Answer:
The aswer is Re= 1867.123
Explanation:
You know that Reynolds is:
[tex]Re=\frac{p*v*D}{u}[/tex]
But the units of p, v, D and u must be in the same reference system. This means that you must handle the same units. So, you must do the corresponding unit conversions . Usually The International System of Units is used, where:
the density p is measured in [tex]\frac{kg}{m^{3} }[/tex] the velocity v in [tex]\frac{m}{s}[/tex], the diameter in m (meters) and the viscosity in [tex]\frac{kg}{m*s}[/tex]
But you can choice other system of units.
The density, in this case, is expressed in [tex]\frac{kg}{m^{3} }[/tex] ( Note that in the statement the data appears as kg / m. But remember that this isn't possible because density is the amount of mass in a given volume. You can assume that the given data is [tex]\frac{kg}{m^{3} }[/tex]).
For density then you shouldn't convert units, because it respects the International System of Units.
The velocity is expressed in [tex]\frac{cm}{s}[/tex]. So, you must change these units to [tex]\frac{m}{s}[/tex]. For that, The Rule of Three is usually used, where it is known that 1 cm is 0.01 cm. So:
1 cm ⇒ 0.01 m
32.9 cm ⇒ x
[tex]x=\frac{32.9*0.01}{1}[/tex]
Finally the velocity is: 0.329 [tex]\frac{m}{s}[/tex]
In the same way, you can convert the units of the diameter.
1 cm ⇒ 0.01 m
1.85 cm ⇒ x
[tex]x=\frac{1.85*0.01}{1}[/tex]
The diameter is: 0.0185 m
Finally, you must convert the viscosity units, applying The Rule of Three:
1 cP ⇒ 0.001 [tex]\frac{kg}{m.s}[/tex]
3.40 cP ⇒ x
[tex]x=\frac{3.4*0.001}{1}[/tex]
So, the viscosity is: 0.0034 [tex]\frac{kg}{m*s}[/tex]
Now, with all units in the same system, you can calculate the Reynolds number.You just have to replace the numbers in the definition and verify that the Reynolds is a dimensionless number.
[tex]Re=\frac{p*v*D}{u} =\frac{1043*0.329*0.0185}{0.0034}[/tex]
Re= 1867.123
Unit Verification:
[tex]Re=\frac{\frac{kg}{m^{3} } *\frac{m}{s} *m}{\frac{kg}{m*s} }[/tex]
By simple simplification, adimensionality can be observed.
