Hydrostatics, Fluid Dynamics, and Electrostatics

MCAT Prep: Physics and Math Part 3

Density

(ρ) = m / v

SI units: kg / m³

Specific gravity

ρ_substance / ρ_water

no units

1000

ρ_water = _____ kg/m³

Weight

ρgV

Pressure

a scalar quantity defined as force per unit area: P = F / A

SI units: pascal = N / m²

static

For ______ fluids of uniform density in a sealed vessel, pressure: P = ρgz

Absolute pressure

in a fluid due to gravity somewhere below the surface is given by the equation P = P_o + ρgz

Gauge pressure

P_g = P - P_atm

Continuity equation

A₁v₁ = A₂v₂

Bernoulli’s equation

P + (1/2)ρv² + ρgh = constant

Archimedes’ Principle

F_buoy = (ρ_fluid) (g) (V_submerged)

sink

If the weight of the fluid displaced is less than the object’s weight, the object will ______

float

If the weight of the fluid displaced is greater than or equal to the object’s weight, then it will _______

Pascal’s principle

a change in the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel

P = F₁ / A₁ = F₂ / A₂ and A₁d₁ = A₂d₂ so, W = F₁d₁ = F₂d₂

Coulomb’s law

F = (kq₁q₂) / r²

SI units: newton

Electric field

E = F_e / q = kQ / r²

SI units: N/C or v/m

same

A positive point charge will move in the __________ direction as the electric field vector

opposite

A negative point charge will move in the __________ direction as the electric field vector

Electrical potential energy

this of a charge q at a point in space is the amount of work required to move it from infinity to that point

U = qΔV = qEd = (kQq)/r

SI units: J

dipole moment

p is the ________ (p = qd)

torque

The dipole feels no net translational force, but experiences a ________ about the center causing it to rotate so that the dipole moment aligns with the electric field

Electrical potential

the amount of work required to move a positive test charge q from infinity to a particular point divided by the test charge: V = U/q

SI units: volt = J/C

Potential difference (Voltage)

(ΔV) = W / q = kQ / r

SI units: volt = J/C

oppositely

When two ________ charged parallel plates are separated by a distance d, an electric field is created, and a potential difference exists between the plates, given by: V = Ed