SPI Physics · Formula sheet
Fluid Mechanics and Properties of Matter formulas
5 formulas and 9 common traps for SPI Physics Fluid Mechanics and Properties of Matter, grouped by subtopic.
Thrust and Liquid Pressure
Learn this subtopic in the notesThrust, pressure and the pressure of a liquid column
Pressure
- thrust (force at right angles), in newtons
- area, in square metres
- depth of liquid, in metres
- density of the liquid, in kg/m³
Pressure in a liquid depends only on depth
Pressure at a depth
- P₀air pressure on the open surface
- depth below the free surface
Common traps
Using g/cm³ in h ρ g
With h in metres and g in m/s², the density must be in kg/m³. An oil of 0.9 g/cm³ is 900 kg/m³; leaving it as 0.9 makes the answer a thousand times too small.
Thinking a heavier-looking face presses harder
The weight is the same whichever face is down. Only the area changes, so the smallest face gives the largest pressure, and opposite faces give the same pressure.
Thinking the wall changes the pressure
Two points at the same depth have the same pressure, whether one is near the wall and the other in the middle. Only depth and the liquid's density matter.
Thinking a wider vessel gives more pressure
A wide tank holds more water than a narrow one of the same height, but the pressure at the bottom is the same. The extra water is spread over a larger base.
Density, Buoyancy and Flotation
Learn this subtopic in the notesDensity and relative density
Buoyant force and the loss of weight in a liquid
Archimedes' principle
Floating and the extra load a floating body can carry
Flotation
Common traps
Giving relative density a unit
Relative density divides one density by another, so the units cancel. Writing kg/m³ after it is wrong.
Forgetting the push back on the water
When a hanging body is dipped in water, the water's balance reading goes UP by the weight the body loses. The total held by the two balances does not change.
Thinking the buoyant force depends on the body's weight
The buoyant force depends on the volume under the liquid and the liquid's density, not on how heavy the body is. Two bodies of the same volume, fully under water, get the same push.
Stopping at the total load
The greatest load a raft can hold includes the people on it. If a person is already aboard, take his mass away too before giving the luggage he can bring.
Using the body's density for the water
The water displaced is the body's volume times the density of WATER, 1000 kg/m³. Multiplying the volume by the body's own density only gives its own mass back.