Please Help! Physics question

Melanie1992

Hi guys im studying for a morphology exam and physics/maths was never my strong points in fact in terrible, im wondering would anyone help me with this question an explain it to me , I would be so grateful. Here goes ;

I go swimming at the local pool, and complete a kilometre in an hour.
The pool is kept at room temperature, and the water has a density of
p = 714 kg/m3
and a dynamic viscosity of µ = 8.9 *10-4 kg/(m*s).
The equation for the Reynolds number is: Re = P*V*L / viscosity (u)


Where v is velocity and L is characteristic length.
My wife then swims the same speed in a swimming pool (at room
temperature) filled with olive oil. Given that olive oil has a density of
875 kg/m3 and a dynamic viscosity of 0.1 kg/(m*s), and assuming she
is 80% of my linear dimensions, what is her Reynolds number as a
percentage of my Reynolds number?

Bit cynical

Melanie1992 wrote: »

I go swimming at the local pool, and complete a kilometre in an hour.
The pool is kept at room temperature, and the water has a density of
p = 714 kg/m3
and a dynamic viscosity of µ = 8.9 *10-4 kg/(m*s).
The equation for the Reynolds number is: Re = P*V*L / viscosity (u) Where v is velocity and L is characteristic length.

Let's label all the quantities in the above paragraph with the subscript 1. So the Reynolds number for the husband is

[latex]\displaystyle{Re_{1}=\frac{\rho_{1}V_{1}L_{1}}{\mu_{1}}}[/latex],

with all the quantities are referring to those in the first paragraph.

My wife then swims the same speed in a swimming pool (at room
temperature) filled with olive oil. Given that olive oil has a density of
875 kg/m3 and a dynamic viscosity of 0.1 kg/(m*s), and assuming she
is 80% of my linear dimensions, what is her Reynolds number as a
percentage of my Reynolds number?

Then let's label all the quantities in the second paragraph with the subscript 2. Then using the same formula given in the question, the Reynolds number for the wife is:

[latex]\displaystyle{Re_{2}=\frac{\rho_{2}V_{2}L_{2}}{\mu_{2}}}[/latex].

Now we are told that the wife has 80% the dimensions of the husband. So [latex]L_2=\left(0.8\right)L_{1}[/latex]. We can substitute this into the second formula.

[latex]\displaystyle{Re_{2}=\frac{\rho_{2}V_{2}\left(0.8\right)L_{1}}{\mu_{2}}}[/latex]

The question asks us for the wife's Reynolds number expressed as a percentage of that of the husband's number, i.e., we want something of the form

[latex]\displaystyle{Re_{2}=x\left(Re_{1}\right) }[/latex],

where [latex]x[/latex] is the quantity we are looking for. Rearranging:

[latex]\displaystyle{x=\frac{Re_{2}}{Re_{1}}}[/latex].

Now we already have formulas for [latex]Re_2[/latex] and [latex]Re_1[/latex] so

[latex]\displaystyle{x=\frac{\left(\frac{\rho_{2}V_{2}\left(0.8\right)L_{1}}{\mu_{2}}\right)}{\left(\frac{\rho_{1}V_{1}L_{1}}{\mu_{1}}\right)}}[/latex].

Simplifying

[latex]\displaystyle{x=\frac{\mu_{2}\rho_{2}V_{2}\left(0.8\right)L_{1}}{\mu_{1}\rho_{1}V_{1}L_{1}}=\left(0.8\right)\frac{\mu_{2}\rho_{2}V_{2}}{\mu_{1}\rho_{1}V_{1}}}[/latex]

When you plug in the numbers this will give your answer as a fraction. Multiply the number by 100 and put the percentage sign in to express it as a percentage.

Melanie1992

Wow!!! Thank you so very much! Really appreciate the help!

Bit cynical

Bit cynical wrote: »

Simplifying

[latex]\displaystyle{x=\frac{\mu_{2}\rho_{2}V_{2}\left(0.8\right)L_{1}}{\mu_{1}\rho_{1}V_{1}L_{1}}=\left(0.8\right)\frac{\mu_{2}\rho_{2}V_{2}}{\mu_{1}\rho_{1}V_{1}}}[/latex]

When you plug in the numbers this will give your answer as a fraction. Multiply the number by 100 and put the percentage sign in to express it as a percentage.

Just realised this last formula is wrong.

Should be

[latex]\displaystyle{x=\frac{\mu_{1}\rho_{2}V_{2}\left(0.8\right)L_{1}}{\mu_{2}\rho_{1}V_{1}L_{1}}=\left(0.8\right)\frac{\mu_{1}\rho_{2}V_{2}}{\mu_{2}\rho_{1}V_{1}}}[/latex]

The only difference is the mu's are swapped around.