Lecture 3 : Fluid Mechanics & Transport (I) Flashcards
1. Assess and calculate viscosity 2. Apply continuity equation for assessing fluids; 3. Evaluate Reynold's number and entrance length in fluid transport
Fluid only refers to liquids. True or False?
False, it is a term used to describe both liquid and gas
Transport of liquid food is mainly concerned with which 2 properties of liquid?
- Density
- Viscosity (calculate the opposing forces that must be overcome)
What is the definition of stress?
Force per unit area
When force acting on a surface is perpendicular to it, this stress is called ____ or normal stress. When the force acts parallel to the surface, the stress is called __________
pressure ; shear stress
What happens to a fluid when shear stress is applied to it?
It deforms (flows), and does not return to its original shape.
What is shear rate?
It is the relative change in velocity divided by the distance travelled by the fluid
What is meant by newtonian and non-newtonian liquids?
- Newtonian liquids: shear rate increases proportionally with shear stress ;
- Non-newtonian liquids: shear rate does NOT increase proportionally with shear stress
write down the equation for shear stress,σ.
σ = μ . (du/dy) ;
where du/dy = 𝛾̇ = shear rate
What is the units for shear stress σ?
σ ≡ N/m^2 ≡ Pa
Force (in newton) / area
What is the units for viscosity μ?
μ ≡ σ /𝛾̇ ≡ Pa / (s^-1) ≡ Pa.s
In cgs units (centrimetre-gram-seconds), what is viscosity expressed in ?
μ ≡ (dyne/cm^2).s ≡ poise
How many pascal seconds is 1 poise and 1 centipoise?
1 poise = 0.1 Pa.s;
Since 1 poise = 100 centipose,
1cP = 0.001 Pa = 10^-3 Pa = 1mPa.s
What is the equation expressing the relationship between dynamic viscosity (μ) and kinematic viscosity (𝑣)?
kinematic viscosity, 𝑣 = μ / 𝜌
𝜌 : density
What is the SI unit and cgs unit of kinematic viscosity?
SI : m^2/s
cgs: strokes ≡ cm^2/s
What is the equation of continuity based on mass flow rate?
ṁ =𝜌Aū
𝜌 : density
A: cross sectional area of pipe
ū : average velocity
What is the equation of continuity based on volumetric flow rate?
For incompressible fluids,
V̇ = Aū
What is Reynold’s number?
It is the ratio of inertia forces (forward force) to viscous forces (opposing forces).
What is the relationship between mass flow rate and the flow profile of the liquid?
Low ṁ = laminar flow
Intermediate ṁ = transitional flow
High ṁ = turbulent flow
What is the range of Reynold’s number for laminar / transitional / turbulent flow?
Laminar : Re < 2100
Transitional: 2100 < Re < 4000
Turbulent: Re > 4000
What is the equation for Reynold’s number?
Re = 𝜌ūD /μ
What is the equation for Reynold’s number, in terms of mass flow rate?
Re = 4ṁ /μπD
What is meant by entrance length?
It is the distance that a fluid travels before being in a fully developed flow (steady state) (parabolic shape for laminar flow).
What is the equation for entrance length, Le, for laminar flow?
Le/D = 0.06 Re
What is the equation for entrance length, Le, for turbulent flow?
Le/D = (4.4Re)^1/6
