Reynolds\' number problem Name In dimensional analysis, a dimensionless quantity

Question

Reynolds' number problem Name In dimensional analysis, a dimensionless quantity is a quantity without a physical unit and is thus a pure number. Such a number is typically defined as a product or ratio of quantities that might have units individually, but these cancel out in the combination. The Reynolds Number is a dimensionless parameter used to predict the onset of turbulance in fluid flows. A common representation of a Reynold's number is Re = rho V L / mu where rho is the density V is the velocity L is a characteristic linear dimension mu is the dynamic viscosity Show that with the density rho, in kg/m3 the velocity in m/s L in m and mu in kg/(m s) the units all cancel out and Re is in fact dimensionless. If the transition from laminar to turbulent flow is anticipated to occur at a Reynold's number of 5,000 and the system has the following values rho 900 kg/m3 (density of motor oil) velocity 10 m/s L 0.1 m (for a 3-4" pipe) mu 2.50E-01 kg/(m s) (motor oil at room temp) What is the Reynolds number in SI units? What is the Reynolds's number in the BGS system of units? Would you expect this flow to be turbulent? would you expect the onset of turbulence to depend on the system of units?

Explanation / Answer

What is the Reynolds number in SI units
ans
Re=vL/

putting value

Re=900*10*.1/2.508*10^-1

Re=3600

as all units cancel out so there is no unit of Reynolds number

in BGS

=56.090lb/ft^3

V=32.8ft/s

L=.33ft

=.16799lb/ft.s

using these values

Re3605 approximately same

yes there will turbulent

no onset turbulent doesn't depends upon system as shown above in both case approximately same value

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