Fluid Dynamics: Classical Mechanics, Dimensional Analysis, Shock Wave and Detonation, Fire Plumes

Fluid Dynamics

Table of Contents
Classical Mechanics of fluids..........................................................................................................3
1.1 Fluid statics...........................................................................................................................3
2 Dimensional analysis....................................................................................................................4
2.1 Find the dimensions of Reynolds number, Re = ρul/μ, where ρ is the density, u is the
velocity, l is a characteristic lengths and μ is the dynamic viscosity of fluid............................4
2.2 Using the approach of dimensional analysis, derive the friction coefficient of pipe flow....4
3. Shock wave and detonation.........................................................................................................5
3.1 Shock wave tube is often used to study detonation...............................................................5
3.2 Deflagration and detonation are two forms of explosion......................................................5
4 Fire Plumes...................................................................................................................................8
4.1 Formulate the ideal fire plume..............................................................................................8
4.2 Through literature search, find out other formulae for the fire plume and compare them
with the formulae of the ideal fire plume and further give your comments on them.................9
References......................................................................................................................................10

Classical Mechanics of fluids
1.1 Fluid statics
A high rise building is 20m high. At the bottom of the building, pressure and temperature of the
air are 101.325 kPa and 298.15K, respectively. It is assumed that the air is static in this questions
a. Calculate density of the air at the building bottom.
P (pressure) = ρgh
ρ (density) = P/gh = 101.325/9.8*0.02 = 516.964285714 kg/m3
Density = 516.96 kg/m3
b. Assuming that density of the air is constant along the building height, calculate respectively
pressure and temperature of the air at the top of the building.
P = ρgh = 516.96 * 9.8 * 0.02 = 101.325 kPa
P = ρRT
T = P/ρR = 101.325 / 516.96 * 8.31 = 0.0325 K
Temperature = 0.0325 Kelvin
c. If temperature is constant along the building height, calculate pressure and density of the air at
the building top.
Pressure, P = ρgh = 516.96 * 9.8 * 0.02 = 101.32416 kPa
Density, ρ = P/gh = 101.32416/9.8*0.02 = 516.96 kg/m3