Fluids/Elasticity of Solids Flashcards
density
ρ = m/V
specific gravity
specific gravity = ρ(substance)/ρ(water)
force of gravity for fluids
Fg = mg = Vρg
- ensure that ρ and V are for the appropriate fluid or object
pressure
P = force/area = F/A
hydrostatic gauge pressure/total pressure
P(gauge) = ρ(fluid)gH P(total) = P(surface) + P(gauge)
Archimide’s principle (buoyant force)
F(buoy) = V(submerged)ρ(fluid)g F(buoy) = weight of fluid displaced
formula for floating object
w(object) = F(buoy)
V(sub)/V(obj) = ρ(obj)/ρ(fluid)
note: fraction of ρobj/ρfluid = portion of object submerged
Specific gravity for object floating in water
w(obj)/Fbuoy = ρ(object)Vg/ρ(fluid)Vg = specific gravity of the object
Pascal’s law (relating force and area of a fluid)
F1/A1 = F2/A2 (pressure conserved)
Pascal’s law (relating force and distance of a fluid and area)
F1d1 = F2d2 (work conserved) A1d1 = A2d2 (volume conserved)
flow rate formula
f = Av (in m^3/s)
f is the volume of fluid that passes a point per unit time
A is area, v is velocity of the fluid
Continuity equation for fluid flow
A1v1 = A2v2
Bernoulli’s equation
P1 + 1/2ρv1^2 + ρgy1 = P2 + 1/2ρv2^2 + ρgy2
y is the heights of points above some chosen reference level.
can only use this equation with non-viscous liquids with steady, laminar flow and gasses with small pressure changes.
Efflux speed
v = √2gD
v is efflux speed.
D is distance from the liquid surface to the hole.
What is the Bernoulli/Venturi effect?
Using the Bernoulli equation (without the ρgy part as y is equal in both cases) the pressure is lower where the flow speed is greater.
P1 + 1/2ρv1^2 = P2 + 1/2ρv2^2
