Calculate the range of sizes of the particles

[Tiberious]

Calculate the range of sizes of the particles. 


ν= velocity of decent
d = diameter
ps = density
η = viscosity
P1 = density

v= (d^2 (p_s-p_1 )g)/〖18〗_η

Rearrange for the diameter.

v= (d^2 (p_s-p_1 )g)/〖18〗_η

〖18〗_η v= d^2 (p_s-p_1 )g

(〖18〗_η v)/(p_s-p_1 )g= d^2

√((〖18〗_η v)/(p_s-p_1 )g)= d

Is the above rearrangement correct ? If not, are there any helpful sites / posts that you are aware of to solve rearranging equation problems ?

 

[Mark44]

Calculate the range of sizes of the particles. 


ν= velocity of decent
d = diameter
ps = density
η = viscosity
P1 = density

v= (d^2 (p_s-p_1 )g)/〖18〗_η

I have a few questions about this equation.
What is the significance of the double brackets on 18: i.e., 〖18〗?
What does this part mean? 〖18〗_η
What densities do ps and P1 represent? Presumably they are the same as p_s and p_1 in your equation.

Rearrange for the diameter.

v= (d^2 (p_s-p_1 )g)/〖18〗_η

〖18〗_η v= d^2 (p_s-p_1 )g

(〖18〗_η v)/(p_s-p_1 )g= d^2

√((〖18〗_η v)/(p_s-p_1 )g)= d

Is the above rearrangement correct ? If not, are there any helpful sites / posts that you are aware of to solve rearranging equation problems ?

 

[Tiberious]

There is no significance in the nested brackets, they only appear when copying from MS Word MathScript to the PhysicsForum.

The 18η is represented in correctly in the above as well due to this conversion.

v = d^2 (ps - p1) g / 18η

This is the relevant equation.

Yes, the first part of the question is as follows.

"An experiment to determine ceramic particle sizes showed that the rate of descent when suspended in a fluid ranged from 1.2× 10–6 m s–1 to 5× 10–6 m s–1. 


The density of the material was 3800 kg m–3 and the density and viscosity of the fluid at room temperature were 1632 kg m–3 and 0.00972 Pas respectively. Calculate the range of sizes of the particles. "

 

[Mark44]

√((〖18〗_η v)/(p_s-p_1 )g)= d
Is the above rearrangement correct ?

Looks fine to me, but is somewhat hard to read.. Using LaTeX (see our tutorial here - https://www.physicsforums.com/help/latexhelp/), it would be $$d = \pm \sqrt{\frac{18\eta v}{(p_s - p_1)q}}$$.
If this is a problem from physics, you probably don't need to be concerned about the negative square root.

If not, are there any helpful sites / posts that you are aware of to solve rearranging equation problems ?

Regarding helpful sites: For this problem, other sites are not needed. Solving for d here is basically two steps:

1. Multiply both sides of the equation by $\frac{18 \eta}{(p_s - p_1)g}$
2. Take the square root of both sides