Chapters 5 and 6 of the textbook covers propertied of fluids (liquids and gases) at rest and in motion and the forces those fluids exert on objects submerged in them.
Formulas:
Fluids in general | |
P = F/A | pressure = force/area |
ρ_{particle} = N/V, ρ = M/V | particle density = number of particles/volume, density = mass/volume |
Ideal gas: PV = N*k*T | Ideal gas law: pressure * volume = number of particles * Boltzmann constant * absolute temperature |
B = w | Buoyant force = weight of the displace fluid |
Incompressible fluids, laminar flow | |
In a pipe: A_{1}*v_{1} = A_{2}*v_{2} | Equation of continuity: (Area 1)*(velocity 1)_{ } = (Area 2)*(velocity 2) |
P + ρgh + ½ρv^{2 }= constant | Bernoulli's equation: pressure + density*g*height + ½*density velocity^{2} = constant |
F/A = ηv_{0}/d | Definition of viscosity η: |
Volume flow rate = pi*(pressure difference)*(pipe diameter)^{4}/[128*(pipe length)*viscosity) | |
Turbulent flow | |
Reynolds number = density * characteristic length * flow speed /viscosity | |
Reynolds number > 2300 --> turbulent flow |
Let us analyze some real-life situations using what we have learned so far.
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