notes
Reynolds Number

Reynolds number is a dimensionless number, whose value gives an idea of whether the flow would be turbulent or laminar.

Types of flow are classified as 2 types: laminar flow and turbulent flow.

Reynolds number helps us to determine whether the flow is laminar or turbulent.

It is denoted by Re. where ‘e’ shows Reynolds.
 Expression: `"R"_e=(rho"vd")/eta`
How does Reynolds number (Re) distinguish laminar flow from tubular?
 If the value of Reynold’s number (Re) reaches 1000 then the flow is laminar.
 When the value of Reynold’s number(Re)is greater than 2000 then the flow is turbulent.
 If the value of (Re)is between 1000 and 2000 then the flow is unstable. The flow is in an intermediate stage.
 At this state, it has some characteristics of laminar flow and some of the turbulent flow.
An alternative expression of `R_e`: Inertial force/force of viscosity.
By using `"R"_e=(rho"vd")/eta`
multiplying both numerator and denominator by v: `"R"_e=(rho"v"^2"d")/(eta"v")`
`=(rhov^2)/(etav/d)`
Multiplying both numerator and denominator by A: `R_e=rhov^2"A"/((etav)/d"A"`
where,
`rho"v"^2"A" = "inertial force"`
`((etav)/d)"A"="Force of viscosity"`
(a) Calculating inertial force
inertial force = ma
`=rho"V" "xv"/t=(rho"V"xx"A"xx"displacement")/"t"`
`=rho"v"^2"A"`
(b) Calculating force of viscosity:
Coefficient of viscosity `eta="stress"/"shearing strain"`
`"F"/"A"/("x"/"lt")`
`"F"/"A"/"v"/"l" = "Fl"/"Av"`
`eta="Fl"/"Av"`
`"F"=(eta"Av")/"l"`
=`((eta"v")/"l")"A"`
Turbulance boon or bane:
Turbulance has both advantages and disadvantages.
Advantages:
Promotes mixing and increases the rate of transfer of mass, momentum, and energy. for example mixer and grinder or a juice mixer.
Disadvantages:
Dissipates kinetic energy in the form of heat.