Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Reynolds Number

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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.

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