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. = ρsubstance/ρwater
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
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 = ρobject/ρfluid
What happens when ρobject >/=/< ρfluid?
- If ρobj < ρfluid, then it will float, as ρobj/ρfluid < 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
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
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.