Fluid Pressure, Pascal's Law and Buoyancy
Pressure at depth h is P = P0 + ρ g h; pressure applied to an enclosed fluid is transmitted undiminished; a submerged body experiences an upthrust equal to the weight of fluid displaced.
What is Fluid Pressure, Pascal's Law and Buoyancy?
Pressure at depth h is P = P0 + ρ g h; pressure applied to an enclosed fluid is transmitted undiminished; a submerged body experiences an upthrust equal to the weight of fluid displaced.
Key formula / rule: P = P0 + ρ g h, independent of container shape.
Key points
- Compute gauge and absolute pressure at a stated depth.
- Apply Archimedes' principle to floating and sinking bodies.
Common exam trap
Assuming a wider vessel gives greater pressure at the same depth.
Definitions
- Term
Fluid Pressure, Pascal's Law and Buoyancy
- Meaning
Pressure at depth h is P = P0 + ρ g h; pressure applied to an enclosed fluid is transmitted undiminished; a submerged body experiences an upthrust equal to the weight of fluid displaced.
- Term
Fluid Pressure, Pascal's Law and Buoyancy — explanation
- Meaning
Pressure depends on depth, not on the shape or the amount of liquid, which is the hydrostatic paradox. Archimedes' principle then follows from the pressure difference between the top and bottom faces.
Learning objectives
Compute gauge and absolute pressure at a stated depth.
Apply Archimedes' principle to floating and sinking bodies.
Formulae
- Key point
P = P0 + ρ g h, independent of container shape.
- Key point
Pascal's law underlies hydraulic force multiplication.
- Key point
Upthrust = weight of displaced fluid; floating requires equal weight and upthrust.
Prerequisites
PHY-U1-NLM-T1-S2-C1
Common mistakes
Assuming a wider vessel gives greater pressure at the same depth.
Using the density of the body instead of the fluid in the upthrust.
Keywords
Fluid
Pressure
Pascal
Buoyancy
Practice preview
What is the gauge pressure at a depth of 10 meters in water (density = 1000 kg/m^3)? (Take g = 10 m/s^2)…
easy
A block of wood floats in water with 60% of its volume submerged. What is the density of the wood? (Density of water = 1000 kg/m^3)…
medium
An open tank contains water up to a height of 5 m. The pressure at the bottom of the tank is P1. If an additional 2 m of oil (density = 800 kg/m^3) is poured on top of the water, what is the new pressure at the bottom of…
medium