Water at 25 C flows through a pipe at 2.543 m/s. The pipe inside diameter is 8.765 cm. Determine the Reynolds number.?

the whole point of this problem is for you chemical engineering students to learn to google, learn what Reynolds number is and how it appears in equation form, and for you to learn how to do the calcs / conversions.

YOU give those three things a try before reading on

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for flow in pipes

.. Re = ρ u D / ν

where

.. Re = Reynolds #

.. ρ = density

.. u = bulk flowrate

.. D = pipe inside diameter

.. ν = viscosity of water

in this case

.. ρ = 0.99704 g/cm³

.. u = 1.543 m/s

.. D = 8.765 cm

.. ν = 0.8937 cP

your job is now to enter those values into an equation and ensure the units cancel out.. Re is dimensionless.

the trick is..

.. 1 cP = 1 centiPoise.

.. 1 Poise = 1 g / (cm x sec)

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here's the setup..

.. .....(0.99704 g/cm³) x (2.543 m/s) x (100cm / 1m) x (8.765 cm)

Re = ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ----- ------ ---- ---- ---- --- = 2.487x10^5

.. ... .... (0.8937 cP) x (1 P / 100 cP) x (1g/(cm x sec) / 1P)

and you should readily see that

.. g / g

.. m / m

.. (cm x cm / cm³) / (1 / cm)

.. (1 / sec) / (1 / sec)

.. cP / cP

all cancel out. leaving the dimensional Re

which you calc by entering

.. 0.99704 x 2.543 x 100 x 8.765 / 0.8937 x 100 =

and rounding to 4 sig figs

You have the following :

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Re = ( D ) ( Vbar ) ( rho ) / ( mu )

D = 8.765 cm = 0.08765 m

Vbar = 2.543 m/s

rho = 997 kg/m^3

mu = 8.91 x 10^-4 Pa - s = 8.91 x 10^-4 N - s / m^2

Re = [( 0.08765 m ) ( 2.543 m/s ) ( 997 kg/m^3 ) ] / [ 8.91 x 10^-4 N-s / m^2 ]

Re = 249411 <-----------------------

Reynolds Number must be dimensionless; therefore,

the units need to be checked as follows:

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Re = [ ( m ) ( m/s) ( kg/m^3 ) ][ m^2 / N - s ]

N = kg - m / s^2

Re = ( m ) ( m/s ) ( kg/m^3 ) ( m^2 / s ) ( s^2 / kg - m )

Re = ( m^4 / m^4 ) ( kg / kg ) ( s^2 / s^2 ) = dimensionless

SI Re = [ ( D in m ) ( Vbar in m/s) ( rho in kg/m^3 ) ] / [ mu in N - s / m^2 ]

For American Engineering units :

AE Re = [ ( D in ft ) ( Vbar in ft/s ) ( rho in lbm/ft^3 ) ( 3600 s/hr ) ]/ [ mu in pdm/ ft- hr ]