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# Reynolds Number

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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: