Students will learn about pressure and solving pressure problems in the context of fluids.
Key Equations
Guidance
- The pressure of 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 Principle reminds 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 a continuity equation which 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 P_{o}.
(a):
(b):
(c):
Watch this Explanation
Time for Practice
- A car is being lifted by a hydraulic jack attached to a flat plate. Underneath the plate is a pipe with radius .
- If there is no net force on the car, calculate the pressure in the pipe.
- The other end of the pipe has a radius of . How much force must be exerted at this end?
- To generate an upward acceleration for the car of , how much force must be applied to the small end of the pipe?
- A SCUBA diver descends deep into the ocean. Calculate the water pressure at each of the following depths.
- Ouch! You stepped on my foot! That is, you put a force of in an area of on the tops of my feet!
- What was the pressure on my feet?
- What is the ratio of this pressure to atmospheric pressure?
Answers to Selected Problems
- a. b. c.
- a. b. c.
- a. b.