fluids

niallofthenine

hi need help with a past paper question in fluids, if anyone can do it I would really appreciate it!

the velocity distribution for the flow of a newtonian fluid between two wide, parallel plates is given by the equation
3v (y)^2
u= 2 [1-(h) ] in words u equals 3v divided by 2 all multiplied by 1 minus y over h squared.

where v is the mean velocity.
the fluid has a viscosity of 1.915 Ns/m^2. when V=0.61m/s and h = 5mm, determine
(A) the shearing stress on the bottom wall.
(B) the shearing stress acting on the plane parallel to the wall.
(C) the shearing stress at midplane, i.e. at centreline.

thanks for looking

niallofthenine

can anyone help?

judas101

i remember questions like this from a long time ago.

after calculating the Reynolds number theyres a few simple formula you use depending on whether the flow is turbulent or laminar.

as entry distance isnt mentioned or cant be calculated (as far as i can see!) you assume fully developed flow.

ill try dig those formulae out from somewhere for you as i cant remember off the top of my head. i reckon for part (c) the shear stress is zero but i could be wrong.

Pherekydes

Perhaps engineering forum? I'll move it there and you can ask to move it back it you want.

rover84

E = Mc2

rover84

rover84 wrote: »

E = Mc2

If you're going to take the piss, at least do it with the correct equation.

Seriously though, cop on.

niallofthenine

thanks for that

godtabh

Can you post the orginal exam question? The way you have written it doenst look right.

niallofthenine

here it is

niallofthenine

i got ananswer of tau= 233.63 n/m^2 but i dont think its right

niallofthenine

@ judas101 I was thinking the same for part C cant prove it though

judas101

What formula are you using?

the only one i can think of is Tau = u x [du/dy]@ y=0 (where u is viscosity)

i dont see how you can quantify du/dy tho.

niallofthenine

Tau = u x [du/dy]@ y=0 (where u is viscosity)

thats the one I was using whether its right or not is a different story.

ibh

niallofthenine wrote: »

thats the one I was using whether its right or not is a different story.

Depending on how big of a hurry you're in for the answer, i'm pretty sure I have that question done somewhere in my notes. If it's not that one then it is damn similar. I won't be able to post it straight away though...

niallofthenine

no real panic but id like to be able to know how to do it! thanks

JoseJones

Tau=(viscosity)(du/dy)

at the bottom wall, y=-h

u=3v/2 - 3vy^2/2h^2

all the above are constants except for y,

du/dy=-3vy/h^2

At bottom wall:

du/dy= -3v(-h)/h^2 = 3v/h

Tau= (viscosity)(3v/h)

just put all the values in and Tau= 700.89N/m^2

At the top wall, the answer will be the same,
and at midplane, y=0 so Tau=0

Your not in first year in UL by any chance?

niallofthenine

year in UL by any chance?

yes indeedie thsnx for that!