Basic Fluid Mechanics - Week 1 Flashcards
behaviour of plastics under stress
the shear stress must reach a minimum value berfore flow commences, thereafter shear stress increases with the rate of shear
- curve with decreasing gradient the higher the rate (shear stress v rate of shear)
mass flow rate ṁ
= ρ A V
denisity (ρ)
cross-sectional area (A)
velocity (V)
behaviour of pseudo-plastics under stress
dynamic viscosity decreases as the rate of shear increases
- curve with decreasing gradient the higher the rate (shear stress v rate of shear)
behaviour of thixotropic substances under stress
dynamic viscosity decreases with the time for which shearing forces are applied
behaviour of dilatant substances under stress
dynamic viscosity increases as the rate of shear increases
- curve with increasing gradient the higher the rate (shear stress v rate of shear)
behaviour of rheopectic materials under stress
dynamic viscosity increases with the time for which shearing forces are applied
Poiseuille equation - pressure drop for laminar flow
∆𝑝 = 8𝜇𝐿𝑄 / 𝜋𝑟^4
dynamic viscosity (𝜇)
length of pipe (L)
volumetric flow rate (Q)
Converting absolute viscosity to kinematic viscosity
ν = μ/ρ
divide by density
Litres to m^3
Divide by 1000
Friction Factor in laminar flow
4f = 64/Re
How do you calculate pressure loss (Δp) and or head loss (h) for both laminar and turbulent flows
Using the Darcy equation
Δp = (4f) L/D ρū^2 / 2
h = Δp/ρg
Process of solving frictional problems
- determine Re
- if laminar 4f = 64/Re or could use Poiseuille equation (∆p)
- if turbulent and Re < 100,000 or k/D < 0.001: 4f = 0.316/Re^0.25
- otherwise read from moody chart
Work out power
P = Q∆p
flow rate (Q)
change in pressure (∆p)
What is head loss
measure of reduction in total head (elevation) loss, amount of PE converted to KE
h = p/ρg
