Hi!
I have a modified Swamee-Jain equation with the Reynolds number being ρUD/μ and the Darcy–Weisbach friction factor f being 8u^2/U^2
This is what the modified equation looks like, http://imgur.com/273VlJi
I need help re-arranging this equation in order to solve for U. NOT for lowercase u, nor for μ. I know how to handle the negative exponent and the base 10 log, but I don't know what to do regarding the 0.9 exponent power. Any help would be appreciated!
EDIT: this is what the original equation looks like http://imgur.com/ah5JBlT
Hi!
I have a modified Swamee-Jain equation with the Reynolds number being ρUD/μ and the Darcy–Weisbach friction factor f being 8u^2/U^2
This is what the modified equation looks like, http://imgur.com/273VlJi
I need help re-arranging this equation in order to solve for U. NOT for lowercase u, nor for μ. I know how to handle the negative exponent and the base 10 log, but I don't know what to do regarding the 0.9 exponent power. Any help would be appreciated!
EDIT: this is what the original equation looks like http://imgur.com/ah5JBlT
You literally just created your account today, and this is your first post.
Wut.
You literally just created your account today, and this is your first post.
Wut.
(ρUD/μ)^(0.9)
(ρUD/μ)^(9/10)
10th_root((ρUD/μ)^9)
you probably already knew that though, im not sure. should be good from there.
looks like a mess i dont want to solve lol
(ρUD/μ)^(0.9)
(ρUD/μ)^(9/10)
10th_root((ρUD/μ)^9)
you probably already knew that though, im not sure. should be good from there.
looks like a mess i dont want to solve lol
In general you can't find a closed-form expression for a variable involved in a transcendental equation, and I suspect this is one of those cases. You should instead look into numerical root-findong methods.
In general you can't find a closed-form expression for a variable involved in a transcendental equation, and I suspect this is one of those cases. You should instead look into numerical root-findong methods.
if you are trying to find a numerical value for U (free-stream fluid velocity in this case) then I would guess there are additional aspects of the model you are using that we/you need to know. From past experience with handling Darcy friction factor equations the easiest way was never direct re-arrangement, you almost always have to eliminate some of your variables first. When I did this stuff it was calculating head loss and shaft work from pumps but I imagine it would be the same for any incompressible viscous flow problem. Perhaps you have some secondary equations for head loss to determine pipe diameter? Knowing the material of the pipe could give you relative roughness to work out your epsilon value or if you know what region the reynolds number is you could sub in one of the approximation models, i.e if you know its laminar then you can set 8u^2/U^2 = 64/Re and simplify from there once you get rid of the other velocity parameter. Maybe you could even use a Moody chart if you can find enough system properties.
tl:dr there is probably a better way to do it than re-arranging, try and use information about the rest of the system to get rid of some variables and also don't shout at me if I'm wrong
if you are trying to find a numerical value for U (free-stream fluid velocity in this case) then I would guess there are additional aspects of the model you are using that we/you need to know. From past experience with handling Darcy friction factor equations the easiest way was never direct re-arrangement, you almost always have to eliminate some of your variables first. When I did this stuff it was calculating head loss and shaft work from pumps but I imagine it would be the same for any incompressible viscous flow problem. Perhaps you have some secondary equations for head loss to determine pipe diameter? Knowing the material of the pipe could give you relative roughness to work out your epsilon value or if you know what region the reynolds number is you could sub in one of the approximation models, i.e if you know its laminar then you can set 8u^2/U^2 = 64/Re and simplify from there once you get rid of the other velocity parameter. Maybe you could even use a Moody chart if you can find enough system properties.
tl:dr there is probably a better way to do it than re-arranging, try and use information about the rest of the system to get rid of some variables and also don't shout at me if I'm wrong
Fate55i.e if you know its laminar then you can set 8u^2/U^2 = 64/Re and simplify from there once you get rid of the other velocity parameter. Maybe you could even use a Moody chart if you can find enough system properties.
tl:dr there is probably a better way to do it than re-arranging, try and use information about the rest of the system to get rid of some variables and also don't shout at me if I'm wrong
That is actually exactly what I am doing now and it's coming out to an input that I can use. Thank you so much!
[quote=Fate55]i.e if you know its laminar then you can set 8u^2/U^2 = 64/Re and simplify from there once you get rid of the other velocity parameter. Maybe you could even use a Moody chart if you can find enough system properties.
tl:dr there is probably a better way to do it than re-arranging, try and use information about the rest of the system to get rid of some variables and also don't shout at me if I'm wrong[/quote]
That is actually exactly what I am doing now and it's coming out to an input that I can use. Thank you so much!
Not even physics, more like transport phenomena in chemical engineering.
Not even physics, more like transport phenomena in chemical engineering.
samjain98physics mains smh
its fluid mechanics
[quote=samjain98]physics mains smh[/quote]
its fluid mechanics