure problems in the context of fluids.

Students will learn about pressure and solving pressure problems in the context of fluids.

Key Equations

P=

F

A

Pressure is force per unit area

P=Po−ρgh Pressure in an incompressible fluid as a function of depth

Guidance

• Thepressureof a fluid is a measure of the forces exerted by a large number of molecules when they collide
  and bounce off its boundary. The unit of pressure is the Pascal (Pa).


• In a fluid at rest, pressure increases linearly with depth –this is due to the weight of the water above it.


• Pascal’s Principlereminds us that, for a fluid of uniform pressure, the force exerted on a small area in contact
  with the fluid will be smaller than the force exerted on a large area. Thus, a small force applied to a small area
  in a fluid can create a large force on a larger area. This is the principle behind hydraulic machinery.


• Liquids obey acontinuity equationwhich is based on the fact that liquids are very difficult to compress. This
  means that the total volume of a fluid will remain constant in most situations. Imagine trying to compress a
  filled water balloon!

Example 1

A weather balloon is ascending through the atmosphere. If the density of air is 1.2 kg/m^3 and atmospheric pressure

at sea level is 101.3 kPa, then what is the pressure on the balloon at (a) 100 m above the ground, (b) 500 m above

the ground, and (c) 1000 m above the ground?

Solution

For all parts of these problems, we’ll be using the equation for pressure given above where the atmospheric

pressure at sea level is Po.

(a):

P=Po−ρairgh

P= 101 .3 kPa− 1 .2 kg/m^3 ∗ 9 .8 m/s^2 ∗100 m

P= 100 .12 kPa