What is a fluid?

A substance that flows. Liquids and gases.


What is the key difference between fluid mechanics and Newtonian mechanics?

Whereas Newtonian mechanics was concerned with mass (F=ma), fluid mechanics is concerned with density, ρ.

What is the formula for denisty?

ρ = mass/volume

What is the specific gravity of a substance?

sp. gr. = ratio of the density of any substance to the density of water. = ρsubstancewater

What is the density of water?



What is the formula for pressure?

P = forceperp/area

What is the SI unit for pressure?

Pascal = Pa = N/m2

What is Patm?

105 Pa

Hydrostatic PressureEdit

What is the force of a column of liquid above a sheet of l*w? What is the pressure?

F = mg = (ρV)g = ρ(lwh)g
P = F/A = F/lw = ρhg = ρgh

Does the shape of the container matter in determining pressure?

No. P = ρgh. Only density and height matter. The liquid flows around any changes in shape.

What is the total/absolute pressure?

Ptotal = Pabove liquid+Pliquid = P0+ρgh

What is the gauge pressure?

Pgauge = Ptotal - Patm = ρgh. The gauge reads just the internal pressure, as Patm is acting on the gauge as well.

Does |pressure| change with direction?

Nope. Pressure always pushes perpendicular to the area. P = ρgh, no term for orientation of the thing.


What is the basis of buoyancy?

The underside of the object is submerged deeper, thus more P = ρgh. So an upward force is created.

What is Archimedes' principle? (Words & formula)

The buoyant force, Fbuoy, is equal to the weight of the fluid displaced by the object.
Fbuoy = ρfluidVsubmergedg

What is the relationship of forces when an object floats?

mg = Fbuoy = ρfluidVsubmergedg = ρobjectVobjectg
Vsubmerged/Vobject = ρobjectfluid

What happens when ρobject >/=/< ρfluid?

If ρobj < ρfluid, then it will float, as ρobjfluid < 1, so V > Vsubmerged. If ρobj = ρfluid, then V = Vsubmerged, and the object will be neutral. And if ρobj > ρfluid, then V < Vsubmerged, it will sink.

How do you find the apparent weight of a submerged object?

Fg-Fbuoy = N
Fbuoy = ρVg

Flow Rate and The Continuity EquationEdit

What is flow rate?

Q = flow rate = Av. Amount of fluid in volume that flows past a give point per second.

Flow rate vs flow speed?

Flow rate is volume/time, flow speed is length/time.

What is (the basis of) the Continuity Equation?

Q1 = Q2 = A1v1 = A2v2

Bernoulli's EquationEdit

What are the assumptions of the Bernoulli equation?

Fluid is incompressible, no viscosity, and flow is streamline.

What is viscosity?

Internal friction for fluids.

What is streamline?

Inject dye and form lines in the stream. If they do no cross then = streamline.

What is Bernoulli's Equation?

P1+ρgy1+(1/2)ρv12 = P2+ρgy2+(1/2)ρv22
Similar to conservation of energy. mgh similar to ρgy, and (1/2)mv2 similar to (1/2)ρv2

Torricelli's TheoremEdit

What is efflux speed?

Punch a hole in a barrel. How fast the water comes out.

What is the derivation of Torricelli's Theorem?

Start from Bernoulli's equation.
Point 1 at the top, point 2 at the hole. P1 = Patm = P2; because both are open to air.
A1 << A2, so v1 << v2. Call v1 about 0.
ρgy1 = ρgy2 + ρv22
v2 = sqrt(2g(y1-y2)) = sqrt(2gh)

The Bernoulli EffectEdit

What is (the derivation of) the Bernoulli Effect?

Combo of flow rate and Bernoulli's equation. P1+(1/2)ρv2 = P2+(1/2)ρv22
↑A → ↓V → ↑P.
Think of it as fast moving stuff has less energy to create pressure with. Stuff moving has lower average density.