CIE A Level Physics復習筆記4.2.3 Derivation of ?p = ρg?h
Derivation of ?p = ρg?h
- Hydrostatic pressure?is the pressure that is exerted by a?fluid?at equilibrium at a given point within the fluid, due to the force of gravity
- The derivation for this equation is shown below:
Hydrostatic pressure derivation
Exam Tip
You will be expected to remember all the steps for this derivation for an exam question. If any equations which look unfamiliar, have a look at the notes for “Density” and “Pressure”.
Using the Equation for Hydrostatic Pressure
- Hydrostatic pressure?is the pressure that is exerted by a?fluid?at equilibrium at a given point within the fluid, due to the force of gravity
- This is when an object is immersed in a liquid, the liquid will exert a pressure, squeezing the object
- The size of this pressure depends upon the density (ρ) of the liquid, the depth (h) of the object and the gravitational field strength (g):
- When asked about the?total pressure?remember to also add the atmospheric pressure
Total pressure = Hydrostatic pressure + Atmospheric pressure
- Atmospheric pressure (also known as barometric pressure) is?101 325 Pa
Worked Example
Atmospheric pressure at sea level has a value of 100 kPa. The density of sea water is 1020 kg m-3.At what depth in the sea would the total pressure be 250 kPa?
A.?20 m? ? ? ? ? ? ? ?B.?9.5 m? ? ? ? ? ? ? ?C.?18 m? ? ? ? ??D.?15 m
Exam Tip
These pressures can vary widely and depend on metric prefixes such as kPa or MPa. When you’re doing calculations make sure all the pressures are in the same units (otherwise you may be out by a factor of 1000!). To be on the safe side, you can convert them all to Pascals.
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