PHYC10004 Chap.9 Fluids: Pressure, Buoyancy and Bernoulli
Fluids: Pressure, Buoyancy and Bernoulli
Week 7 of PHYC10004 is a self-contained block on fluids. It begins with density and pressure, and the result that pressure in a fluid at rest depends only on depth, p = p_atm + ρgh, whatever the shape of the container.
Pascal's principle explains hydraulic machines, and integrating pressure over a wall gives the total force on a dam.
Archimedes' principle states that the buoyant force equals the weight of fluid displaced, which settles whether objects float, how much of a floating object lies below the surface and how much a submerged object appears to weigh. The laboratory programme uses it to measure densities.
For moving fluids, the continuity equation says the volume flow rate is the same everywhere in a pipe, and Bernoulli's equation, a statement of energy conservation, links pressure, speed and height along a streamline. Together they explain Venturi meters, draining tanks and why fast-moving air has lower pressure. Recent papers have given fluids one question of eleven marks each year.
What this chapter covers
- 01
Density and Pressure
- 02
Pressure at Depth
- 03
Gauge and Absolute Pressure
- 04
Pascal's Principle
- 05
Archimedes' Principle
- 06
Floating and Submerged Objects
- 07
The Continuity Equation
- 08
Bernoulli's Equation
- 09
Venturi Meters and Draining Tanks
Worked example · free
How much load sinks a floating log
- 1Floating: weight equals buoyant force, so the submerged fraction is ρ_log/ρ_water = 600/1025 = 0.59.
- 1Weight of the log: 600 × 0.80 × 9.8 = 4.7 × 10³ N.
- 1Buoyant force when fully submerged: 1025 × 0.80 × 9.8 = 8.0 × 10³ N.
- 1Extra force needed: 8036 − 4704 = 3.3 × 10³ N, the weight of about 340 kg.
Key terms
- Density
- Density is mass per unit volume, ρ = M/V, measured in kg/m³; water has a density of 1000 kg/m³.
- Gauge Pressure
- Gauge pressure is the pressure above atmospheric, ρgh at depth h in a liquid, the quantity read by most pressure gauges.
- Pascal's Principle
- Pascal's principle states that a change of pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid.
- Buoyant Force
- The buoyant force is the upward force a fluid exerts on an immersed object, equal to the weight of the fluid the object displaces.
- Volume Flow Rate
- Volume flow rate is the volume of fluid passing a section per second, R = Av, which is constant along a pipe for an incompressible fluid.
- Bernoulli's Equation
- Bernoulli's equation states that p + ρgh + ½ρv² is constant along a streamline in steady, incompressible, non-viscous flow.
Fluids: Pressure, Buoyancy and Bernoulli FAQ
Why does pressure depend only on depth and not on container shape?
In a fluid at rest each horizontal layer must support the weight of fluid directly above it, and pressure acts equally in all directions at a point. The pressure at a given depth is therefore ρgh above the surface pressure, whether the container is a narrow tube or a wide lake.
How do I know whether an object floats?
Compare its average density with the fluid's. If it is less dense, it floats with the submerged fraction equal to the ratio of the densities; if it is denser, it sinks, and its apparent weight is its true weight minus the weight of fluid displaced.
Why does fast-moving fluid have lower pressure?
Bernoulli's equation is energy conservation per unit volume. Along a horizontal streamline, if the kinetic energy term ½ρv² increases because the fluid speeds up, the pressure term must fall by the same amount, as in the narrow throat of a Venturi meter.
What assumptions does Bernoulli's equation need?
The flow must be steady, the fluid incompressible and non-viscous, and the points compared must lie on the same streamline. The lectures warn that constant density will not always hold, and real fluids lose energy to viscosity.
Exam move
Practise fluids as chains of short steps, because that is how papers set them. Start with pressure at depth, distinguishing gauge from absolute, then pressure forces on windows and walls. Draw a free-body diagram for every buoyancy problem, floating, hanging from a string and fully submerged. For flow, always apply continuity before Bernoulli, then the hydrostatic link to a manometer or open column.
Convert areas and volumes to SI units before substituting, and check that water's density is 1000 kg/m³.
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